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GAMESS-UK USER'S GUIDE and REFERENCE MANUAL Version

1. CCTH This directive may be used to define a convergence threshold for CCSD iterations and comprises a single data line read to the variables TEXT IAMP using format A l With TEXT set to the character string CCTH IAMP is an integer parameter used in defining the threshold At convergence the magnitude of the CCSD T and T amplitudes will be converged to within an absolute error 10 4 Again this directive may be omitted when the default value 10 will be used Let us now consider the corresponding calculation with inclusion of the triples T component to the correlation energy A valid data sequence for performing such a calculation is shown below where we are still performing all the computation in a single job TITLE H2CO TZVP VALENCE CCSD T CCSD T ENERGY 114 2714886289 SUPER OFF NOSYM NOPRINT ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ACTIVE 3 TO 50 END CORE 1 TO 2 END RUNTYPE CI CCSD T 48 6 6 CCTH 10 CCIT 30 ENTER 26 COUPLED CLUSTER CALCULATIONS 168 Now let us consider performing the CC calculation above in a sequence of jobs where the first job carries out the SCF the second the transformation and CCSD T First the closed shell case valid data sequences for performing the calculation are shown below Run I The Scf Job TITLE H2CO TZVP SCF PRIOR TO CCSD T CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM N 0 0 1
2. 31 J M Foster and S F Boys Rev Mod Phys 32 1960 300 doi 10 1103 RevModPhys 32 300 J Pipek and P G Mezey J Chem Phys 90 1989 4916 doi 10 1063 1 456588 32 A J Stone Chem Phys Lett 83 1983 233 doi 10 1016 0009 2614 81 85452 8 33 T Amos and L C Snyder J Chem Phys 41 1964 1773 doi 10 1063 1 1726157 34 D Moncrieff and V R Saunders ATMOL Introduction Notes UMRCC May 1986 Cyber 205 Note Number 32 UMRCC September 1985 V R Saunders and M F Guest ATMOL3 Part 9 RL 76 106 1976 M F Guest and V R Saunders Mol Phys 28 1974 819 doi 10 1080 00268977400102171 35 C J Cerjan and W H Miller J Chem Phys 75 1981 2800 doi 10 1063 1 442352 36 S Bell and J S Crighton J Chem Phys 80 1984 2464 doi 10 1063 1 446996 37 J Simons P Jorgensen H Taylor and J Ozment J Phys Chem 87 1983 2745 doi 10 1021 j100238a013 A Banerjee N Adams J Simons and R Shepard J Phys Chem 89 1985 52 doi 10 1021 j100247a015 38 J Baker J Comp Chem 7 1986 385 doi 10 1002 jcc 540070402 39 R J Buenker in Proc of the Workshop on Quantum Chemistry and Molecular Physics Wollongong Australia 1980 R J Buenker in Studies in Physical and Theoretical Chem istry 21 1982 17 40 S Zarrabian and R J Harrison Chem Phys Lett 81 1989 393 doi 10 1016 0009 2614 89 87358 0 REFERENCES 199 41 T J Lee J E Rice and A P Rendell The TITA
3. Had the results of the RHF computation in 4 been available then the data line VECTORS 5 6 GVB CALCULATION ON THE FORMALDEHYDE MOLECULE 17 would have provided the canonicalised RHF orbitals as a starting point for the UHF iterative process Assuming that the SCF calculations of 82 84 and 5 been performed in sequence the status of the user sections on the Dumpfile would appear as follows with each of the vectors available for subsequent analysis see Part 8 Section Contents X A Closed shell RHF vectors Bo a spin UHF vectors 2Bo G spin UHF vectors Bo Open shell RHF vectors Bo Canonicalised Open shell RHF vectors 2B Open shell RHF vectors 2B Canonicalised Open shell RHF vectors NOOB WNEH 5 1 Direct UHF Calculation on the formaldehyde cation The following data sequence would be required in performing a direct UHF calculation on the cation using the eigenvectors from the closed shell run Note that the BYPASS directive shown in the example above is no longer appropriate RESTART TITLE H2CO 2B2 3 21G BASIS DIRECT UHF CALCULATION CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT UHF VECTORS 1 ENTER Note the revised form of the SCFTYPE directive requesting the direct UHF option The default Dumpfile sections are again used for storage of the a spin section 2 and spin section 3 orbitals Had the results of the RH
4. e the semi transformed ED4 and transformed ED6 integral files e the Direct Cl file ED5 which acts to carry data between the various phases of the calculation and must be preserved between separate jobs e the Scratch file ED7 e temporary files for sorting both transformed integrals the Sortfile and intermediate matrices in the Cl calculation the P Sortfile Any restart jobs will require ED6 and ED5 being saved in addition to the Dumpfile ED3 and Mainfile ED2 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM in the SCF run In all direct Cl calculations the user must specify the division of the molecular orbital space into an internal and external space where the internal space comprises all orbitals that appear in any of the nominated reference functions The latter are defined by use of the CONF directive The set of internal orbitals must appear first in the list of active orbitals followed by the set of external orbitals An additional reordering is performed by the code whereby MOs of common irreducible representation are grouped together both in the internal and external space This re ordering is driven off the symmetry characteristics of the input MOs as reported by the 23 DIRECT CI CALCULATIONS 109 parent SCF calculation If for any reason these orbitals are contaminated the
5. 0 0 1 1 203 24 TABLE CI CALCULATIONS 159 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT TABLE BYPASS SELECT BYPASS SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 413141819 12345 17 END CI BYPASS NATORB BYPASS ENTER Configuration Selection RESTART CI TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT SELECT SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 END CI BYPASS NATORB BYPASS ENTER Diagonalisation and Natural Orbital Generation RESTART CI TITLE H2C0 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 25 FULL CI CALCULATIONS 160 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT SELECT BYPASS SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 413141819 1234517 END CI NATORB ENTER 25 Full CI Calculations Full Cl calculations are performed under control of the RUNTYPE CI specification with data input characterising the nature of the Cl introduced by a data line with the keyword FULLCI in the first data field Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS Before detailing example data files for performing full Cl calcula tions on th
6. 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 10 10 CONF 222 222 2222 NATORB 10 O PRINT ENTER 2222200 2220220 202202 Because the ZORA directive includes the relativistic contributions in the 1 electron integrals the Cl part of the input need not be changed 33 MULTIPLE RUNTYPE CALCULATIONS 190 33 Multiple RUNTYPE Calculations In previous releases of the program and indeed in all discussion of the available options so far we have assumed that each invocation of the RUNTYPE directive i e each task to be performed is carried out in a single run of the program It is also possible to simplify this modus operandi through the issuing of multiple RUNTYPE s within a single run of the program This is still however subject to certain constraints which are summarised below As will become clearer from Parts 3 and 4 of the manual the directive data structure of GAMESS UK involves two categories of directives Class1 and Class 2 with the former preceding the latter in the data stream A schematic representation of the structure of a typical data file is shown below Class 1 Directives TITLE END BASIS Class 2 Directives RUNTYPE SCFTYPE RHF ENTER 1 Broadly speaking multiple RUNTYPE s may be issued subject to the constraint that the Class 1 directives defining the molecular geometry ZMATRIX GEOMETRY the spin multiplicity and charge MULT CHARGE and the basis set
7. 114 2714886289 SUPER OFF NOSYM BYPASS TRANSFORM ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ACTIVE 3 TO 50 END CORE 1 TO 2 END RUNTYPE CI CCSD T 48 6 6 CCTH 10 CCIT 30 ENTER 27 CI Geometry Optimisation Energy only geometry optimisation for direct Cl full Cl and CCSD wavefunctions may be per formed using a variant of the RUNTYPE OPTIMIZE directive In each case the data line RUNTYPE OPTIMIZE CI requests use of the Fletcher Powell optimiser with subsequent data used to identify the under lying Cl wavefunction to be employed in the energy calculation We illustrate such usage below for the cases of direct Cl Full Cl and CCSD calculations Note that FP optimisation may also 27 CI GEOMETRY OPTIMISATION 170 be performed for Table Cl wavefunctions see below although experience to date suggests that the such optimisations are unlikely to lead to converged geometries given the implicit lack of rigour associated with configuration selection 27 1 Direct CI Geometry Optimisation I CISD calculations TITLE H2CO 3 21G FP GEOMETRY OPT TOTAL CI ENERGY 113 43777426 ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE CI DIRECT 16 8 14 CONF 22222222 ENTER Here DIRECT requests a direct Cl wavefunction with CONF quantifying attributes of the Cl calculation II MRDCI
8. 29 A Green s function 2ph TDA calculation of the valence IEs 30 RPA calculations of excitation energies 31 Multi configurational Linear Response MCLR calculations of excitation energies 32 ZORA Relativistic effects 33 Combining multiple calculations in a single job step 1 1 Treatment of Molecular Symmetry Before considering aspects of data specification it is important that the user has at least a rough idea of the varying methods that GAMESS UK employs in the treatment of molecular symmetry The aim is of course to try and optimise performance while maintaining simplicity of related data specification There are two fundamental and related levels at which symmetry will be employed 1 at the molecular level when the program will deduce the point group symmetry based on the geometry provided and subsequently in default use that information in minimising the number of integrals that need be constructed for example in SCF calculations At this level the program in most instances is capable of handling both Abelian and non Abelian point groups on an equal footing 2 at the orbital level both at the basis function and molecular orbital MO level when the symmetry characteristics of MOs will be used in optimising subsequent post Hartree Fock calculations This requirement is met through the internal use of symmetry adapted basis functions While this technique is limited to Abelian point groups the program will au
9. CANONICAL 2 FOCK DENSITY FOCK PRINT CIVECTOR DIRECT 16 10 10 CONF 2222222200 2222222020 2222222002 2222220220 2222220202 2222220022 2222222101 2222220121 2222221210 2222221012 2222221i1i141 END TRIAL DIAG REF STATE 2 PRINT MP 3 ENTER 2 In this case the MCSCF ORBITALS directive asks the program to construct a CAS space The directives STATE and WEIGHT make the program optimise 2 states where the ground state isn t taken into account in the optimisation This way we are guaranteed to find the first excited state From the MCSCF run we only obtain the orbitals due to differences in the representation of the Cl vector we cannot transfer that information from the MCSCF to the Cl module Therefore we have to reconstruct the reference wavefunction in the Cl module itself First we specify all the reference configurations that were present in the MCSCF calculation for example with the CONF directive Next we ask for the first excited state in that reference space in the TRIAL DIAG directive Having constructed the correct reference wavefunction we can simply apply perturbation theory to it using the MP directive 23 DIRECT CI CALCULATIONS 121 23 6 Direct CI Restarting Calculations In the examples considered above we have assumed that the Direct Cl job completes in the time allocated This may not be the case and we need consider restarting the computation in a controlled fashion Such a requirement may be met in RUNTYPE Cl pr
10. tions e DOC orbitals in the active space which are formally doubly occupied and which will be permitted variable occupancy in the MCSCF treatment e UOC orbitals in the active space which are formally unoccupied corresponding to SCF virtual MOs but which will be permitted variable occupancy in the MCSCF Other valid orbital TAGs used in characterising open shell configurations include ALP AOS and BOS see 4 3 2 The following points should be noted e An examination of the input SCF MOs reveals that the 12 orbitals to be included in the primary space correspond to the first 12 SCF MOs This may not always be the case and the user may have to resort to the SWAP directive to ensure the primary MOs occur first in the list Note also that the FZC orbitals must precede the orbitals permitted variable occupancy in the active list e Note the PRINT keyword on the CONFIG directive This requests output of the complete list of configurations characterised by occupation number pattern e Two sets of eigenvectors are generated in a CASSCF calculation the non canonicalised CASSCF MOs that are used during the CASSCF process and a second set the canoni calised vectors which are generated on termination of the CASSCF process The latter exhibit energy weighting in the virtual manifold and act as the most obvious starting point for a post Hartree Fock computation e Two sections will be used to house these eigenvectors In default t
11. 012345 13 17 18 ROOTS 1 THRESH 30 10 CI DIAG EXTRAP 2 ENTER Now BYPASS is appended to both the ADAPT and TRAN data lines since the associated processing has been completed in the previous job 24 4 Conventional Table CI Freezing and Discarding Orbitals In the examples above we have assumed that all MOs typically generated at SCF time are active in the subsequent Cl calculation In many instances however this will not be the case for the user may wish to e freeze inner shell orbitals performing a valence only CI calculation e discard certain virtual orbitals from the Cl calculation typically the high energy inner shell complement orbitals The final subset of orbitals to be included in the Cl is controlled by the specification of additional data for the TRAN sub module The freezing of core or inner shell orbitals and the discarding of virtual orbitals is signaled by appropriate keywords on the TRAN directive CORE and DISCARD respectively with subsequent data lines nominating the number and sequence nos of those orbitals within each IRrep to be frozen or discarded Note that the sequence numbers to be specified refer to the Table reordered orbital set defined above Consider the previous H2CO calculation Suppose we wish to freeze both the Ols and Cls orbitals with SCF sequence numbers 1 and 2 respectively and to discard the two highest energy virtual orbitals with SCF sequence numbers 21 and 22 The c
12. 15 5 Energy only Geometry Optimisation ooo a a a aa 65 15 6 Post Hartree Fock Geometry Optimisation ooo 66 15 6 1 CASSCF Geometry Optimisation o oo o e e e 66 15 6 2 MCSCF Geometry Optimisation ooo e 67 15 6 3 MP2 Geometry Optimisation o s se s acs a ores e i a e e E s 69 16 Transition State Optimisation 71 16 1 DFT Transition State Optimisation oaoa o e e 20020022 ee 75 16 2 CASSCF Transition State Optimisation oa o o a e 76 16 3 MCSCF Transition State Optimisation o ses c 0 800 taere ba 78 16 4 MP2 Transition State Optimisation 2 a a e ee ee 79 17 Force Constant Calculations 82 17 1 Numerical Force Constants o oo 83 17 1 1 CASSCF Force Constants o 2 ocs s ssw Yew 2 ee ee ae Se eni k 85 17 1 2 MCSCF Force Constants lt 266 02 6 eae ndo tasad ietis 87 17 2 Analytic Force Constants ooa a 89 18 Polarisability Calculations 97 19 Hyperpolarisability Calculations 100 20 Magnetisability Calculations 101 21 Infra red Intensity Calculations 102 CONTENTS 22 Calculation of Raman Intensities 23 Direct Cl Calculations 23 1 Direct Cl Single reference CISD Calculations 23 2 Direct Cl Default CISD Calculations 004 23 2 1 Closed shell Systems 23 2 2 Open shell Systems 23 3 Direct Cl Freezing and Discarding Orbitals 23 4 Direct Cl Multi reference Cl Calculations 0004 23 5 Direct Cl Mu
13. 3 21G BASIS semi direct MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES ALL CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 END ROOTS 1 THRESH 2 2 CI NATORB ENTER Now let us consider performing the closed shell calculation above in a sequence of jobs where the first job carries out the SCF the second the Table Cl calculation Valid data sequences for performing the calculation are shown below Run I The SCF Job TITLE H2CO 3 21G SCF PRIOR TO TABLE CI CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER The only obvious point to note is the use of the SUPER directive in requesting full integral list generation required in the subsequent symmetry adaption and integral transformation Run II The Table CI Job RESTART 24 TABLE CI CALCULATIONS 148 TITLE H2CO 3 21G BASIS semi direct MRDCI 4M 1R SUPER OFF NOSYM BYPASS SCF ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES ALL CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 END ROOTS 1 THRESH 2 2 CI NATORB ENTER Considering the changes to the co
14. BASIS appear only once in the job Thus a schematic representation of a multiple RUNTYPE job is given below Class 1 Directives TITLE BASIS Class 2 Directives 1st Task RUNTYPE SCFTYPE RHF ENTER 1 Class 2 Directives 2nd Task RUNTYPE SCFTYPE RHF VECTORS 1 33 MULTIPLE RUNTYPE CALCULATIONS 191 ENTER 2 Class 2 Directives 3rd Task RUNTYPE SCFTYPE RHF VECTORS 1 ENTER 3 We delay a fuller discussion of multiple RUNTYPE s until a later Part of the manual but note the following points prior to illustrating this usage through a number of examples e The molecular geometry used in the n th RUNTYPE invocation is that determined in the preceding RUNTYPE e The ENTER directive terminates data for a given RUNTYPE It follows that the habit of stacking old data cards after the ENTER directive is now to be avoided The following examples illustrate multiple RUNTYPE usage 1 Optimisation of the geometry of H2CO and subsequent direct Cl calculation at this opti mised geometry 2 An SCF calculation of H2CO and subsequent wave function analysis 3 Using a HESSIAN calculation to obtain the starting hessian and subsequent location of the H2CO to t HCOH transition structure 4 Optimisation of the geometry of H2CO and subsequent evaluation of the Raman intensities at this optimised geometry 33 1 Geometry Optimisation and Direct CI Calculation In this example we initially perform a geom
15. CASSCF 3 21G BASIS 10E IN 9 M O BYPASS ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END SCFTYPE CASSCF CONFIG PRINT NOSORT FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END SUPERCI 1 TO 7 NEWTON 8 TO 20 HESSIAN 8 TO 20 ENTER Note the NOSORT keyword now appearing on the CONFIG directive This parameter deactivates generation of the reordered Loop Formulae tape ED10 this file is only required during 1 step Newton Raphson optimisation which has not been requested here The SIMUL Directive may be used to specify the 1 step NR method 10 MCSCF CALCULATION 28 10 MCSCF Calculation We now consider the data input requirements for the 2nd order MCSCF module We again wish to perform a CASSCF calculation on the X Aj state of formaldehyde using a full valence crite rion in specifying the active space We assume that the calculation is to proceed in two stages with initial generation of the closed shell SCF orbitals followed by the MCSCF computation As mentioned above generation of a valid Mainfile for direct use in the MCSCF calculation requires the data line SUPER OFF NOSYM in the closed shell run hence allowing BYPASS ing in the MCSCF computation Closed shell SCF Data TITLE H2CO 3 21G CLOSED SHELL SCF SUPPRESS SKELETONISATION SUPER OFF NOSYM ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER MCSCF Data RESTART TITLE
16. L v Szentpaly Chem Phys Lett 89 1982 418 doi 10 1016 0009 2614 82 80012 2 B Ne A Bergner M Dolg W Kuechle H Stoll H Preuss Mol Phys 80 1993 1431 doi 10 1080 00268979400100024 Mg P Fuentealba L v Szentpaly H Preuss H Stoll J Phys B 18 1287 1985 Al G Igel Mann H Stoll H Preuss Mol Phys 65 1988 1321 doi 10 1080 00268978800101811 Hg Rn W Kichle M Dolg H Stoll H Preuss Mol Phys 74 1245 1991 doi 10 1080 00268979100102941 Ac Lr W Kuchle to be published 14 K A Bergner M Dolg W K chle H Stoll H Preuss Mol Phys 80 1993 1431 doi 10 1080 00268979400100024 Ca M Kaupp P v R Schleyer H Stoll H Preuss J Chem Phys 94 1991 1360 doi 10 1063 1 459993 Rf Db M Dolg H Stoll H Preuss R M Pitzer J Phys Chem 97 1993 5852 doi 10 1021 j100124a012 15 P J Knowles and H J Werner Chem Phys Lett 115 1985 259 doi 10 1016 0009 2614 85 80025 7 16 B Jonsson B O Roos P R Taylor and P E M Siegbahn J Chem Phys 74 1981 4566 doi 10 1063 1 441645 B O Roos P Linse P E M Siegbahn and M R A Blomberg Chem Phys 66 1982 197 doi 10 1016 0301 0104 82 88019 1 P J Knowles G J Sexton and N C Handy Chem Phys 72 1982 337 doi 10 1016 0301 0104 82 85131 8 The original CASSCF module as developed by Dr P J Knowles was incorporated into GAMESS in April 1983 17 A D Becke Physical Reviews A38 1988
17. OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE XTOL 0 0001 ENTER 21 INFRA RED INTENSITY CALCULATIONS 104 Run II Calculation of Infra red Intensities Note the form of the RESTART directive below since the geometry optimisation has been conducted immediately prior to the INFRARED run it is sufficient to use just RESTART when the optimised geometry will be read from the Dumpfile and override the ZMATRIX data in the input stream RESTART TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF INFRARED ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END RUNTYPE INFRARED ENTER Example 2 Open shell RHF Intensities Run I Initial Closed shell SCF TITLE H2CO 3 21G CLOSED SHELL SCF AT 3A GEOMETRY ZMATRIX ANGSTROM Q 0 1 C0 X 1 1 0 2 90 0 H 1 CH 2 HCO 3 DI1 H 1 CH 2 HCO 3 DI2 VARIABLES cO 1 203 CH 1 099 HCO 121 8 DI1 15 0 DI2 164 0 END ENTER Run II Geometry Optimisation RESTART NEW TITLE H2C0 3 21G BASIS 3A STATE OPTIMISATION 21 INFRA RED INTENSITY CALCULATIONS 105 MULT 3 ZMATRIX ANGSTROM 0 0 1 CO X 11 0 2 90 0 H 1 CH 2 HCO 3 DI1 H 1 CH 2 HCO 3 DI2 VARIABLES CO 1 203 CH 1 099 HCO 121 8 DI1 15 0 DI2 164 0 END RUNTYPE OPTIMIZE SCFTYPE GVB OPEN 2 2 LEVEL 3 1 0 XTOL 0 0001 EN
18. SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI SELECT BYPASS SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 CI BYPASS DIAG BYPASS ENTER Selection and Hamiltonian Construction RESTART CI TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT BYPASS 24 TABLE CI CALCULATIONS 143 TRAN BYPASS SELECT SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 413141819 1234517 DIAG BYPASS ENTER Diagonalisation RESTART CI TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT BYPASS TRAN BYPASS SELECT BYPASS SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 CI BYPASS ENTER 24 8 Semi direct Table CI Calculations The formal limits that apply to conventional calculations are significantly extended in the semi direct module There is now a limit of 800 000 selected configurations derived from an initial list of configurations generated by single plus double excitations from a user specified list of reference functions the number of which may not exceed 256 The selection and extrapolation procedure m
19. VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE FORCE 17 FORCE CONSTANT CALCULATIONS SCFTYPE CASSCF CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END ENTER Example 2 The H2CO to H2 CO transition structure 86 We now assume that the Dumpfile used when performing the transition state optimisation is no longer available and that the user will perform the calculation from scratch using just the computed geometry from the optimisation Initially the user should perform an SCF calculation to generate a trial set of vectors for input to a single point CASSCF run at the transition state geometry shown below followed by the force constant run CASSCF run at the transition state geometry RESTART NEW TITLE H2 CO lt gt H2CO 1A 3 21G CASSCF AT OPT TS GEOMETRY ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES co 1 2034714 CHH 1 3040587 XH 0 7415226 ANGI 41 4929919 ANG2 56 6341870 END SCFTYPE CASSCF CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END ENTER m o gt oe AO BR PONE CASSCEF force constants RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 3 21G CASSCF FORCE CONSTANTS FREQ 1762 3 770 4 901 5 1252 8 1720 4 3184 8 ZMAT ANGS 0 C 1 CO X 2 1 0 1 90 0 17 FORCE CONSTANT CALCULATIONS 17 1 2 X 2 CHH 3 ANG1 1 180 0 X 41 0 2 90 0 3 0 0 X 4 1 0 5 ANG2 3 0 0 H 4 XH 6 90 0 2 180 0 H 4 XH
20. calculation for the 1b 2b pair we must reorder the input MOs exchanging the 2b and 1b MO i e the 7th and 8th input orbitals No reordering of the virtual orbitals is necessary since the 2b MO already occupies the 9th position in the list 2 In the RHF and UHF examples above GAMESS UK will automatically based on the z matrix geometry specification deduce the molecular point group and hence generate and 6 GVB CALCULATION ON THE FORMALDEHYDE MOLECULE 19 retain only the unique integrals required in the process of constructing a skeletonised Fock matrix 1 Such a symmetry truncated integral list is however NOT usable in pair GVB CASSCF MCSCF or Cl calculations and again considerable caution should be exercised when considering use of an integral file generated in an earlier SCF run directly in a subsequent post Hartree Fock calculation under control of the BYPASS directive There are several ways to proceed in such cases e simply omit the BYPASS directive in the subsequent run The program will choose the correct format based on the SCFTYPE specification and regenerate the integral file in the appropriate way e In many instances this regeneration process is too expensive and the user must suppress the skeletonisation process when the integral file is first generated This is again achieved under control of the SUPER directive Specifically the data line SUPER FORCE NOSYM presented in the initial clo
21. sort the user must repeat that processing with an increased allocation of time e Any restart jobs will require some if not all of the files associated with RUNTYPE Cl processing The safest course of action is to save all the files i e ED2 ED4 ED5 ED6 23 DIRECT CI CALCULATIONS 122 and of course the Dumpfile ED3 In some environments it may be essential to minimize the amount of disk space retained between jobs in which case the user should be aware of the crucial files involved in restarting each of the sub tasks associated with Cl processing Together with the Dumpfile these are the SCF ED2 the Transformation ED2 ED4 and ED6 the Direct Cl ED5 and ED6 Thus if the user is confident that all SCF and Transformation processing will complete in the time allocated with any possible restart localised to the Cl phase then ED4 and even ED2 may be relegated to scratch status 23 7 Direct CI Property Calculations Computing the default set of one electron properties at completion of Cl processing may be readily accomplished through the addition of the PROPERTY ATOMS data line Note that any such calculation will retrieve the spinfree and where relevant the spin NOS from the Dumpfile such orbitals having been written to the default sections 11 for the spinfree and 12 for the spin NOs or to those sections nominated on the NATORB directive TITLE H2CO 3 21G CISD DCI PROPERTIES CALCULATION SUPER OFF NOS
22. 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES CO 1 20061 TYPE 3 ANG1 36 981 TYPE 3 ANG2 68 824 TYPE 3 CHH 1 189447 TYPE 3 XH 0 563628 TYPE 3 END RUNTYPE FORCE ENTER mm oh oo a O RR RONE 17 FORCE CONSTANT CALCULATIONS 85 17 1 1 CASSCF Force Constants In the examples below we present the data files for force constant determination based on both CASSCF and MCSCF wavefunctions for i the ground state of formaldehyde and ii the H2CO to H2 CO transition structure both conducted in a 3 21G basis Example 1 Force Constants for HCO Initially we show the CASSCF geometry optimisation data followed by the force constant run CASSCF geometry optimisation RESTART TITLE H2C0 CASSCF GEOM OPT 10E IN 9 M 0 TOTAL ENERGY 113 359134854 ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE CASSCF CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END XTOL 0 0005 ENTER Note the XTOL directive this is used to converge the geometry optimisation more stringently a typical tactic when subjecting the optimised geometry to a subsequent frequency analysis CASSCEF force constants RESTART TITLE H2CO CASSCF FORCE CONSTANTS GEOM OPT 10E IN 9 M O FREQ 1186 7 1291 8 1546 9 1710 5 2823 3 2871 9 ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0
23. 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES cO 1 134 ANG1 43 7 ANG2 57 8 CHH 1 292 XH 0 664 END BASIS 6 31G RUNTYPE SADDLE FCM ENTER m om bb me a O Pe BUNE Example 5 Open shell RHF Force Constants In this example we demonstrate HESSIAN usage in an open shell RHF force constant calcu lation for the 35A state of HCO The calculation is performed in three stages a an initial closed shell SCF calculation to provide trial eigen vectors b the open shell RHF geometry optimisation note the use of the LEVEL directive in increasing the default level shifters and XTOL in providing more stringent criteria for convergence of the geometry optimisation and c the final force constant calculation at the converged geometry Run I Initial Closed shell SCF TITLE 17 FORCE CONSTANT CALCULATIONS H2CO 3 21G CLOSED SHELL SCF AT 3A GEOMETRY ZMATRIX ANGSTROM Cc 0 1 C0 X 11 0 2 90 0 H 1 CH 2 HCO 3 DI1 H 1 CH 2 HCO 3 DI2 VARIABLES CO 1 203 CH 1 099 HCO 121 8 DI1 15 0 DI2 164 0 END ENTER Run ITI Geometry Optimisation RESTART NEW TITLE H2CO 3 21G BASIS 3A STATE OPTIMISATION MULT 3 ZMATRIX ANGSTROM Q 0 1 C0 X 1 1 0 2 90 0 H 1 CH 2 HCO 3 DI1 H 1 CH 2 HCO 3 DI2 VARIABLES cO 1 203 CH 1 099 HCO 121 8 DI1 15 0 DI2 164 0 END RUNTYPE OPTIMIZE SCFTYPE GVB OPEN 2 2 LEVEL 3 1 0 XTOL 0 0001 ENTER Run III Force Constant Evaluation RESTART TITLE H2C0
24. 1 SPIN 1 CNTRL 16 SINGLES ALL CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 END ROOTS 1 24 TABLE CI CALCULATIONS 150 THRESH 2 2 CI NATORB ENTER Now that TRAN is now appended to the BYPASS directive since the associated processing has been completed in the previous job 24 10 Semi direct Table CI Default MRDCI Calculations In order to simplify the process of configuration specification and data preparation the semi direct module now provides a set of default options that require little or no data input While these defaults are not expected to cover most in depth requirements they do provide a starting point for users and a route to subsequent more extensive calculations To illustrate this default working of the module we consider below a number of example calculations A Semi direct Table Cl calculation is to performed on the formaldehyde molecule Given the following data sequence TITLE H2CO 3 21G DEFAULT TABLE CI OPTIONS ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT ENTER then the calculation undertaken will be based on the following 1 Integral transformation will use the set of orbitals from section 1 the default section for output of the closed shell SCF eigenvectors 2 The table ci data base will be generated rather than restored from the library file 3 A Cl wavefunction of Ay symmetry i e SYMM
25. 1 90 0 X 2 CHH 3 ANG1 1 180 0 X 4 1 0 2 90 0 3 0 0 X 4 1 0 5 ANG2 3 0 0 H 4 XH 6 90 0 2 180 0 H 4 XH 6 90 0 2 0 0 VARIABLES co 1 1565619 CHH 1 2935171 XH 0 6562584 ANG1 42 5942740 ANG2 57 8778292 END BASIS 6 31G RUNTYPE SADDLE ED3 XTOL 0 0005 SCFTYPE MP2 ENTER Having computed the initial hessian either numerically or analytically a further 5 energy and gradient calculations are required in locating the MP2 transition structure to be compared with 12 such calculations when using the initial SCF hessian 4 For the present transition state there is in fact nothing to be gained by first locating the HF transition structure the following data illustrates this point We first compute ana lytically the MP2 hessian at the initial trial geometry then restore this hessian using the RUNTYPE SADDLE FCM syntax in searching for the MP2 transition structure This requires the same number of energy plus gradient calculations five in total as required when using the converged HF 6 31G structure as a starting point We further illustrate HESSIAN usage in 816 2 below MP2 Hessian Construction TITLE H2 CO lt gt H2CO 1A TS MP2 6 31G COMPUTE INITIAL HESSIAN ZMAT ANGS 17 FORCE CONSTANT CALCULATIONS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES cO 1 134 ANG1 43 7 ANG2 57 8 CHH 1 292 XH 0 664 END BASIS 6 31G RUNTYPE HESSIAN ENT
26. 1 of the Dumpfile the default section for housing closed shell SCF vectors see Table 1 This could equally be achieved by explicit section specification i e ENTER 1 9 The following data sequence would be required in performing a minimal basis set STO 3G calculation at the above nuclear geometry Note that the BASIS directive is now used to specify STO3G while in the absence of the VECTORS directive the default ATOMS option is again used in generating a trial set of vectors 2 CLOSED SHELL SCF CALCULATION Table 3 RUNTYPE Options Within GAMESS UK RUNTYPE INTEGRAL RUNTYPE SCF RUNTYPE OPTIMIZE RUNTYPE OPTXYZ RUNTYPE SADDLE RUNTYPE FORCE RUNTYPE HESSIAN RUNTYPE POLARISABILITY RUNTYPE HYPER RUNTYPE MAGNET RUNTYPE RAMAN RUNTYPE INFRARED RUNTYPE ANALYSE RUNTYPE TRANSFORM RUNTYPE CI RUNTYPE GF RUNTYPE TDA RUNTYPE RESPONSE Single point integral calculation Single point integral plus SCF calculation Geometry optimisation internal coordinates Geometry optimisation cartesian coordinates Saddle point location Force constant evaluation Analytic Force constant evaluation Polarisability calculation Hyperpolarisability calculation Magnetisability calculation Calculation of Raman Intensities Calculation of IR intensities Wavefunction analysis Integral transformation CI calculation Green s Function OVGF calculation Green s Function 2ph TDA calculation Response calculations of Excitation Energie
27. 3 CCSD Geometry Optimisation Date requirements follow in straightforward fashion from the examples provided above for direct Cl and Table Cl calculations TITLE H2CO FP GEOMETRY OPT CCSD ENERGY 114 08113594505 ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END BASIS DZ RUNTYPE OPTIMIZE CI CCSD ENTER 28 Green s Function Calculations I The OVGF Method GAMESS UK incorporates two modules designed to incorporate the effects of electron corre lation in the computation of molecular ionisation potentials The first of these methods the OVGF or outer valence green s function method provides a quantitative account of ionisation phenomena when the independent particle picture of ionisation holds and as such is most applicable in the treatment of outer valence orbitals 46 OVGF calculations are performed under control of the RUNTYPE GF specification with data input characterising the nature of the calculation introduced by a data line with the character string l P in the first data field Termination of this data is accomplished by presenting a valid Class 2 directive such as ENTER Before detailing example data files for performing OVGF calculations on the X A state of formaldehyde we mention some general points on conducting such calculations 1 OVGF calculations are limited to the treatment of ionization in closed shell molecules 2 RUNTYPE GF is in fact
28. 5 SYMM 2 5 SYMM 3 5 SPLIT 0 MAXIT 50 END SCFTYPE MCSCF THRESH 4 MCSCF ORBITAL FZC1 FZC1 FZC1 DOC1 DOC3 DOC1 DOC2 DOC3 UOC2 U0C1 VOC3 UOC END ENTER The following points should be noted 1 The ORBITALS SECTIONS and SYMM directives are obligatory the MCLR data being terminated by the END keyword 2 The set of active orbitals must be specified by means of the ORBITAL directive The individual lines of this directive are identical to those presented in the preceding MCSCF calculation see 10 3 In order to perform an MCLR calculation several vectors have to be retrieved from the Dumpfile The SECTIONS directive specifies in which sections of the Dumpfile the corresponding vectors are stored Thus the data lines SECTIONS SCF 1 MCSCF 8 CANONICAL 10 CIVEC 9 instruct the program to read the SCF eigenvectors from section 1 the MCSCF MOs from section 8 the pseudocanonical MCSCF orbitals from section 10 and the MCSCF Cl 31 LINEAR RESPONSE CALCULATIONS I THE MCLR METHOD 188 vector from section 9 of the Dumpfile Note that these section numbers correspond to the default ENTER sections associated with the MCSCF module see Table 1 and with the default section for the MCSCF natural orbitals this may be overwritten using the CANONICAL directive 4 As with RPA calculations the SYMM directive controls the calculation of excited states Note that the syntax of this directive is different from the corresponding di
29. ANG2 57 8 TYPE 3 CHH 1 292 TYPE 3 XH 0 664 TYPE 3 END BASIS STO3G RUNTYPE SADDLE ENTER mim ho oe a naO RR RUN E 6 31G DFT S VWN Optimisation DUMPFILE ED3 350 TITLE H2 CO lt gt H2CO 1A TS 6 31G DFT S VWN TOTAL ENERGY 113 4117918572 au ZMAT ANGS 0 C 1 CO X 2 1 0 1 90 0 X 2 CHH 3 ANG1 1 180 0 X 4 1 0 2 90 0 3 0 0 16 TRANSITION STATE OPTIMISATION 76 X 41 0 5 ANG2 3 0 0 H 4 XH 6 90 0 2 180 0 H 4 XH 6 90 0 2 0 0 VARIABLES co 1 1525832 TYPE 3 CHH 1 2981078 TYPE 3 XH 0 6596229 TYPE 3 ANG1 43 4018534 TYPE 3 ANG2 57 3815232 TYPE 3 END BASIS 6 31G RUNTYPE SADDLE ED3 1 DFT S VWN VECTORS GETQ ED3 1 ENTER The following points should be noted 1 the starting variables for the initial geometry in the DFT calculation have been taken from the output of the previous HF optimisation 2 the initial hessian is that from the previous HF STO 3G calculation restored from the STO3G Dumpfile using the RUNTYPE SADDLE ED3 data line 3 the initial vectors in the DFT calculation will be the final set of HF STO3G SCF orbitals restored from section 1 of the STO3G Dumpfile 16 2 CASSCF Transition State Optimisation We again use the H2CO to H2 CO transition structure location to illustrate performing CASSCF and MCSCF optimisations In both cases we perform the calculation in two steps initially locating the transition state at the HF SCF level then using the resulting geometry and in some case
30. CALCULATIONS 116 SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI CORE 1 2 END ACTIVE 3 TO 20 END DIRECT 12 6 12 CONF 222222 ENTER The following points should be noted e both ACTIVE and CORE are control directives of the integral transformation module As such they should be presented in the data stream prior to the specification of the direct Cl data i e before the DIRECT data line e the values of NELEC NINT and NEXT specified on the DIRECT data line are modified to reflect the impact of CORE and ACTIVE This involves in the present case reducing the values from the all electron calculation NELEC 16 NINT 8 NEXT 14 to NELEC 12 only 12 electrons now explicitly considered NINT 6 two orbitals have been frozen and NEXT 12 two orbitals having been discarded e the CONF data line now comprises six integers specifying the double occupancy of the internal orbital set e the default settings of CORE and ACTIVE are hopefully self evident 23 4 Direct ClI Multi reference CI Calculations In the simplest case specification of additional reference functions in the Direct Cl input data is accomplished through the CONF directive with each reference function characterised by an additional data line of NINT integers defining the orbital occupation pattern of the required function There is the constraint imposed however that the NINT internal orbitals appea
31. CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END ENTER 67 Assume that the above optimisation had converged and at some point after the user wishes to compute a number of properties of the CASSCF wavefunction but no longer has access to the Dumpfile used above This may be accomplished using the following data sets the first to compute an initial SCF wavefunction at the optimised CASSCF geometry the second to re do a single point CASSCF calculation at this geometry using the PROPERTY ATOMS directive see 12 to obtain a variety of one electron properties Run I The Initial SCF Calculation TITLE H2CO 3 21G SCF AT CASSCF GEOMETRY ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES co 1 2406313 CH 1 1136939 HCO 123 1820211 END ENTER Run IT The CASSCF Property Analysis RESTART TITLE H2CO CASSCF PROPERTIES AT OPTIMISED GEOM ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES co 1 2406313 CH 1 1136939 HCO 123 1820211 END SCFTYPE CASSCF CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END PROPERTY ATOMS ENTER 15 6 2 MCSCF Geometry Optimisation Run I The Initial SCF Calculation 15 GEOMETRY OPTIMISATION TITLE H2CO 3 21G SCF STARTUP FOR MCSCF GEOM OPTIMISATION ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END ENTER Run IT The MCSCF Optimisation RESTART T
32. DFT Directive Options s ea atos soes e re aaia Ee opoh ie k la a 11 4 Specification of Functionals ooa oaa a a ee 11 5 Specification of Integration Grids gt s s co moce g ee 11 5 1 The QUADRATURE Directive ooa a a a a ILo Coulomb MENE coser ee hd eG he ee we ee Re e Se 12 M ller Plesset MP2 and MP3 Calculations 12 1 MP2 Calculations lt lt 0 0 gos wale SS ee we a ee Bae a db eas 12 2 MP3 Calculations 1 4 24 284065444 bed ae be ee aR a 12 3 Freezing and Discarding Orbitals cs s csoc ee ee ee ae ees 12 4 Direct MP2 Calculations ooa ee 13 Analysing the Wavefunction 13 1 One electron Property Evaluation 0 000 0022 13 2 Simplified Property Specification 2 0 2 ee 13 3 Localised Orbitals sr oa we a ea ee a 13 4 Distributed Multipole Analysis 0 00 000000 2p eee 15 17 17 20 21 21 22 23 24 28 31 31 32 33 34 34 35 35 40 41 43 44 44 CONTENTS iil 135 Graphical Ana DSS suck 6 amp A oo Ge we we a ee A he E 52 13 6 Population Analysis ss i senoressa KA oa adua e LOR ER ai aba 54 13 7 Morokuma Energy Decomposition Analysis a a a a 55 14 Restarting Integral and SCF Computations 56 15 Geometry Optimisation 58 15 1 Internal Coordinate Optimisation o o aoa e ee 59 15 2 Determining the Initial Hessian ooa aa ee 61 15 3 Cartesian Coordinate Optimisation ooo aa a e a a 64 15 4 Mixed Z matrix and Cartesian Optimisation o oo 65
33. ENTER Run II Calculation of Raman Intensities RESTART TITLE H2CO 3 21G DEFAULT BASIS RAMAN INTENSITIES ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE RAMAN ENTER 23 DIRECT CI CALCULATIONS 108 23 Direct CI Calculations Direct Cl calculations are performed under control of the RUNTYPE CI specification with data input characterising the nature of the Cl introduced by a data line with the keyword DIRECT in the first data field Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS or ENTER Before detailing example data files for performing direct Cl calculations on the X Aj state of formaldehyde we mention some general points on conducting such calculations 1 RUNTYPE Cl is in fact a combination of tasks requesting integral generation SCF integral transformation and finally the Cl calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below Several files will be generated under RUNTYPE CI processing For Direct Cl calculations these include e the Mainfile ED2 and Dumpfile ED3
34. Frequencies for H2CO Locating the H2CO to t HCOH transition structure with subsequent determination of the vibrational frequencies Using a HESSIAN calculation to obtain the starting hessian required in locating the H2CO to t HCOH transition structure Locating the H2CO to H2 CO transition structure Open shell RHF geometry optimisation and force constants for the 3A state of H2CO MP2 geometry optimisation and force constants for H2CO Example 1 Vibrational Frequencies for HCO Run I Geometry Optimisation 17 FORCE CONSTANT CALCULATIONS 91 TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE XTOL 0 0001 ENTER Run II Force Constant Evaluation Note the form of the RESTART directive below since the geometry optimisation has been conducted immediately prior to the HESSIAN run it is sufficient to use just RESTART when the optimised geometry will be read from the Dumpfile and override the ZMATRIX data in the input stream RESTART TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF FREQUENCIES ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE HESSIAN ENTER Example 2 The H2CO to t HCOH transition structure Run I Transition Structure Determination Here we are
35. I The Scf Job TITLE H2CO 3 21G SCF PRIOR TO DIRECT CI CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER The only obvious point to note is the use of the SUPER directive in requesting full integral list generation required in the subsequent transformation Run II The Transformation and CI Job RESTART TITLE H2CO 3 21G CISD DIRECT CI CALCULATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 8 14 CONF 22222222 ENTER The following points should be noted e The SCF computation is BYPASS ed e The SCF vectors from the first run are restored in default from Section 1 of the Dumpfile and subsequently used in the transformation 23 DIRECT CI CALCULATIONS 112 The calculation may be further subdivided by splitting Run Il above into separate integral transformation and Cl runs using the RUNTYPE TRANSFORM specification with subsequent BYPASS ing of the transformation in the Cl job Thus Run Ila The Transformation Job RESTART TITLE H2CO 3 21G CISD DIRECT CI CALCULATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE TRANSFORM ENTER Run IIb The Direct CI Job RESTART TITLE H2CO 3 21G CISD DIRECT CI CALCULATION SUPER OFF NOSYM BYPASS TRANSFORM ZMATRIX A
36. INFRARED processing e For SCF intensities these include the Mainfile ED2 and Dumpfile ED3 the Scratch file ED7 the semi transformed ED4 and transformed ED6 integral files note that ED4 is also used as a scratch file in the solution of the coupled Hartree Fock equations the Hamiltonian file ED12 which acts to store the derivative Fock operators temporary files for sorting both transformed integrals the Sortfile and inter mediate matrices in the Hessian calculation e The generation of MP2 intensities is significantly more complex in addition to the files generated under SCF processing additional temporary files will be required including EDO ED11 ED16 ED17 ED18 ED18 ED19 MTO and MT1 Any restart jobs will require ED6 and ED12 being saved in addition to the Dumpfile ED3 and Mainfile ED2 The following examples demonstrate INFRARED usage where in each case we show data files for performing the appropriate geometry optimisation together with data for determining the intensities under RUNTYPE INFRARED processing 1 Optimisation of the geometry and calculation of the SCF infra red intensities for HCO 2 Open shell RHF geometry optimisation and intensities for the 3A state of HCO 3 MP2 geometry optimisation and infra red intensities for H2CO Example 1 SCF Infra red Intensities for HCO Run I Geometry Optimisation TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF
37. SCF computation The same process will be undertaken in the GVB and CASSCF restart jobs with sections 4 and 5 GVB and sections 7 and 8 CASSCF being used to restart SCF processing see Table 1 Note also that at the outset of a specific computation the program generates the trial MOs and stores these in the default vectors section or that Section nominated on the ENTER line This activity precedes integral evaluation so even if the starting job had dumped during computation of the two electron integrals an appropriate set of eigenvectors will have already been generated The REST parameter on the SCFTYPE directive of the GVB run instructs the program to restore the set of Cl pair coefficients from the Dumpfile and not to use the default settings This is crucial when restarting GVB geometry optimisations Several changes in the CASSCF data file should be noted The BYPASS keyword on the CONFIG data line instructs the program to bypass generation of the Loop Formula tape ED9 assuming of course that this file had been saved from the startup run Geometry Optimisation In the examples above we have considered performing a single point calculation i e at a particu lar geometry using the various SCFTYPE options available within GAMESS UK Each category of wavefunction may in addition be used in optimising the molecular geometry through cal culation of not only the energy but also the gradient of the energy In the present section
38. THRESH 2 2 ENTER The following points should be noted e t is assumed that the complete sequence of sub tasks is to be carried out If any task is to be BYPASS ed then the associated data line must be present e The transformation module will again use the default section number corresponding to the closed shell SCF vectors section 1 as the location of the molecular orbital coefficient array e The SYMMETRY SPIN SINGLES and ROOTS directives of the SELECT sub module may all be omitted since the required specification corresponds in each case to the default values Note however that the CNTRL directive must be specified in any SELECT data in which the CONF directive is also present in contrast to the conventional module e To provide compatibility with the DIRECT Cl module an alternative form of the CONF directive may also be used where the configurations are defined in terms of occupation patterns rather than by the orbital numbering In this case a second keyword OCCUPA TION is specified on the CONF data line thus in the present example we may also use the following CONF data 24 TABLE CI CALCULATIONS 158 CONF OCCUPATION 2 2 2 2 2 2 2 2 o 0 0 2 2 2 2 2 2 o 2 2 0 0 2 2 2 2 2 2 2 0 o 0 2 2 2 2 2 2 2 1 1 1 O 1 END where the occupations specified correspond to the occupancies of the input SCF MOs At this stage we leave it to the user to confirm that this data is equivalent to the CONF specification in the example a
39. TITLE H2C0 3A2 UHF 3 21G DEFAULT BASIS 1 E PROPERTIES ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE ANALYSE SCFTYPE UHF PROPERTY 4c 40 END VECTORS 10 ENTER 13 ANALYSING THE WAVEFUNCTION 48 As presented above the NATORB directive will request generation of the spinfree natural orbitals Two variants of the directive allow for i generation of the spin natural orbitals and ii annihilation of the UHF wavefunction and subsequent generation of both spin and spinfree NOs The associated data requirements are straightforward e Generation of the spin NOs is driven by the keyword SPIN presented immediately after the NATORB initiator Thus the data line NATORB SPIN 11 PRINT would result in the routing of the spin NOs to section 11 of the Dumpfile e Annihilation of the UHF wavefunction and subsequent generation of the NOs from the annihilated density matrices is driven by specification of the keyword ANNIHILATE as the final character string on the NATORB data line Thus the data sequence NATORB 12 PRINT ANNIHILATE would route the spinfree NOs of the annihilated UHF wavefunction AUHF to section 12 of the Dumpfile The theory behind the AUHF analysis can be found in 33 Note that the NOs of the UHF and AUHF wave function are in fact identical the only difference lying in the occupation numbers Now let us consider the date requirements when computing properties
40. TITLE H2CO 2B2 3 21G CISD DIRECT CI CALCULATION SUPER OFF NOSYM CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI OPEN 1 1 DIRECT 15 8 14 SPIN DOUBLET CONF 22222221 NATORB 11 12 PRINT ENTER Considering the changes to the closed shell run the following points should be noted e Of the three integers on the DIRECT data line NINT and NEXT remain unchanged while NELEC the number of active electrons is now 15 e The occupation number of the 8th SCF MO on the CONF data line is now 1 reflecting the open shell orbital occupancy e The OPEN directive is now present specified prior to the direct Cl data e An additional directive is required in the direct Cl data SPIN defining the spin multiplicity of the Cl wavefunction e NATORB now requests the spinfree and spin NOs to be routed to sections 11 and 12 respectively of the Dumpfile 23 DIRECT CI CALCULATIONS 111 e The set of vectors used in the integral transformation will be restored in default from the Dumpfile section containing the energy ordered SCF orbitals as written to by the SCF process section 5 see Table 1 Now let us consider performing the two calculations above splitting each into a sequence of jobs where the first job carries out the SCF the second the transformation and Cl First the closed shell case valid data sequences for performing the calculation are shown below Run
41. TYPE 3 specification compared to 12 when using the initial SCF hessian Note that the MCSCF module is approximately 3 times faster than the CASSCF module for this calculation 16 4 MP2 Transition State Optimisation We again use the H2CO to H2 CO transition structure location to illustrate performing MP2 optimisations First we follow the CASSCF and MCSCF examples performing a 6 31G basis calculation in two steps Having located the transition state at the HF SCF level we then use the resulting geometry and possibly the hessian as a starting point for the MP2 calculation The data for the HF and MP2 optimisations are as follows HF Optimisation TITLE H2 CO lt gt H2C0 1A TS 6 31G SCF TOTAL ENERGY 113 629882925 ZMAT ANGS 0 C 1 CO X 2 1 0 1 90 0 X 2 CHH 3 ANG1 1 180 0 X 41 0 2 90 0 3 0 0 X 41 0 5 ANG2 3 0 0 16 TRANSITION STATE OPTIMISATION 80 H 4 XH 6 90 0 2 180 0 H 4 XH 6 90 0 2 0 0 VARIABLES CO 1 134 TYPE 3 ANG1 43 7 TYPE 3 ANG2 57 8 TYPE 3 CHH 1 292 TYPE 3 XH 0 664 TYPE 3 END BASIS 6 31G RUNTYPE SADDLE ENTER MP2 Optimisation RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 6 31G BASIS MP2 TOTAL ENERGY 113 8779369833 ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES co 1 1565619 TYPE 3 CHH 1 2935171 TYPE 3 XH 0 6562584 TYPE 3 ANG1 42 5942740 TYPE 3 ANG2 57 8778292 TYPE 3 END BASIS 6 31G RU
42. The OVGF Method 29 Green s Function Calculations Il The TDA Method 30 Linear Response Calculations The RPA Method 30 1 Direct RPA calculations 2 radna na a a k 31 Linear Response Calculations II The MCLR Method 32 ZORA relativistic effects 33 Multiple RUNTYPE Calculations 33 1 Geometry Optimisation and Direct Cl Calculation 33 2 SCF Calculation and Property Evaluation 004 4 33 3 Initial Hessian and Transition State Location 024 4 33 4 Geometry Optimisation and Raman Intensities 33 5 MCSCF Force Constant Calculation 2 0 0008 eee 174 177 179 183 185 189 1 INTRODUCTION 1 The main purpose of this chapter is to provide an overall guide to using the program without the tedium often associated with an extensive catalogue of data input requirements We aim to achieve this by describing a sequence of data files demonstrating use of the program in a variety of calculations on the formaldehyde molecule H2CO The role and specification of the directives found in these examples will be presented in later Parts of the manual Specifically Introduction we consider here data files for performing 10 11 12 13 14 15 16 17 18 19 20 21 Closed shell SCF calculations Closed shell Direct SCF calculations An open shell restricted Hartree Fock calculation on the formaldehyde cation H2CO 2B2 and corresponding
43. The Stuttgart relativistic large core ECP due to Preuss at al 13 STRSC The Stuttgart relativistic small core ECP due to Preuss at al 14 A full list of the elements for which ECPs and associated basis sets are available for each of the seven library sets above is given in Tables 5 and 6 of Part 3 of the manual Considering the non local ECP example given above the following data sequence would be required to perform the corresponding local ECP calculation using the LANL2 ECP TITLE H2CO 1Ai LOCAL LANL2 ECP CALCULATION ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS ECP LANL2 PSEUDO ECP 0 LANL2 0 C LANL2 C ENTER 8 IN CORE SCF CALCULATIONS 23 The local ECP is requested through the ECP field on the PSEUDO directive The subsequent data lines of this directive again allocate an ECP stored in one of the ECP Libraries program resident to the atoms specified in the z matrix through TAG specification In this case the LANL2 parameter requests the ECP due to Hay and Wadt 6 the LANL2 library ECPs for carbon and oxygen are again tagged as C and O respectively Note that compatibility with the previous versions of the code has been maintained so that presenting the following data sequence TITLE H2CO 1Ai LOCAL ECP CALCULATION ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS ECPDZ PSEUDO ECP 00 cc ENTER will a
44. XTOL 0 0001 ENTER Run II Magnetisability Calculation RESTART TITLE H2CO 3 21G DEFAULT BASIS MAGNETISABILITY ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE MAGNET VCD ENTER 21 Infra red Intensity Calculations Analytic calculations of infra red intensities may be carried out for both closed shell SCF and RHF open shell wavefunctions together with MP2 closed shell wavefunctions The following points should be noted 1 Infra red intensity calculations are performed under control of the RUNTYPE INFRARED directive 2 RUNTYPE INFRARED is in fact a combination of tasks requesting integral generation SCF gradient evaluation with additional evaluation of derivative Fock operators integral transformation solution of the coupled Hartree Fock CHF equations calculation of the dipole moment derivatives calculation of the two electron second derivative contribution and finally determination of the infra red intensities While in most cases it is feasible to perform all steps in a single calculation it may be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 21 INFRA RED INTENSITY CALCULATIONS 103 3 Several files will be generated under RUNTYPE
45. and MULT specify the charge and spin multiplicity of the system with the default referencing a closed shell neutral system 3 The ADAPT directive specifies that the SCF computation is to be performed in a sym metry adapted basis 4 The SUPER directive specifies the format to be used in generation of the two electron integral file The program incorporates three options namely e P Supermatrix 2J K e separate J and K Supermatrices in practice 2J K and K e conventional 2 electron integral format In default efficiency considerations are used in deciding the appropriate format based on the particular computation to be undertaken as defined by the SCFTYPE directive Considerable Caution must be exercised when considering usage of the Mainfile produced in one phase of the computation in some subsequent phase and specification of the SUPER directive provides some control over this usage The default and available integral options are summarised in Table 2 where the specified defaults are those appropriate to RUNTYPE SCF 2 CLOSED SHELL SCF CALCULATION 6 Table 2 GAMESS UK Integral Options as a function of SCFTYPE SCFTYPE Default Available Closed shell SCF P P J K 2 electron integral UHF J K J K 2 electron integral Open shell RHF J K J K 2 electron integral GVB J K J K 2 electron integral MP2 2 electron integral 2 electron integral MP3 2 electron integral 2 electron integral CASSCF 2 electron integral 2 electron integ
46. by specifying the DFT options described below on one or more data lines each containing the character string DFT in the first data field the user may present as many data lines as desired in specifying these options providing the mechanism for presenting long option lists over several lines Note that the DFT data lines should be presented after both RUNTYPE and SCFTYPE directives if present and before the VECTORS directive if present Thus the default DFT specifications invoked by the data input above may also be invoked by explicit specification thus TITLE H2CO 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END DFT B LYP QUADRATURE MEDIUM ENTER or by specifying the functional and quadrature settings on separate DFT data lines thus TITLE H2C0 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END DFT BLYP DFT QUADRATURE MEDIUM ENTER or even TITLE H2C0 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END DFT BECKE88 DFT LYP DFT QUADRATURE MEDIUM ENTER 11 DFT CALCULATIONS 34 11 4 Specification of Functionals As described above The default functional used in the current DFT implementation is the so called B LYP functional employing the Becke88 excha
47. calculations TITLE H2CO TZVP MRDCI DIRECT CI CI TOTAL ENERGY 114 26950815 SUPER OFF NOSYM ZMATRIX ANGSTROM Cc 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 2359174 CH 1 0991666 HCO 122 7868963 END BASIS TZVP RUNTYPE OPTIMIZE CI DIRECT 16 10 42 CONF 222 Here the CONF directive is used to specify a 3 reference function multi root direct Cl wavefunc tion Note that in practice the above calculation would typically be performed in two steps an 27 CI GEOMETRY OPTIMISATION 171 initial SCF calculation would be required to identify the MOS to be specified when quantifying the reference functions under control of the CONF data in the second job III Open Shell calculations We consider performing the calculation in several steps where the first two carry out an RHF open shell geometry optimisation and the third the corresponding Cl optimisation Runs I and II The SCF Optimisation TITLE H2CO 3 21G CLOSED SHELL STARTUP ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END ENTER The first step is merely used to generate a suitable set of MOS for initiating the SCF geometry optimisation on the ion below RESTART NEW TITLE H2C0 3 21G GEOMETRY OPTIMISATION SCF MULT 2 CHARGE 1 ZMATRIX ANGSTROM 0 0 1 c0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE ENTER Run
48. data sequence for performing such a calculation is shown below TITLE H2C0 3 21G DEFAULT BASIS DIRECT MP2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT MP2 ENTER Note the change in syntax of the SCFTYPE directive when specifying the DIRECT option The third parameter on the data line MP2 points to the particular category of M ller Plesset 13 ANALYSING THE WAVEFUNCTION 45 wavefunction required i e MP2 At present this is the only option supported in direct mode and is only applicable to closed shells Note that the default file output in such calculations is confined to ED3 and ED7 the Dump and Scratch file respectively Note also that such calculations are memory intensive with the MEMORY pre directive in the above example see the machine specific Parts used to increase the default memory allocation in the present run 13 Analysing the Wavefunction GAMESS UK includes a variety of tools for analysing wavefunctions driven by the RUNTYPE ANALYSE directive It is now possible to e Calculate a variety of 1 electron properties e Generate a localised orbital representation of an SCF wavefunction using either the dipole centroid technique due to Foster and Boys or the overlap based criterion due to Pipek and Mezey 31 e Provide graphical analysis of molecular wavefunctions The program is capable of gener ating contour and perspective plots which depict
49. direct ROHF calculation An open shell unrestricted Hartree Fock calculation on the formaldehyde cation H2CO 2B and corresponding direct UHF calculation GVB 1 PP and direct GVB calculations on the ground state molecule A pseudopotential calculation on the ground state molecule A CASSCF calculation on the ground state molecule MCSCF calculations on the ground state molecule DFT calculations on the ground state molecule and cation M ller Plesset MP2 and MP3 calculations single and multi reference Analysis of the ground state wavefunction Morokuma Energy Decomposition Analysis Restarting Integral and SCF Computations Geometry Optimisation in internal coordinates Geometry Optimisation in cartesian coordinates Transition State Optimisation Numerical Force Constant Evaluation Analytic Force Constant calculations Polarisability calculations Hyperpolarisability calculations Magnetisability calculations 1 INTRODUCTION 2 22 Calculation of infra red intensities 23 Calculation of Raman intensities 24 Direct Cl calculations on the ground state molecule and ion 25 Conventional and Semi direct Table Cl calculations on the ground and first excited state of the molecule 26 Full Cl calculations on the ground state molecule and ion 27 Closed shell coupled cluster calculations CCSD and CCSD T on the ground state molecule 28 A Green s function OVGF calculation of the valence lEs
50. e TABLE generates an input a data base of pattern symbolic matrix elements for use in both the selection process and in solving the secular problem e SELECT performs configuration generation and subsequent selection based on a user specified set of reference configurations and appropriate thresholds Note that the semi direct module requires at least two reference configurations e Cl provides pre processing prior to the semi direct evaluation of the Cl eigenfunc tions followed by calculation in semi direct fashion of one or more Cl eigenfunc tions of the secular problem In contrast to the conventional module just two secular problems are solved as part of the extrapolation process one at the lowest threshold Tmin and one at the threshold Tmin Tinc e NATORB generate the spin free natural orbitals for one or more of the calculated Cl eigenvectors Note that this module is now executed in default The remaining analysis modules remain optional and may be used to further analyse one or more of the Cl eigenvectors e PROP compute various 1 electron properties of the Cl wavefunctions Note that the natural orbitals generated above may be routed to the Dumpfile and examined by the other analysis modules of GAMESS UK in a subsequent job e TM compute the transition moments between nominated Cl eigenvectors Note at this point that there may be additional data input associated with each of the sub modules e g for defini
51. evident one orbital containing one electron Again in more general cases the OPEN directive must be used to define the shell structure characterising the Hartree Fock wavefunction 3 Two sets of eigenvectors are generated in an open shell RHF calculation the non canonicalised locked eigenvectors that are used during the SCF process and a second set the canoni calised vectors which are generated on termination of the SCF process The latter exhibit energy weighting in the virtual manifold and act as the most obvious starting point for a post Hartree Fock computation 4 Two sections will be used to house these eigenvectors In default the non canonicalised vectors will be written to section 4 of the Dumpfile while the canonicalised vectors will be written to section 5 see Table 1 5 Explicit specification of these sections thus requires two integers on the ENTER directive Presenting the data line ENTER 4 5 will result in the same eigenvector section storage as the default 6 In the absence of the SUPER directive the default Mainfile format for an open shell RHF calculation J K will apply 4 RHF OPEN SHELL CALCULATION 11 While the above data structure appears the most straightforward way of accomplishing the com putation it relies on the initial trial eigenvector guess generated through the default ATOMS option providing the required open shell electronic configuration Such a situation is unlikely to hold in all ca
52. from the Cl calculation typically the high energy inner shell complement orbitals In contrast to the Conventional Table Cl module the final subset of orbitals to be included in the Table Cl calculation is now controlled by the CORE and ACTIVE directives of the integral transformation module The freezing of core or inner shell orbitals is achieved by nominating the sequence nos of those orbitals to be frozen under control of the CORE directive The discarding of orbitals is performed under control of the ACTIVE directive which specifies the sequence nos of the active set of orbitals to appear in the Cl Note that the sequence numbers to be specified refer to the input orbitals typically those produced by the SCF code and not the Table reordered orbital as in the conventional module Consider the previous H2CO calculation Suppose we wish to freeze both the Ols and Cis orbitals with SCF sequence numbers 1 and 2 respectively and to discard the two highest 24 TABLE CI CALCULATIONS 155 energy virtual orbitals with SCF sequence numbers 21 and 22 The CORE and ACTIVE data will then appear as follows CORE 1 2 END ACTIVE 3 TO 20 END The core orbitals are both of a symmetry and have sequence numbers 1 and 2 The virtual orbitals are of bz SCF sequence no 21 and a SCF sequence no 22 symmetry and as the highest orbital of each IRrep correspond to the 6th orbital of bo symmetry and the 12th orbital of a symmetry respectiv
53. latter obtain dispersion coefficients Static polarisabilities only are available for open shell SCF wavefunctions and for closed shell MP2 wavefunctions The following points should be noted 1 Polarisability calculations are performed under control of the RUNTYPE POLARISABIL ITY directive and are available for for closed shell SCF and MP2 wavefunctions and open shell RHF wavefunctions but not at present UHF CASSCF or MCSCF or ECP based calculations 2 For SCF wavefunctions the dipole dipole dipole quadrupole and quadrupole quadrupole polarisabilities are calculated For closed shell MP2 wavefunctions only the former terms are calculated 3 RUNTYPE POLARISABILITY is in fact a combination of tasks requesting integral gen eration SCF integral transformation and solution of the coupled Hartree Fock equations While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 4 Several files will be generated under RUNTYPE POLARISABILITY processing For SCF wavefunctions these include e the Mainfile ED2 and Dumpfile ED3 e the Scratch file ED7 e the semi transformed ED4 and transformed ED6 integral files note that ED4 is als
54. longer holds and as such is applicable to the treatment of ionisation processes throughout the whole energy scale It has been widely employed in the study of phenomena associated with the breakdown of the molecular orbital picture of ionisation e g satellite bands TDA calculations are performed under control of the RUNTYPE TDA specification with data input characterising the nature of the calculation introduced by a data line with the character string l P in the first data field Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS ore ENTER Before detailing example data files for performing TDA calculations on the X A state of formaldehyde we mention some general points on conducting such calculations 1 TDA calculations are limited to the treatment of ionization in closed shell molecules 2 RUNTYPE TDA is in fact a combination of tasks requesting integral generation SCF integral transformation and finally the Green s function calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 3 Several files will be generated under RUNTYPE GF processing These include the follow
55. of MOs is available e g in an MP2 calculation In both cases the user will need to generate the associated set of spinfree natural orbitals and present these as input to the analysis module Such orbitals are generated under control of the NATORB directive which may used to route the natural orbitals to a nominated section on the Dumpfile The following data sequences would be required when evaluating the properties based on a UHF wavefunction First the data for the UHF calculation itself 13 ANALYSING THE WAVEFUNCTION AT Table 6 The One electron Operators and Operator Numbers Operator Operator Operator Operator Number Number 1 Potential 11 Third Moment combined 2 Diamagnetic Shielding 12 Hexadecapole Moment 3 Electric Field 13 Fourth Moment even 4 Electric Field Gradient 14 Fourth Moment odd 5 Dipole Moment 15 Overlap 6 Quadrupole Moment 16 Planar Charge Density 7 Diamagnetic Susceptibility 17 Line Charge Density 8 Second Moment 18 Charge Density 9 Octupole Moment 19 Isotropic ESR Coupling Constants 10 Third Moment 20 Anisotropic ESR Coupling Constants TITLE H2CO 3A2 UHF 3 21G DEFAULT BASIS MULT 3 ZMATRIX ANGSTROM c 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE UHF NATORB 10 PRINT ENTER Having routed the spinfree natural orbitals to section 10 on the Dumpfile the properties calcu lation proceeds by nominating this section on the VECTORS line thus RESTART NEW
56. the Dumpfile ED3 and the transformed integral file ED6 must be saved The MCLR calculation may be performed in situ or as a restart job In the following we perform a similar MCLR calculation to that described in the RPA section above An MCLR calculation is to performed on the formaldehyde molecule in a DZ s p Rydberg basis with estimates required of the excitation energies for the lowest 5 states of A B and B symmetry Let us consider performing this calculation in two separate jobs where the first carries out the SCF the second the MCSCF and MCLR calculation First the closed shell case valid data sequences for performing the calculation are shown below Run I The closed shell Scf Job TITLE H2CO CLOSED SHELL DZ R SP TOTAL ENERGY 113 8308839 SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 The second restart job requiring both the Mainfile and Dumpfile from Run I may be driven as follows RESTART TITLE H2C0 DZ R SP MCSCF 10E 9 M 0 TOTAL ENERGY 113 9547201 SUPER OFF NOSYM NOPRINT BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END 31 LINEAR RESPONSE CALCULATIONS I THE MCLR METHOD 187 BASIS DZ 0 DZ C DZ H So 1 0 0 02 PO 1 0 0 02 END RUNTYPE RESPONSE MCLR ORBITAL FZC1 FZC1 FZC1 DOC1 DOC3 DOC1 DOC2 DOC3 UOC2 UV0OC1 VOC3 U0C1 END SECTIONS SCF 1 MCSCF 8 CANONICAL 10 CIVEC 9 SYMM 1
57. the RPA or Random Phase Approximation is applicable in the treatment of excited states that are dominated by single excitations from a zero order closed shell SCF wavefunction Both RPA and MCLR calculations are performed under control of the RUNTYPE RESPONSE specification with subsequent keyword specification detailing the method to be employed RPA calculations of excitation energies and oscillator strengths are thus initiated by specifying the data line RUNTYPE RESPONSE RPA in the input file Data input characterising the details of the calculation is presented immediately after the RUNTYPE data line Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS Before detailing example data files for performing RPA calculations on the singly excited states of formaldehyde we mention some general points on conducting such calculations 1 RPA calculations are limited to the treatment of excited states of closed shell molecules 2 RUNTYPE RESPONSE is in fact a combination of tasks requesting integral generation SCF integral transformation in conventional RPA calculations and finally the response calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in
58. the computation of certain one electron properties The following points should be noted e the properties evaluated include the electrostatic potential electric field electric field gradient and electron density at each of the atomic centres plus the dipole second moment quadrupole moment third and octupole moments at the computed centre of mass of the system under study In addition the spin densities will also be computed in the case of open shell systems e this analysis if requested is available on completion of SCF OPTIMIZE OPTXYZ SADDLE and Cl processing The following data sequence would be required to generate the above list of properties on completion of an SCF calculation of the formaldehyde molecule 13 ANALYSING THE WAVEFUNCTION 50 TITLE H2CO 3 21G BASIS SCF DEFAULT 1 E PROPERTIES ZMATRIX ANGSTROM N Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END RUNTYPE SCF PROPERTY ATOMS ENTER In this example the set of MOs to be used in the property evaluation will be retrieved from that section written in the SCF process namely section 1 of the Dumpfile i e the default section number for the underlying closed shell SCFTYPE see Table 1 A somewhat different approach may be required when computing the one electron properties derived from a wavefunction with more than one set of MOs e g a UHF wavefunction or in cases where only the total density matrix and not an associated set of MOs
59. the latter stages of the computation We illustrate this point below 3 Several files will be generated under conventional RPA processing These include the following e the Mainfile ED2 and Dumpfile ED3 e the semi transformed ED4 and transformed ED6 integral files e the Scratch file ED7 e temporary files for sorting both transformed integrals the Sortfile Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 4 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines associated with conventional RPA processing requires the data line SUPER OFF NOSYM in the SCF run 30 LINEAR RESPONSE CALCULATIONS I THE RPA METHOD 181 5 In RPA calculations the user must specify the number of states of each irreducible repre sentation for which excitation energies and corresponding oscillator are to be computed Such states are defined by use of the SYMM directive with a separate data line required for for each irreducible representation Thus calculation of the excitation energies for the lowest five states of each of the optically allowed symmetries Biu B2u B3u of a molecule with Do symmetry requires the data lines SYMM 2 1 TO 5 SYMM 3 1 TO 5 SYMM 5 1 TO 5 where the first integer nominates the irreducible representation An RPA calculation is to performed on the formaldehyde molecule with estimates required of the exci
60. these cases the optimisation converges to give identical results to the first Direct Cl example presented above Note that this arises from the use of zero threshold specification the inherent lack of accuracy associated with finite threshold specification is likely to case convergence problems when trying to optimize the geometry as noted above Conventional Table CI Data TITLE H2CO MRDCI CISD FP OPTIMIZATION CI ENERGY 113 43777426 ZMATRIX ANGSTROM 0 O 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE CI MRDCI ADAPT 27 CI GEOMETRY OPTIMISATION 173 TRAN 1 SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES 1 CONF 012345 13 17 18 ROOTS 1 THRESH O 0 CI DIAG EXTRAP OFF ENTER Note that the example above corresponds to a CISD calculation Semi direct Table CI Data TITLE H2CO TABLE CI 4M 1R FP OPTIMIZATION ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE CI MRDCI DIRECT TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES ALL CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 END ROOTS 1 THRESH O 0 CI ENTER This semi direct optimisation is now using a reference set of 4 functions remember again that it is not possible to conduct CISD calculations with this module 28 GREEN S FUNCTION CALCULATIONS I THE OVGF METHOD 174 27
61. to 30 LINEAR RESPONSE CALCULATIONS I THE RPA METHOD 184 have the possibility to interrupt a calculation and restart it at a subsequent point This feature performed under control of the DUMP and RESTORE directives is also described in Part 7 Let us consider the corresponding data files to those above for performing a direct RPA calcu lation on the formaldehyde molecule with estimates again required of the excitation energies for the lowest 5 states of each irreducible representation A valid data sequence for performing such a calculation is shown below We assume that the SCF calculation is also performed in direct fashion TITLE H2CO TZVP R SP BASIS DIRECT RPA EXCITATION ENERGIES ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP 0 TZVP C TZVP H So 1 0 0 02 PO 1 0 0 02 END SCFTYPE DIRECT RUNTYPE RESPONSE RPA DIRECT TDA SYMM 1 1 TO 5 SYMM 2 1 TO 5 SYMM 3 1 TO 5 SYMM 4 1 TO 5 ANALYSE ENTER Now let us consider performing the above calculation in two separate jobs where the first car ries out the direct SCF the second the direct RPA calculation First the direct SCF valid data sequences for performing the calculation are shown below Run I The direct Scf Job TITLE H2CO TZVP R SP BASIS DIRECT SCF PRIOR TO RPA ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP 0 31 LINEAR RESPONSE C
62. 1 00000000 1 00000000 1 00000000 1 00000000 1 00000000 38 11 DFT CALCULATIONS 39 e Although the Coulomb fitting may improve efficiency a significant additional improve ment can be obtained if the 3 center 2 electron integrals can be stored in memory The MEMORY subdirective sets aside the maximum amount of memory that is not needed for other purposes to hold the 3 center 2 electron integrals If not all the integrals fit in memory then those that cannot be stored will be recomputed To switch this option on replace the data line DFT JFIT JFITG in the above example with the line DFT JFIT MEMORY JFITG e The example above involves explicit specification of the fitting basis set A simpler mode of specification is also supported enabling the user to request either the DGauss Al or A2 basis sets the Demon fitting basis 29 or the fitted basis sets tabulated by Ahlrichs and co workers 30 These are requested through keyword specification on the JBAS data line thus DFT JBAS A1 DGAUSS DFT JBAS A2 DGAUSS DFT JBAS DEMON DFT JBAS AHLRICHS The following data set is thus equivalent to those presented above TITLE H2CO 6 31G BLYP DFT WITH A1 DGAUSS COULOMB FITTING ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 121 8 H 1 CH 2 121 8 3 180 0 VARIABLES cO 1 203 CH 1 099 END BASIS 6 31G RUNTYPE OPTIMISE SCFTYPE DIRECT RHF DFT BLYP DFT JFIT MEMORY JFITG DFT SCHWARZ 6 DFT JBAS A1 DGAUSS ENTER 12 M LLER PL
63. 1 099 2 121 8 3 180 0 END SCFTYPE MP3 ENTER 12 M LLER PLESSET MP2 AND MP3 CALCULATIONS 44 12 3 Freezing and Discarding Orbitals In the examples above we have assumed that all SCF MOs are active in the subsequent M ller Plesset calculation In many instances however this will not be the case for the user may wish to e freeze inner shell orbitals performing a valence only Mgller Plesset calculation e discard certain virtual orbitals from the M ller Plesset calculation typically the high energy inner shell complement orbitals The ACTIVE directive is provided for controlling the final subset of orbitals for inclusion in the M ller Plesset calculation The freezing of core or inner shell orbitals and the discarding of virtual orbitals is achieved by nominating under control of the ACTIVE directive the sequence nos of the active set of SCF orbitals to appear in the calculation Consider the MP2 RHF H2CO calculation above The following data sequence would be required to freeze both the Ols and Cis orbitals with SCF sequence numbers 1 and 2 respectively and to discard the highest virtual orbital with SCF sequence number 22 TITLE H2CO 3 21G BASIS MP2 RHF VALENCE ONLY ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MP2 ACTIVE 3 TO 21 END ENTER 12 4 Direct MP2 Calculations We wish to perform a direct MP2 calculation equivalent to that above A valid
64. 1 203 6 GVB CALCULATION ON THE FORMALDEHYDE MOLECULE 20 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END ENTER GVB 1 PP Data RESTART TITLE H2CO GVB 1 PP 3 21G BASIS 1B1 gt 2B1 BYPASS SUPER FORCE NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE GVB 1 SWAP 78 END ENTER Note that the GVB module uses the same Dumpfile sections for storage of the locked eigenvec tors section 4 and energy ordered vectors section 5 as the open shell RHF module 6 1 Direct GVB Calculation on the formaldehyde molecule The following data sequences would perform in direct fashion the initial closed shell and sub sequent GVB 1 PP calculation shown above Note the form of the SCFTYPE directive in the GVB run and the appearance of the DIRECT keyword The integer specified after the GVB keyword again indicates the number of GVB pairs in the present case just 1 Closed shell SCF TITLE H2CO 3 21G BASIS DIRECT CLOSED SHELL SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT ENTER GVB 1 PP Data RESTART TITLE 7 ECP CALCULATION ON THE FORMALDEHYDE MOLECULE 21 H2CO DIRECT GVB 1 PP 3 21G BASIS 1B1 gt 2B1 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT GVB 1 SWAP 78 END ENTER 7 ECP Calculation on the formaldehyde molecule We outline b
65. 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ENTER The only obvious point to note is the use of the SUPER directive in requesting full integral list generation required in the subsequent transformation Run II The Transformation and CCSD T Job RESTART TITLE H2C0 TZVP VALENCE CCSD T CCSD T ENERGY 114 2714886289 SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ACTIVE 3 TO 50 END CORE 1 TO 2 END RUNTYPE CI CCSD T 48 6 6 CCTH 10 CCIT 30 ENTER The following points should be noted e The SCF computation is BYPASS ed e The SCF vectors from the first run will be restored from Section 1 of the Dumpfile the default section associated with the closed shell SCF MOs The calculation may be further subdivided by splitting Run above into separate integral trans formation and CCSD runs using the RUNTYPE TRANSFORM specification with subsequent 27 CI GEOMETRY OPTIMISATION 169 BYPASS ing of the transformation in the CC job Thus Run Ila The Transformation Job RESTART TITLE H2CO TZVP INTEGRAL TRANSFORMATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP RUNTYPE TRANSFORM ACTIVE 3 TO 50 END CORE 1 TO 2 END ENTER Run IIb The CCSD T Job RESTART TITLE H2CO TZVP VALENCE CCSD T CCSD T ENERGY
66. 15 6 0 0 16 7 0 0 18 8 0 0 20 9 0 0 b 2 7 10 2 0 9 11 0 0 13 12 0 0 19 13 0 0 b 3 5 14 2 0 8 15 2 0 11 16 0 0 14 17 0 0 17 18 0 0 The data for performing the Table Cl calculation is shown below TITLE H2CO 3 21G DEFAULT BASIS MRDCI 1M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT TRAN CORE DISCARD 2000 12 1010 12 6 SELECT SYMMETRY 1 SPIN 1 CNTRL 12 SINGLES 1 CONF 0123 10 14 15 ROOTS 1 THRESH 30 10 24 TABLE CI CALCULATIONS 139 CI DIAG EXTRAP 2 ENTER The following points should be noted e the number of active electrons in the Cl specified on the CNTRL data line is now 12 e the integers specified on the CONF data line now label the six doubly occupied orbitals in the revised numbering scheme outlined above 24 5 Conventional Table CI Multi reference CI Calculations Specification of additional reference functions in the Table Cl input data is accomplished through the CONF directive with each reference function characterised by an additional data line of integers defining e the number and sequence numbers of any open shell orbitals and e the sequence numbers of the doubly occupied orbitals Consider initially a 4 reference Cl calculation for H2CO comprising the SCF configuration that arising from the double excitation 1b to 2b that from the double excitation 2b to 3bg and that from th
67. 2 121 8 3 180 0 END RUNTYPE ANALYSE LOCAL 3 TO 8 END VECTORS 1 ENTER 20 Note that the localised orbital module is the only analysis module that creates a new set of eigenvectors and the user must specify the destination section on the Dumpfile for these orbitals i e no default section will be employed In this case the final set of LMOs will be output to Section 20 of the Dumpfile 13 4 Distributed Multipole Analysis The following data sequence would be required in requesting a distributed multipole analysis of the SCF MOs 32 where the DMA directive instigates the process RESTART TITLE H2C0 3 21G DEFAULT BASIS DMA ANALYSIS ZMATRIX ANGSTROM N 1 1 203 1 1 099 2 121 8 1 1 099 2 121 8 3 180 0 mzmoa END RUNTYPE ANALYSE DMA VECTORS 1 ENTER 13 5 Graphical Analysis The following data sequence would be required in generating grids of total density atom difference density electrostatic potential and orbital amplitude for subsequent graphical analysis 13 ANALYSING THE WAVEFUNCTION 53 The GRAPHICS directive introduces data defining the required graphics processing with GDEF data defining the grid of points involved and subsequent CALC and PLOT directives introducing data specifying the required computation associated with the grid CALC and corresponding graphical output to be generated PLOT RESTART TITLE H2CO 3 21G DEFAULT BASIS GRAPHICAL ANALYSIS ZMATRIX ANGSTROM N c 0 1 1 203
68. 3 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ACTIVE 5 TO 22 END CORE 1 TO 4 END RUNTYPE CI FULLCI 18 4 4 ENTER The following points should be noted 25 FULL CI CALCULATIONS 162 e both ACTIVE and CORE are control directives of the integral transformation module As such they should be presented in the data stream prior to the specification of the full Cl data i e before the FULLCI data line e The FULLCI data line carries three integers defining in order NACT the number of active orbitals in the Cl 18 in this case NALPHA the number of a electrons 4 in this example the four highest doubly occupied SCF MOs NBETA the number of electrons again 4 in the closed shell molecule example Note that the values of NACT NALPHA and NBETA reflect the impact of CORE and ACTIVE had we been considering an all electron calculation the integer values would have been 22 8 and 8 respectively e The set of molecular orbitals to be used in the transformation and subsequent Cl are restored from the section associated with the ENTER directive either the default sec tion here section 1 that for the closed shell SCF module or that explicitly nominated nominated In this example such usage is clear but the user need consider this usage in cases e g open shell calculations where multiple section specification may arise In such cases of multiple specification the final ENTER section nominated will be used as the eig
69. 3 17 SS 5a1 gt 6a1 double 3 5 6 18 1 2 3 4 13 17 5a1 gt 6a1 single 1 18 1 2 3 4 5 14 17 E 1b1 gt 2b1 double 3 13 14 18 1 2 3 4 5 17 1b1 gt 2b1 single 1 18 1 2 3 4 5 13 19 ae 1b2 gt 3b2 double 3 17 18 19 1 2 3 4 5 13 1b2 gt 3b2 single The sequence of data lines defining the Semi direct Table Cl calculation is again terminated by the ENTER directive Note at this stage that the full data specification corresponding to the defaults generated from the above data file is as follows TITLE H2CO 2B2 3 21G EXPLICIT DATA FOR DEFAULTS 113 06446075 MULT 2 CHARGE 1 SUPER OFF NOSYM ZMAT ANGSTROM N Cc 0 1 1 203 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 24 TABLE CI CALCULATIONS 154 END RUNTYPE CI OPEN 1 1 ACTIVE 1 TO 22 END MRDCI DIRECT TABLE SELECT CNTRL 15 SPIN 2 SYMM 3 SINGLES ALL CONF 1 18 18 5 6 18 18 13 14 18 18 17 18 19 oa 13 17 13 17 13 17 14 17 17 13 19 13 wewewe PRPrRPrP RP RP RB NONNNNNNN Wwwwww w PPP PPS ama a D END THRESH 10 10 ROOTS 1 CI NATORB CIVEC 1 ENTER 24 11 Semi direct Table CI Freezing and Discarding Orbitals In the examples above we have assumed that all MOs typically generated at SCF time are active in the subsequent Cl calculation In many instances however this will not be the case for the user may wish to e freeze inner shell orbitals performing a valence only CI calculation e discard certain virtual orbitals
70. 3 21G BASIS 3A STATE HESSIAN MULT 3 ZMATRIX ANGSTROM Cc 0 1 C0 X 11 0 2 90 0 H 1 CH 2 HCO 3 DI1 H 1 CH 2 HCO 3 DI2 VARIABLES 17 FORCE CONSTANT CALCULATIONS cO 1 203 CH 1 099 HCO 121 8 DI1 15 0 DI2 164 0 END RUNTYPE HESSIAN SCFTYPE GVB OPEN 2 2 LEVEL 3 1 0 ENTER Example 6 MP2 Force Constants Run I Geometry Optimisation TITLE H2CO 3 21G DEFAULT BASIS MP2 RHF OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE MP2 XTOL 0 0001 ENTER Run II MP2 Vibrational Frequencies RESTART TITLE H2CO 3 21G DEFAULT BASIS MP2 RHF FREQUENCIES ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE HESSIAN SCFTYPE MP2 ENTER 96 Performing an analogous MP2 computation to the SCF calculation of Example 1 follows straight forwardly by introduction of the SCFTYPE MP2 data line 18 POLARISABILITY CALCULATIONS 97 18 Polarisability Calculations Analytic calculations of molecular polarisabilities may be conducted at both the SCF and MP2 levels In the former case the coupled Hartree Fock calculations of polarisabilities may be extended to include both frequency dependence and magnetisabilities it is thus possible to evaluate static and frequency dependent polarisabilities for closed shell SCF wavefunctions and from the
71. 3 specification on the VARIABLE definition lines The eigenvectors from the STO 3G calculation are taken to initiate the extended calcu lation through the data line VECTORS GETQ ED3 1 1 where the first integer specified defines the starting block of the Dumpfile from the minimal basis calculation the second integer the section wherein lies the minimal basis eigenvectors the closed shell SCF default vectors section Example 2 The H2CO to H CO transition structure STO 3G Calculation TITLE H2CO lt gt H2 CO 1A TS STO3G ZMAT ANGS 16 TRANSITION STATE OPTIMISATION co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES CO 1 134 TYPE 3 ANG1 43 7 TYPE 3 ANG2 57 8 TYPE 3 CHH 1 292 TYPE 3 XH 0 664 TYPE 3 END BASIS STO3G RUNTYPE SADDLE ENTER mo Mh oe a aO Be PUNE 3 21G Calculation DUMPFILE ED3 350 TITLE H2 CO lt gt H2C0 1A TS 3 21G BASIS ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES CO 1 134 TYPE 3 ANG1 43 7 TYPE 3 ANG2 57 8 TYPE 3 CHH 1 292 TYPE 3 XH 0 664 TYPE 3 END RUNTYPE SADDLE ED3 1 VECTORS GETQ ED3 1 1 ENTER m oho oe AO BP PUNE 74 Note that alternative methods for locating transition states are available within the program namely 1 a modified variant of the synchronous transit algorithm due to Bell a
72. 3098 18 C Lee W Yang and R G Parr Physical Reviews B37 1988 785 789 19 M E Mura and P J Knowles J Chem Phys 104 1996 9848 9858 doi 10 1063 1 471749 20 C W Murray N C Handy and G J Laming Mol Phys 78 1993 997 doi10 1080 00268979300100651 21 R E Stratmann G E Scuseria and M J Frisch Chem Phys Lett 257 1996 213 223 doi 10 1016 0009 2614 96 00600 8 22 A D Becke J Chem Phys 98 1993 5648 doi 10 1063 1 464913 REFERENCES 198 23 S J Vosko L Wilk and M Nusair Can J Phys 58 1980 1200 doi 10 1139 p80 159 24 J P Perdew Physical Review B33 1986 8822 8824 25 A D Becke J Chem Phys 107 1997 8554 doi 10 1063 1 475007 26 F A Hamprecht A J Cohen D J Tozer and N C Handy J Chem Phys 109 1998 6264 6271 doi 10 1063 1 477267 27 P J Wilson T J Bradley and D J Tozer J Chem Phys 115 2001 9233 9242 doi 10 1063 1 1412605 28 B I Dunlap J W D Connolly and J R Sabin On some approximations in applications of Xa theory J Chem Phys 71 1979 3396 3402 doi 10 1063 1 438728 29 N Godbout D R Salahub J Andzelm and E Wimmer Can J Chem 70 1992 560 doi 10 1139 v92 079 30 K Eichkorn O Treutler H Ohm M Haser and R Ahlrichs Chem Phys Lett 240 1995 283 doi 10 1016 0009 2614 95 00621 A K Eichkorn F Weigend O Treutler and R Ahlrichs Theor Chim Acta 97 1997 119 doi 10 1007 s002140050244
73. 4 6026 doi 10 1063 1 447604 9 W J Stevens P G Jasien M Krauss and H Basch Can J Chem 70 1992 612 doi 10 1139 v92 085 10 T R Cundari and W J Stevens J Chem Phys 98 1993 5555 doi 10 1063 1 464902 11 H T H Dunning Jr and P J Hay Methods of Electronic Structure Theory Vol 3 H F Schaefer II Ed Plenum Press 1977 Li Ne Na Ar L F Pacios and P A Christiansen J Chem Phys 82 1985 2664 doi 10 1063 1 448263 K Ca Sc Zn Ga Kr M M Hurley et al J Chem Phys 84 1986 6840 doi 10 1063 1 450689 Rb Sr Y Cd In L A LaJohn et al J Chem Phys 87 1987 2812 doi 10 1063 1 453069 Xe M M Hurley et al J Chem Phys 84 1986 6840 doi 10 1063 1 450689 Cs La Hf Hg TI Rn R B Ross W C Ermler P A Christiansen et al J Chem Phys 93 1990 REFERENCES 197 6654 doi 10 1063 1 458934 erratum doi 10 1063 1 468517 Ba Ce Lu R B Ross W C Ermler S Das To be published Fr Ra Ac Pu W C Ermler R B Ross P A Christiansen Int J Quant Chem 40 1991 829 12 Sc Co Cu Zn M M Hurley et al J Chem Phys 84 1986 6840 doi 10 1063 1 450689 Ni Y Cd L A LaJohn et al J Chem Phys 87 1987 2812 doi 10 1063 1 453069 La Hf Hg Tl Tn R B Ross W C Ermler P A Christiansen et al J Chem Phys 93 1990 6654 doi 10 1063 1 458934 erratum doi 10 1063 1 468517 13 Li Be Na P Fuentealba H Preuss H Stoll
74. 6 90 0 2 0 0 VARIABLES co 1 2034714 CHH 1 3040587 XH ANGI 41 4929919 ANG2 56 6341870 END RUNTYPE FORCE SCFTYPE CASSCF CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END ENTER MCSCEF Force Constants Example 1 Force Constants for HCO 0 7415226 87 Initially we show the MCSCF geometry optimisation data followed by the force constant run MCSCF geometry optimisation RESTART TITLE H2CO MCSCF GEOM OPT 10E IN 9 M O TOTAL ENERGY ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE XTOL 0 0005 SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC3 DOC1 DOC2 DOC3 VOC2 VOC1 UVOC3 U0C1 END ENTER 113 359135534 Note again use of the XTOL directive to converge the geometry optimisation more stringently than the default 17 FORCE CONSTANT CALCULATIONS 88 MCSCE force constants RESTART TITLE H2CO 3 21G MCSCF FORCE CONSTANTS 10E IN 9 M O FREQ 1187 2 1290 9 1544 9 1709 4 2822 0 2866 0 ZMATRIX ANGSTROM 0 O 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE FORCE SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC3 DOC1 DOC2 DOC3 VOC2 VOC1 UVOC3 U0C1 END ENTER Example 2 The H2CO to H CO transition structure We now assume that the Dumpfile used when performing the transition state optimisation is no longer available and that the user will
75. 8 where the four orbitals 5 5a 6 6a 1 13 1b and 14 2b precede the doubly occupied orbitals in the list 24 2 Conventional Table CI Calculations There is a formal limit of 200 000 selected configurations derived from an initial list of con figurations generated by single plus double excitations from a user specified list of reference functions The selection and extrapolation procedure may be applied on up to twenty roots of a given secular problem 24 TABLE CI CALCULATIONS 128 Table 7 Irreducible Representations and Associated Indexing used in the Table CI Module Point Group IRrep Sequence No Cs al a C2 a b Ci ag au Coy al by b2 a2 CONDO A UNEJ AUNE A UOUN eEeJIN KIN FIN e 24 TABLE CI CALCULATIONS 129 1 The Conventional Table Cl module comprises a set of 9 sub modules which must be user driven either implicitly or explicitly see below through data input These sub modules are as follows ADAPT generation of a symmetry adapted list of integrals derived by a pseudo transformation from the list of raw integrals TRAN integral transformation using the list of adapted integrals generated above together with a molecular orbital coefficient array nominated by the user Note that in contrast to the Direct Cl module transformation is an integral part of the Conventional Table Cl module required by both the SELECT and Cl sub modules see
76. 9 2 HCO 3 180 0 VARIABLES CO 1 203 HCO 121 8 END and ZMATRIX 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 PHI CONSTANTS PHI 180 0 CH 1 099 VARIABLES CO 1 203 HCO 121 8 END are equivalent in constraining the optimisation such that only r C O and HCO are varied 3 Finally we consider three complete data files for carrying out the H2CO optimisation First we show 2 possible jobs for an SCF optimisation the first representing the startup job the second a possible restart job to complete the computation assuming the first had dumped on time Optimisation Startup Data TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE ENTER 15 GEOMETRY OPTIMISATION 61 Optimisation Restart data RESTART OPTIMIZE TITLE H2CO 3 21G RESTART OPTIMISATION ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE ENTER DFT Geometry Optimisation The following data file is for performing the corresponding DFT optimisation using the B3LYP functional in direct SCF mode TITLE H2CO 3 21G BASIS DFT B3LYP OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE DIRECT DFT B3LYP ENTER 15 2 Determining th
77. ALCULATION ON THE FORMALDEHYDE MOLECULE 22 e in the absence of the VECTORS directive the ATOMS option is requested by default 7 2 Note that at present only the ATOMS and HCORE options are available in ECP calcu lations as the basis specific options such as EXTGUESS and MINGUESS have not been modified to account for the valence only nature of the computation Local Pseudopotential Calculation In contrast to Version 6 2 of the code where only two libraries of ECPs CEP and the Hay Wadt ECP now code named LANL were included seven semi local ECP sets are now available code named as follows 1 CEP or SBKJC available in Version 6 2 of the code the the Compact Effective Potentials CEPs are due to i Stevens et al 8 for the elements Li Ar ii Stevens at al 9 for the elements K Rn and iii Cundari et al 10 for the Lanthanides LANL available in version 6 2 of the code the LANL ECPs are due to Hay and Wadt 6 and cover the elements Na Bi LANL2 The Hay and Wadt ECPs with the inner valence forms used for transition metals etc These are as provided in the Gaussian and NWChem suite of programs CRENBL The small core potential due to Christiansen et al 11 These ECPs are sometimes referred to as shape consistent because they maintain the shape of the atomic orbitals in the valence region CRENBS The averaged relativistic large core ECPs due to Ermler and co workers 12 STRLC
78. ALCULATIONS I THE MCLR METHOD 185 TZVP C TZVP H So 1 0 0 02 PO 1 0 0 02 END SCFTYPE DIRECT ENTER The second restart job requiring only the Dumpfiles from Run may be driven as follows Run II The direct RPA Job RESTART TITLE H2CO TZVP R SP BASIS DIRECT RPA CALCULATION BYPASS SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP 0 TZVP C TZVP H So 1 0 0 02 PO 1 0 0 02 END SCFTYPE DIRECT RUNTYPE RESPONSE RPA DIRECT TDA SYMM 1 1 TO 5 SYMM 2 1 TO 5 SYMM 3 1 TO 5 SYMM 4 1 TO 5 ANALYSE ENTER 31 Linear Response Calculations II The MCLR Method The second module for performing calculations of electronic transition energies and correspond ing oscillator strengths is the Multiconfigurational Linear Response MCLR procedure 48 MCLR calculations are also performed under control of the RUNTYPE RESPONSE specifica tion with subsequent keyword specification specifying the method thus RUNTYPE RESPONSE MCLR 31 LINEAR RESPONSE CALCULATIONS I THE MCLR METHOD 186 Data input characterising the details of the calculation is presented immediately after the RUNTYPE data line Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS A necessary condition for performing an MCLR calculation is the successful completion of a corresponding multiconfigurational SCF calculation with the MCSCF module from which
79. BLES 20 MAGNETISABILITY CALCULATIONS 101 cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE XTOL 0 0001 ENTER Run II Hyperpolarisability calculation RESTART TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF HYPERPOLARIZABILITY ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE HYPER ENTER 20 Magnetisability Calculations Analytic calculations of molecular magnetisabilities may be conducted for closed shell SCF wavefunctions only The following points should be noted 1 Magnetisability calculations are performed under control of the RUNTYPE MAGNET directive 2 RUNTYPE MAGNET is in fact a combination of tasks requesting integral generation SCF integral transformation and solution of the coupled Hartree Fock equations While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation Example Magnetisability of HCO Run I Geometry Optimisation TITLE H2CO 3 21G DEFAULT BASIS GEOMETRY OPTIMISATION ZMATRIX ANGSTROM Cc 21 INFRA RED INTENSITY CALCULATIONS 102 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE
80. CONTENTS i Computing for Science CFS Ltd CCLRC Daresbury Laboratory Generalised Atomic and Molecular Electronic Structure System GAMESS UK USER S GUIDE and REFERENCE MANUAL Version 8 0 June 2008 PART 2 PROGRAM USAGE and SAMPLE DATA M F Guest J Kendrick J H van Lenthe and P Sherwood Copyright c 1993 2008 Computing for Science Ltd This document may be freely reproduced provided that it is reproduced unaltered and in its entirety Contents 1 Introduction 1 1 1 Treatment of Molecular Symmetry 2 2 200000 ee 2 1 2 The Role of the Dumpfile a aaa 000020202004 3 2 Closed Shell SCF Calculation 4 2 1 Spherical Harmonic Basis Sets ooo 3 Closed Shell Direct SCF Calculation 9 4 RHF Open Shell Calculation 9 4 1 Direct RHF Open Shell Calculation 2 a a a 0 0 00000202 2 nee 13 CONTENTS 5 UHF Calculation on the formaldehyde cation 5 1 Direct UHF Calculation on the formaldehyde cation 6 GVB Calculation on the formaldehyde molecule 6 1 Direct GVB Calculation on the formaldehyde molecule 7 ECP Calculation on the formaldehyde molecule 7 1 Non Local Pseudopotential Calculation o o oa a a 7 2 Local Pseudopotential Calculation ooo a a a a 8 In core SCF Calculations 9 CASSCF Calculations 10 MCSCF Calculation 11 DFT Calculations 11 1 The DFT Directive and Default Settings ooo a a a 11 2 DFT Basis Sets no coe ek a we A Ere deb wl angre bis e a ak 11 3
81. Configuration data SELECT CI FTN036 CI Vectors CI NATORB PROP TM Note again that specification of additional reference functions in the Table Cl input data is again accomplished through the CONF directive in contrast to CONF specification in the conventional module however the data lines specifying the configurations are now terminated by a single data line containing the character string END in the first data field Each reference function is characterised by an additional data line of integers defining e the number and sequence numbers of any open shell orbitals and e the sequence numbers of the doubly occupied orbitals Consider initially a 4 reference Cl calculation for H2CO comprising the SCF configuration that arising from the double excitation 1b to 2b that from the double excitation 2b to 3bg and that from the excitation 1b 2b to 2b23b2 This leads to the following occupation patterns for the 4 reference functions Reference la 2a 3a 4a 1b 5a 1by 2b 2b 3b 2 Function 1 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 0 2 2 0 3 2 2 2 2 2 2 2 0 0 2 4 2 2 2 2 2 2 1 1 1 1 Then each data line of the CONF directive will reflect the occupation patterns above CONF 012345 13 17 18 oa Ref 1 012345 14 17 18 sf Ref 2 012345 13 17 19 and Ref 3 413141819 1234517 ae Ref 4 END one the directive terminator The full data input for the job would be as follows 24 TABLE CI CALCULATIONS 147 TITLE H2CO
82. ER m ob bd et OO Be PON B MP2 Transition State Location RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 6 31G BASIS MP2 TOTAL ENERGY 113 877936986 ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES cO 1 134 ANG1 43 7 ANG2 57 8 CHH 1 292 XH 0 664 END BASIS 6 31G RUNTYPE SADDLE FCM SCFTYPE MP2 XTOL 0 0005 ENTER Mm ob bh a a O Be PON RB 17 Force Constant Calculations 82 GAMESS UK may now perform a force constant calculation together with associated vibra tional frequencies either e analytically driven by the RUNTYPE HESSIAN directive for SCF and MP2 wavefunc tions or 17 FORCE CONSTANT CALCULATIONS 83 e numerically through RUNTYPE FORCE specification Analytic second derivatives are of course considerably faster and more accurate than numerical differentiation and it is strongly recommended that the analytic option be employed when applicable vide infra As a rough guide the time required for evaluation of SCF second derivatives is approximately three times that required for gradient evaluation depending upon the number of atoms and the symmetry of the molecule The MP2 second derivatives take some 4 5 times longer than the MP2 gradient and 2 3 times longer than the SCF force constants The following points should be noted 1 In both numerical and analytic force constant calculations the program p
83. ESSET MP2 AND MP3 CALCULATIONS 40 12 Me ller Plesset MP2 and MP3 Calculations In this section the traditional Mgller Plesset calculations are discussed These calculations are based on a single closed shell Hartree Fock reference determinant Also available are multi reference MP2 and MP3 calculations Because the latter option is part of the Direct Cl module these calculations are described in section 23 M ller Plesset calculations are performed under control of SCFTYPE specification with the level of treatment either MP2 or MP3 nominated by keyword A second keyword may also be required requesting the level of underlying SCF either RHF closed shells or UHF open shell systems Before detailing example data files for performing such calculations we mention some general points 1 M ller Plesset processing involves a combination of tasks including integral generation SCF integral transformation and finally the Mgller Plesset calculation itself 2 Several files will be generated under such processing These include e the Mainfile ED2 and Dumpfile ED3 e the semi transformed ED4 and transformed ED6 integral files e the Scratch file ED7 e temporary files for sorting transformed integrals the Sortfile and intermediate ma trices in the Mgller Plesset calculation The number of such files is a function of the underlying SCF RHF closed shells or UHF open shell systems and the level of Maller Plesset theory r
84. ETRY 1 4 A singlet Cl wavefunction i e SPIN 1 5 The number of active electrons in the Cl will be set to be those involved in the SCF calculation i e CNTRL 16 6 Singly excited configurations with respect to each of the default reference configurations SINGLES ALL will be included regardless of their computed energy lowerings 7 The set of reference configurations to be employed will include the SCF configuration plus those generated from this configuration by including i for each symmetry IRREP 24 TABLE CI CALCULATIONS 151 the doubly excited configuration arising from excitation of the highest occupied DOMO of that symmetry to the lowest virtual orbital VMO of the same symmetry and ii the lowest singly excited configuration again arising from the highest occupied DOMO to the lowest VMO of the same symmetry In the present example this will correspond to the SCF configuration the double and single excitation arising from the DOMO 5a to VMO 6a the double and single excitation arising from the DOMO 1b to VMO 2b and the double and single excitation arising from the DOMO 2b2 to VMO 3be No reference configurations will be included involving orbitals of ag symmetry given the absence of such orbitals involved in the occupied manifold This results in a total reference set of 7 functions as shown thus in the job output numbers of open shells and corresponding main configurations 0 1 2 3 4 5 13 17 18 4 SCF configurat
85. F computation in 84 been available then the data line VECTORS 5 would have provided the canonicalised RHF orbitals as a starting point for the UHF iterative process 6 GVB Calculation on the formaldehyde molecule Before considering the detailed data input we should draw attention to certain aspects of 6 GVB CALCULATION ON THE FORMALDEHYDE MOLECULE 18 Table 5 Orbital Numbering in H2CO MO Sequence Symmetry MO Sequence Symmetry Number Number 1 la 9 2b 2 2a 10 6a 3 3a 11 3b2 4 4a 12 Tay 5 1b 6 day 7 1b 8 2be e the ordering expected of the trial input molecular orbitals and e the treatment of molecular symmetry within the GAMESS UK program The following points should be noted 1 In the general case of a GVB 5 calculation on an open shell system comprising m doubly occupied orbitals n open shell orbitals and 2p GVB orbitals that is p GVB pairs the program expects the trial vectors to be organised thus orbitals 1 gt m doubly occupied m i gt mtn open shell orbitals m n 1 gt mtnt 2 the first GVB pair with the strongly occupied MO preceding the weakly occupied MO m n 2p 1 gt m n 2p the component orbitals of the p th GVB pair It is the users responsibly to ensure through use of the SWAP directive that the input orbitals are so arranged In the present case an examination of the closed shell SCF MOs reveals the ordering shown in Table 5 Thus to perform a GVB 1 PP 5
86. GSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE XTOL 0 0001 SCFTYPE MP2 THRESH 7 ENTER 16 Transition State Optimisation 71 In the present section we consider the format of the data required when performing transition state optimisations using the modified trust region procedure 35 available in GAMESS UK We provide appropriate data for locating both e the saddle point for the isomerisation process H2CO to hydroxycarbene t HCOH A and 16 TRANSITION STATE OPTIMISATION 72 e the HCO X A to H CO molecular dissociation transition state The following points should be noted 1 transition state optimisation is requested by specifying the SADDLE option of the RUNTYPE directive Restarting such calculations after a controlled dump again involves the SADDLE specification on the RESTART directive 2 Optimisation is again conducted in a system of internal coordinates specified through the VARIABLES and VARIABLE definition lines of the Z matrix The user must define both the geometry of the initial structure and the method s to be used in generating the initial Hessian matrix While we confine the discussion to numerical evaluation of this initial Hessian at present the user should consult 16 2 for guidance in performing this task by the more efficient analytic route In both examples below we follow the established technique of e locating th
87. H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE ANALYSE GRAPHICS GDEF TYPE 2D POINTS 99 TITLE SQUARE 2D GRID 99 99 CALC TYPE ATOM TITLE H2CO ATOM DIFFERENCE SECTION 150 PLOT TYPE LINE TITLE ATOM DIFFERENCE DENSITY LINEPRINTER PLOT CALC TYPE DENS SECTION 151 TITLE H2CO TOTAL DENSITY PLOT TYPE LINE TITLE DENSITY LINEPRINTER PLOT CALC TYPE MO 2 TITLE H2CO MO 2 AMPLITUDE SECTION 152 PLOT TYPE LINE TITLE MO 2 LINEPRINTER PLOT GDEF TYPE 2D POINTS 25 TITLE SQUARE 2D GRID 25 25 CALC TYPE POTE 13 ANALYSING THE WAVEFUNCTION 54 TITLE H2CO POTENTIAL SECTION 153 PLOT TYPE LINE TITLE POTENTIAL LINEPRINTER PLOT VECTORS 1 ENTER The resolution of each plot is controlled by the size of the grid via the POINTS sub directive of GDEF Note that the TYPE sub directive of CALC defines the type of grid ATOM DENS MO and POTE for atom difference total density orbital amplitude and electrostatic potential respectively In the present example output is restricted to the line printer through the LINE parameter in the PLOT data 13 6 Population Analysis The following data sequence would be required in performing an extended population analysis of the valence SCF MOs where the MULLIKEN directive specifies those orbitals for which printed output is required The ATOM and ORBITAL keyword request the emphasis in the analysis generated through the grouping of b
88. H2CO CASSCF 3 21G BASIS 10E IN 9 M 0 SUPER OFF NOSYM NOPRINT BYPASS ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MCSCF THRESH 4 MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC3 DOC1 DOC2 DOC3 VOC2 VOC1 UVOC3 U0C1 END PRINT ORBITALS VIRTUALS NATORB CANONICAL 10 FOCK DENSITY FOCK ENTER Data input characterising the MCSCF calculation is introduced by the MCSCF directive and comprises the PRINT ORBITAL and CANONICAL directives This data defines 10 MCSCF CALCULATION 29 1 the active orbital space for the calculation This involves classifying the input MOs as either primary or secondary in character with the primary orbitals classified by type 2 an initial reference configuration typically the Hartree Fock configuration to be used in generating the complete Cl expansion This involves the explicit assignment of occupation numbers and symmetries through orbital TAGs to the primary orbitals Both definitions are controlled by the ORBITAL directive each orbital in the primary space MOs 1 12 are classified by type where the following types are introduced e COR core orbital an orbital which will remain doubly occupied in all configurations Note the contrast to the CASSCF module the FZC tag may now be used to specify an orbital that remains strictly frozen at its input expansion e DOC orbitals in the active space which are formally doubly occupied and whi
89. III The Direct CI Calculation RESTART NEW TITLE H2CO 3 21G FP GEOMETRY OPTIMISATION FROZEN CORE DISCARDED VMOS MULT 2 CHARGE 1 ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO 27 CI GEOMETRY OPTIMISATION 172 H 1 CH 2 HCO 3 180 0 VARIABLES co 1 2408256 HESS 691212 CH 1 0818145 HESS 751037 HCO 118 2135930 HESS 674146 END RUNTYPE OPTIMIZE CI ACTIVE 3 TO 20 END CORE 1 2 END DIRECT 11 6 12 CONF 222221 ENTER In this example we illustrate the freezing and discarding of MOs under control of the ACTIVE and CORE directives Note that some care must be taken when reducing the orbital space in FP Cl optimisations In open shell calculations the Cl step will derive the orbital set at each point from the second section specified on the ENTER directive i e the energy ordered MOs If this ordering varies from point to point in the FP optimisation and symmetry is used in minimising the configuration space it is quite likely that this space will vary during successive points with disastrous consequences on the optimisation pathway As a general rule the user should only consider freezing or discarding orbitals that are well separated from those MOs included in the Cl space i e inner shell or inner shell complement MOs 27 2 Table CI Geometry Optimisation The examples below are provided to demonstrate the data requirements when performing FP optimisations with the both the conventional and direct Table Cl modules In
90. ITLE H2CO MCSCF GEOM OPT 10E IN 9 M O TOTAL ENERGY 113 359134855 ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC3 DOC1 DOC2 DOC3 VOC2 VOC1 UVOC3 U0C1 END XTOL 0 0005 ENTER The following points should be noted 68 e Note the XTOL directive this is used to converge the geometry optimisation more strin gently a typical tactic when subjecting the optimised geometry to a subsequent frequency analysis e It is NOT possible to use FZC orbitals frozen core orbitals those that will remain doubly occupied in all configurations when performing MCSCF geometry optimisations Presenting such a designator in the ORBITAL data e g FZC1 FZC1 FZC1 DOC1 DOC3 DOC1 DOC2 DOC3 UOC2 UOC1 UOC3 UOC1 will lead to the following error diagnostic 3K ak ak ak ak ak 3k ak ak k ak 3k k ak 3k ak ak 3K ak ak 3K aK ak 3K aK 3K 3K ak O ak 3K 3K CII K IOI I 2K K K 2K x x x cannot use FZC mos with MCSCF gradients k use the COR descriptor for these orbitals FEO 3k ak ak k ak 3k ak a 3k ak ak 3K ak ak 3K aK ak 3K aK 3K 3K ak 3K 3K ak 3K 3K ak 3K 3K ICI I 3K IOI I I 3K K K 2K 15 GEOMETRY OPTIMISATION 69 e Note that the MCSCF module is approximately twice as fast as the CASSCF module for this calculation e Assume that the above optimisation had converged and at some point after the user wis
91. J Hehre W A Lathan R Ditchfield M D Newton and J A Pople GAUSSIAN 70 Prog No 236 QCPE Indiana University 1973 J S Binkley R A Whiteside R Krishnan R Seeger D J DeFrees H B Schlegel S Topiol L R Kahn and J A Pople GAUSSIAN80 QCPE 13 1980 406 3 See for example Carnegie Mellon Quantum Chemistry Archive 2nd edn R A Whiteside M J Frisch J S Binkley D J DeFrees H B Schlegel K Raghavachari and J A Pople 1981 which contains approximately 3500 SCF structures 4 J S Binkley J A Pople and W J Hehre J Am Chem Soc 102 1980 939 doi 10 1021 ja00523a008 M S Gordon J S Binkley J A Pople W J Pietro and W J Hehre J Am Chem Soc 104 1982 2797 doi 10 1021 ja00374a017 M J Frisch J A Pople and J S Binkley J Chem Phys 80 1984 3265 doi 10 1063 1 447079 and ref erences cited therein K D Dobbs and W J Hehre J Comp Chem 7 1986 359 378 doi 10 1002 jcc 540070313 ibid 8 1987 861 879 doi 10 1002 jcc 540080614 880 893 doi 10 1002 jcc 540080615 5 F W Bobrowicz and W A Goddard in Modern Theoretical Chemistry Vol 3 ed H F Schaefer Plenum New York 1977 79 6 P J Hay and W R Wadt J Chem Phys 82 1985 270 doi 10 1063 1 448799 284 doi 10 1063 1 448800 299 doi 10 1063 1 448975 7 Ph Durand and J C Berthelat Theoret Chim Acta 38 1975 283 doi 10 1007 BF00963468 8 W J Stevens H Basch and M Krauss J Chem Phys 81 198
92. LE data line Run I Generating the Trial Hessian TITLE 17 FORCE CONSTANT CALCULATIONS 93 HCOH lt gt H2CO 1A TS 6 31G ZMAT ANGS 0 0 1 CO H 1 CH1 2 OCH1 H 1 CH5 2 H5C0 3 180 0 VARIABLES OCH1 56 3 co 1 27 CH1 1 22 CH5 1 10 H5CO 115 8 END BASIS 6 31G RUNTYPE HESSIAN ENTER Run IT Restoring the Trial Hessian in Saddle Point Location RESTART NEW TITLE HCOH lt gt H2CO 1A TS 6 31G ZMAT ANGS Cc 0 1 C0 H 1 CH1 2 OCH1 H 1 CH5 2 H5C0 3 180 0 VARIABLES OCH1 56 3 co 1 27 CH1 1 22 CH5 1 10 H5CO 115 8 END BASIS 6 31G RUNTYPE SADDLE FCM ENTER Example 4 The H2CO to H CO transition structure Again we generate the initial hessian at the starting geometry to be employed in the saddle point location in Run and restore this hessian through FCM specification on the SADDLE directive in Run Il Run I Generating a Trial Hessian TITLE H2CO lt gt H2 CO 1A TS 6 31G ZMAT ANGS 0 C 1 Co X 2 1 0 1 90 0 X 2 CHH 3 ANG1 1 180 0 17 FORCE CONSTANT CALCULATIONS 94 X 41 0 2 90 0 3 0 0 X 41 0 5 ANG2 3 0 0 H 4 XH 6 90 0 2 180 0 H 4 XH 6 90 0 2 0 0 VARIABLES cO 1 134 ANG1 43 7 ANG2 57 8 CHH 1 292 XH 0 664 END BASIS 6 31G RUNTYPE HESSIAN ENTER Run II Restoring the Trial Hessian in TS Location RESTART NEW TITLE H2CO lt gt H2 CO 1A TS 6 31G ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90
93. N Set of Electronic Structure Programs 1991 42 T J Lee and J E Rice Chem Phys Lett 150 1988 406 doi 10 1016 0009 2614 88 80427 5 43 G E Scuseria A C Scheiner T J Lee J E Rice and H F Schaefer J Chem Phys 86 1987 2881 doi 10 1063 1 452039 44 T J Lee A P Rendell and P R Taylor J Phys Chem 94 1990 5463 doi 10 1021 j100377a008 45 A P Rendell T J Lee and A Komornicki Chem Phys Lett 178 1991 462 doi 10 1016 0009 2614 91 87003 T 46 L S Cederbaum and W Domcke Adv Chem Phys 36 1977 205 47 J Schirmer and L S Cederbaum J Phys B11 1978 1889 doi 10 1088 0022 3700 11 11 006 48 C Fuchs V Bonati Koutecky and J Kouteck J Chem Phys 98 1993 3121 doi 10 1063 1 464086 49 H J J van Dam J H van Lenthe and P Pulay Mol Phys 93 1998 431 doi 10 1080 002689798169122 50 H J Werner Mol Phys 89 1996 645 doi 10 1080 002689796173967 51 K Andersson P A Malmqvist and B O Roos J Chem Phys 96 1992 1218 doi 10 1063 1 462209 52 K Wolinski H L Sellers and P Pulay Chem Phys Lett 140 1987 225 doi 10 1016 0009 2614 87 80448 7 53 S Faas J G Snijders J H van Lenthe E van Lenthe and E J Baerends Chem Phys Lett 246 1995 632 doi 10 1016 0009 2614 95 01156 0
94. NAL RPA CALCULATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END BASIS TZVP 0 TZVP C TZVP H Ss 0 1 0 0 02 PO 1 0 0 02 END RUNTYPE RESPONSE RPA TDA SYMM 1 1 SYMM 2 1 SYMM 3 1T SYMM 4 1 TO ANALYSE ENTER TO 5 TO 5 05 5 The following points should be noted e The SCF computation is BYPASS ed e The SCF vectors from the first run will be restored from Section 1 of the Dumpfile the default section associated with the closed shell SCF MOs 30 1 Direct RPA calculations For large atomic orbital basis sets the integral transformation step in conventional calculations can become prohibitive In this case it is possible to resort to a direct implementation of the RPA procedure which breaks up the four index transformation into two two index transformation whenever the RPA matrix acts on a trial vector The direct RPA module is requested by the RUNTYPE directive RUNTYPE RESPONSE RPA DIRECT In this case the only preparatory run is a closed shell SCF calculation which may be direct or conventional when the integrals may be generated in either supermatrix or 2E format Only the Dumpfile of the SCF calculation must be kept All directives that are available for conventional RPA calculations can also be used for the direct RPA case with two exceptions see Part 7 Since direct RPA calculations on larger systems are rather time consuming it is desirable
95. NGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 8 14 CONF 22222222 ENTER 23 2 Direct CI Default CISD Calculations In order to simplify the process of configuration specification and data preparation the Direct Cl module now provides a set of default options that require little or no data input While these defaults are not expected to cover most in depth requirements they do provide a starting point for users and a route to subsequent more extensive calculations To illustrate this default working of the module we consider below a number of example calculations based on those described in the preceding sections 23 DIRECT CI CALCULATIONS 113 23 2 1 Closed shell Systems A Direct Cl calculation is to performed on the formaldehyde molecule Given the following data sequence TITLE H2CO 3 21G DEFAULT DIRECT CI CISD OPTION ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI ENTER then the calculation undertaken will be based on the following 1 The format of the 2e integral file will be automatically set to the required SUPER OFF NOSYM triggered by the presence of the Cl runtype Integral transformation will use the set of orbitals from section 1 the default section for output of the closed shell SCF eigenvectors All orbitals will be deemed ACTIVE in the transformation The Direct Cl module is the default m
96. NTYPE SADDLE XTOL 0 0005 SCFTYPE MP2 ENTER m om gt oe aA OO BP PONE The following points should be noted 1 the starting variables for the initial geometry in the MP2 calculation have been taken from the output of the previous HF optimisation 2 the initial vectors in the MP2 calculation will be the final set of HF 6 31G SCF orbitals restored from section 1 of the Dumpfile 3 While the subject of a later section we note here that the initial hessian for MP2 optimi sations may be computed analytically under RUNTYPE HESSIAN control and this will typically be far more efficient than using numerical evaluation through TYPE 3 specifica tion on the VARIABLES data lines The above example is still using numerical evaluation we provide the data for analytic computation below Note again that using the HF 16 TRANSITION STATE OPTIMISATION 81 hessian through RUNTYPE SADDLE ED3 specification may not provide the optimal choice for post HF calculations With systems of fewer than 10 atoms it is often more efficient as above to utilise the TYPE 3 feature or RUNTYPE HESSIAN to compute the initial hessian assuming the initial geometry is close to the final structure Using the HF 6 31G hessian would be accomplished with the following data where we are using the HF 6 31G TS geometry RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 6 31G MP2 TOTAL ENERGY 113 8779369833 ZMAT ANGS 0 C 1 c0 X 2 1 0
97. OFF NOSYM CHARGE 1 MULT 2 ZMATRIX ANGSTROM N Cc 0 1 1 203 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI OPEN 1 1 DIRECT 15 8 14 SPIN DOUBLET CONF 22222221 NATORB 11 12 PRINT ENTER 23 3 Direct CI Freezing and Discarding Orbitals In the examples above we have assumed that all MOs typically generated at SCF time are active in the subsequent Cl calculation In many instances however this will not be the case for the user may wish to e freeze inner shell orbitals performing a valence only CI calculation e discard certain virtual orbitals from the Cl calculation typically the high energy inner shell complement orbitals The CORE and ACTIVE directives are provided for controlling the final subset of orbitals for inclusion in the Cl The freezing of core or inner shell orbitals is achieved by nominating the sequence nos of those orbitals to be frozen under control of the CORE directive The discarding of orbitals is performed under control of the ACTIVE directive which specifies the sequence nos of the active set of orbitals to appear in the Cl Consider the H2CO calculation above The following data sequence would be required to freeze both the Ols and Cis orbitals with SCF sequence numbers 1 and 2 respectively and to discard the corresponding inner shell complement virtual orbitals with SCF sequence numbers 21 and 22 TITLE H2CO 3 21G CISD VALENCE ONLY DIRECT CI 23 DIRECT CI
98. ONS H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI ACTIVE 1 TO 22 END MRDCI DIRECT TABLE SELECT CNTRL 16 SPIN 1 SYMM 1 SINGLES ALL CONF 0 13 17 18 13 17 18 eorr NONN 14 17 18 13 14 1 2 18 19 13 17 19 NONONO nwe we ww NANAN ASA wawanwan END THRESH 10 10 ROOTS 1 CI NATORB CIVEC 1 ENTER 152 Let us now consider a Semi direct Table Cl calculation on the B2 state of H2COt again using default options available within the module A valid data sequence for performing such a calculation is shown below where we are still performing all the computation in a single job TITLE H2CO 2B2 3 21G DEFAULT MRDCI SETTINGS 113 06446075 MULT 2 CHARGE 1 ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT ENTER Considering the changes to the closed shell run the following points should be noted e The set of vectors used in the Table Cl transformation will be the energy ordered SCF orbitals from section 5 of the Dumpfile the default section in the absence of section specification on the ENTER directive 24 TABLE CI CALCULATIONS 153 The symmetry and spin of the Cl wavefunction will be deduced from the preceding SCF calculation i e a Cl wavefunction of Bz symmetry corresponding to SYMMETRY 3 and a doublet Cl wavefunction corresponding to SPIN 2 The number of active electrons in the Cl will be set to be those involved in the SCF ca
99. RBITAL COR1 COR1 COR1 DOC1 DOC3 DOC1 DOC2 DOC3 UOC2 UOC1 VOCs UOC1 END follows straightforwardly from the above output Note that a list of irreducible representations IRreps and their associated indices for each of the abelian point groups are given in Table 7 The following points should be noted e An examination of the input SCF MOs reveals that the 12 orbitals to be included in the primary space correspond to the first 12 SCF MOs If this not the case the ordering specified by the ORBITAL directive will be imposed by the program so in contrast to the CASSCF module the user need not resort to the SWAP directive Note however that the FZC orbitals must precede the orbitals permitted variable occupancy in the active list e The integer specified on the CANONICAL directive defines the section number on the Dumpfile for output of the MCSCF natural orbitals Note that the two data lines PRINT ORBITALS VIRTUALS NATORB CANONICAL 10 FOCK DENSITY FOCK now define the defaults Version 6 3 onwards and may be omitted when the MCSCF natural orbitals will be written to section 10 of the Dumpfile Such orbitals may be subsequently retrieved in for example Direct Cl calculations e Two sections on the Dumpfile that may be specified via the ENTER directive are again written during an MCSCF calculation the first containing the non canonicalised orbitals that are used during the MCSCF process and the second a variety of restart information gen
100. RGE 1 ZMAT ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI ENTER As with the closed shell run above no explicit data is required to define the nature of the Cl calculation In practice the defaults adopted correspond to the following 1 The Cl will be based on the high spin open shell RHF calculation 2 The set of vectors used in the transformation will be the energy ordered SCF orbitals from section 5 of the Dumpfile the default section in the absence of section specification on the ENTER directive 3 The symmetry and spin of the Cl wavefunction will be deduced from the preceding SCF calculation i e a doublet Cl wavefunction of Bz symmetry corresponding to SPIN 2 4 The number of active electrons in the Cl will be set to be those involved in the SCF calculation i e 15 5 The reference configuration to be employed will be just the open shell SCF configuration The internal space comprises the doubly plus singly occupied SCF orbitals with the external space comprising the SCF virtual orbitals All electrons will be deemed active in the Cl 23 DIRECT CI CALCULATIONS 115 6 The spinfree natural orbitals will be written to section 11 and the spin natural orbitals to section 12 of the Dumpfile The full data specification corresponding to the defaults generated from the above data file is as shown before namely TITLE H2CO 2B2 3 21G CISD DIRECT CI CALCULATION SUPER
101. RYHIGH The VERYHIGH accuracy grid is meant only for benchmark calcu lations It is designed to be significantly more accurate than the high accuracy grid The directive may be omitted when ACCU will be set to the default MEDIUM quadrature setting Example TITLE H2CO 6 31G CLOSED SHELL DFT B3LYP HIGH QUADRATURE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS 6 31G DFT B3LYP DFT QUADRATURE HIGH ENTER Directives permitting a more detailed specification of the quadrature grids are described in part 4 of the manual 11 6 Coulomb fitting The efficiency of DFT calculations on medium sized molecules can be enhanced by avoiding the evaluation of 4 center 2 electron integrals This requires the user i to request a functional 11 DFT CALCULATIONS 36 without Hartree Fock exchange and ii to fit the total electron density to an auxiliary basis set The Coulomb energy contributions can then be evaluated using the fitted density requiring at worst 3 center 2 electron integrals The basic theory behind this has been published by Dunlap et al 28 The technology implemented allows Coulomb fitting to be used in both energy and gradient evaluations using the JFIT and JFITG directives respectively Furthermore the number of 3 center 2 electron integrals that will be evaluated can be reduced using the Schwarz inequality to discard small integrals Below is an example of a formaldehyde calcul
102. SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SS Multi reference MP2 model 1 vef gt F lt ref sin gt F lt sin doub gt F lt doub Nref 3 Spin 1 E reference 113 2222609769 E correlation 0 1660233176 total 113 3882842945 lt psi1 psi1 gt 0 63871E 01 residue 0 46973E 07 singles vacuum 0 240888E 03 0 240306E 01 n 1 0 250548E 03 0 567533E 01 n 2 0 000000E 00 0 847480E 01 SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SS SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SS where E reference gives the energy of the multi configuration reference wavefunction 118 E correlation is the amount of correlation energy obtained from the MP2 calculation jpsil psil is the norm of the first order correction to the wavefunction as obtained by the MP2 calculation This number may be used as a diagnostic to judge whether the perturbation approach is valid 23 DIRECT CI CALCULATIONS 119 The multi reference MP3 job corresponding to the MP2 example above is as follows TITLE H2CO 3 21G CISD 3 REFERENCE MP3 SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 10 10 MP 3 CONF 222222 222222 222220 ENTER NON 2 2 2 ONO NOOO Because the MP3 energy can be obtained from the first order
103. TER Run III Calculation of Infra red Intensities RESTART TITLE H2CO 3 21G BASIS 3A STATE INFRARED MULT 3 ZMATRIX ANGSTROM Cc 0 1 C0 X 11 0 2 90 0 H 1 CH 2 HCO 3 DI1 H 1 CH 2 HCO 3 DI2 VARIABLES cO 1 203 CH 1 099 HCO 121 8 DI1 15 0 DI2 164 0 END RUNTYPE INFRARED SCFTYPE GVB OPEN 2 2 LEVEL 3 1 0 ENTER Example 3 MP2 Infra red Intensities Run I Geometry Optimisation TITLE H2CO 3 21G DEFAULT BASIS MP2 RHF OPTIMISATION ZMATRIX ANGSTROM Cc 22 CALCULATION OF RAMAN INTENSITIES 106 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE MP2 XTOL 0 0001 ENTER Run II MP2 Intensities RESTART TITLE H2CO 3 21G DEFAULT BASIS MP2 RHF INFRARED ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE INFRARED SCFTYPE MP2 ENTER 22 Calculation of Raman Intensities The calculation of Raman Intensities is only available for closed shell SCF wavefunctions and is performed under control of the RUNTYPE RAMAN specification This involves the calculation of a force constant matrix together with the analytic evaluation of polarizability derivatives 1 RUNTYPE RAMAN is in fact a combination of tasks requiring integral generation SCF gradient evaluation with additional evaluation of derivative Fock operators integral transformation soluti
104. TYPE MP2 XTOL 0 0001 ENTER 19 HYPERPOLARISABILITY CALCULATIONS 100 Run II Polarisability Calculation RESTART TITLE H2CO DZ BASIS MP2 RHF POLARISABILITY ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END BASIS DZ RUNTYPE POLARISABILITY SCFTYPE MP2 ENTER 19 Hyperpolarisability Calculations Analytic calculations of molecular hyperpolarisabilities may be conducted for both closed shell SCF and open shell RHF wavefunctions These are third derivatives of the energy and require preceding calculations of the first derivative wavefunctions The following points should be noted 1 Hyperpolarisability calculations are performed under control of the RUNTYPE HYPER directive 2 RUNTYPE HYPER is in fact a combination of tasks requesting integral generation SCF integral transformation and solution of the coupled Hartree Fock equations While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation Example Hyperpolarisability of HCO Run I Geometry Optimisation TITLE H2CO 3 21G DEFAULT BASIS GEOMETRY OPTIMISATION ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIA
105. X directive Consider the data from the SCF computations on formaldehyde ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END The following data depicts the corresponding ZMATRIX required when optimising the geometry ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END where r C H r C O and angle HCO have been declared as variables with symbolic names CH CO and HCO respectively Both of the above data sequences are equivalent in the context of a single point SCF calculation The following points should be noted 1 In the sequence above the dihedral angle of 180 0 has been used to define the required planar geometry while use of a single variable for both CH bonds and HCO angles leads to a system of Ca geometry The optimisation will be conducted subject to these con straints with the symmetry of the starting geometry maintained throughout optimisation 15 GEOMETRY OPTIMISATION 60 Any attempt to change molecular point group during optimisation will lead to an error condition 2 As with the dihedral angle above any parameter in the z matrix which is not declared a variable will remain fixed during optimisation This may be controlled either by specifying the parameter by value in the definition lines of the z matrix or through CONSTANTS data lines Thus the data sequences ZMATRIX ANGSTROM Cc 0 1 C0 H 1 1 099 2 HCO H 1 1 09
106. Y 0 00000000 1 10092542 1 43475395 1 0 H 0 00000000 1 10092542 1 43475395 1 0H 0 00000000 0 00000000 0 00000000 8 0 0 END MOROKUMA FRAG 1 FRAG1 BASIS SV 4 31G ENTER TITLE MOROKUMA TEST ADAPT OFF NOSYM GEOMETRY 3 24201636 2 02583666 0 00000000 1 0 H 4 24693920 4 71362490 0 00000000 1 0H 4 77568401 2 98417857 0 00000000 8 0 0 END MOROKUMA FRAG 2 FRAG2 BASIS SV 4 31G ENTER TITLE MOROKUMA TEST ADAPT OFF NOSYM GEOMETRY 0 00000000 1 10092542 1 43475395 1 0H 0 00000000 1 10092542 1 43475395 1 0H 0 00000000 0 00000000 0 00000000 8 0 0 3 24201636 2 02583666 0 00000000 1 0 H 4 24693920 4 71362490 0 00000000 1 0 H 4 77568401 2 98417857 0 00000000 8 0 0 END BASIS SV 4 31G MOROK INTERACT FRAG1 FRAG2 VECTORS ATOMS ENTER 14 Restarting Integral and SCF Computations In all the examples considered so far we have assumed that the particular activity requested in general some SCF computation completes in the time allocated to the job This is often not the case and we need to consider restarting the computation in a controlled fashion Such a 14 RESTARTING INTEGRAL AND SCF COMPUTATIONS 57 requirement is most often met in SCF computations when either e integral evaluation has not been completed or e SCF convergence has not been achieved either due to lack of time or to convergence problems when the maximum number of iterative cycles has been exceeded Restarting the computation is achieved under control of
107. YM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI PROPERTY ATOMS DIRECT 16 8 14 CONF 22222222 ENTER To further illustrate property evaluation for Cl wavefunctions let us consider a Cl calculation on the 3A state of H2CO First the data for the open shell SCF calculation TITLE H2CO DZ BASIS 3A2 GRHF TOTAL ENERGY 113 73954029 AU MULT 3 SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 23 DIRECT CI CALCULATIONS 123 END BASIS DZ ENTER Having generated the SCF wavefunction the following data sequence would be used for a single reference Cl calculation with the spinfree and spin natural orbitals routed to sections 11 and 12 of the Dumpfile by default subsequent property generation may be requested by presenting the data line PROPERTY ATOMS RESTART NEW TITLE H2CO DZ BASIS 3A2 CISD DIRECT CI 113 934177537 AU MULT 3 SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM N C 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS DZ RUNTYPE CI PROPERTY ATOMS DIRECT 16 9 15 SPIN 3 CONF 2222222141 ENTER Note that properties could also have been calculated after the Cl job by specifying the appropri ate natural orbitals under RUNTYPE ANALYSE The data below would compute the isotropic ESR coupling constants property index 19 at carbon oxygen and hydrogen where the spin NOS are no
108. YPE directive in the optimisa tion job The FCM input is identical to that in the FCMIN directive see part4 Determining the Trial Hessian TITLE H2CO 3 21G DETERMINING THE INITIAL HESSIAN ZMATRIX ANGSTROM Cc 0 1 C0 15 GEOMETRY OPTIMISATION 63 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE HESSIAN ENTER Optimisation data Restoring the Initial Hessian RESTART NEW TITLE H2CO 3 21G RESTORING THE INITIAL HESSIAN ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE FCM ENTER Note that if this restoring of the Hessian is carried out in initialising the optimisation an identical RUNTYPE specification must be presented in any subsequent restart of the optimisation failure to adhere to this will lead to a PARAMETER ERROR diagnostic and job failure Experience suggests that the most efficient way to proceed when performing geometry optimi sation on small medium sized molecules with extended basis sets larger than minimal or 3 21G is to e perform the geometry optimisation in a smaller basis set e input the resulting Hessian to the extended basis set calculation by reading the matrix directly from the Dumpfile associated with the small calculation Such input is controlled through the RUNTYPE directive which takes the form RUNTYPE OPTIMIZE ED4 1 Here is it assumed that th
109. a CASSCF only module hereafter referred to as CASSCF 9 CASSCF CALCULATIONS 25 e a more general MCSCF module capable also of performing CASSCF calculations 15 The first module is invoked through the SCFTYPE CASSCF option the second through the SCFTYPE MCSCF option In choosing between the two alternative codes the user should note that the MCSCF module is significantly more flexible and efficient than the original CASSCF module capable of handling far larger MCSCF expansions Geometry optimisations and nu merical force constant calculations are possible with both options This section will deal with driving the CASSCF option with the following section dealing with MCSCF execution We wish to perform a CASSCF 16 calculation on the X Aj state of formaldehyde using a full valence criterion in specifying the active space Thus in addition to the doubly occupied SCF MOs 1ay 5a 1by and 1b9 2b the formally vacant SCF virtual orbitals the 6a and 7a 2b and 3b MOs are to be permitted variable occupancy in the MCSCF treatment Restricting the 1a Ols 2a Cls and 3a 02s MOs to be doubly occupied throughout yields a CASCI secular space of 1408 configurations for this so called 10 electron in 9 orbital CASSCF calculation We again assume that the calculation is to proceed in two stages with initial generation of the closed shell SCF orbitals followed by the CASSCF computation As mentioned above generation of a valid Mainf
110. a combination of tasks requesting integral generation SCF integral transformation and finally the Green s function calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 3 Several files will be generated under RUNTYPE GF processing These include the follow ing e the Mainfile ED2 and Dumpfile ED3 e the semi transformed ED4 and transformed ED6 integral files 28 GREEN S FUNCTION CALCULATIONS I THE OVGF METHOD 175 e the Scratch file ED7 e temporary files for sorting both transformed integrals the Sortfile Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 4 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM in the SCF run 5 In OVGF calculations the user must specify those valence shell molecular orbitals to be included in the valence ionisation computation These orbitals are defined by use of the l P directive Any core orbitals should be removed from computation using the CORE directive of the integral transformation module An OVGF calculat
111. ach set to the value 2 corresponding to the doubly occupied orbitals of the SCF reference function e The NATORB directive requests generation of the natural orbitals NOs of the Cl wave function with the spinfree NOs to be output to section 11 of the Dumpfile The second integer on this line refers to routing of the spin natural orbitals set to O here given a 23 DIRECT CI CALCULATIONS 110 closed shell system while the PRINT keyword requests printing of the NOs Note that both spinfree and spin natural orbitals are now generated in default Version 6 3 onwards so that the NATORB directive may now be omitted The spinfree natural orbitals will then be written to section 11 and the spin natural orbitals open shell systems to section 12 of the Dumpfile e The set of molecular orbitals to be used in the transformation and subsequent Cl are restored from the section nominated on the ENTER directive In this example such usage is clear but the user need consider this usage in cases e g open shell calculations where multiple section specification may arise In such cases of multiple specification the final ENTER section nominated will be used as the eigenvector source Let us now consider a direct Cl calculation on the B2 state of HxCO again using the SCF configuration as the sole reference function A valid data sequence for performing such a calculation is shown below where we are still performing all the computation in a single job
112. aldehyde cation TITLE H2CO 2B2 3 21G DEFAULT BASIS UHF CALCULATION CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE UHF ENTER The following points should be noted 1 The SCFTYPE directive is now required in requesting the UHF option Note that the OPEN directive used in RHF calculations should not be introduced when requesting a UHF calculation if present it will be ignored 2 Two sets of eigenvectors are generated in an open shell unrestricted Hartree Fock UHF calculation the a spin SCF MOs and spin orbitals In default the a spin MOs will be written to section 2 of the Dumpfile and the 8 spin MOs to section 3 see Table 1 3 Explicit specification of these sections thus requires two integers on the ENTER directive Presenting the data line 5 UHF CALCULATION ON THE FORMALDEHYDE CATION 16 ENTER 2 3 will result in the same eigenvector section storage as the default 4 In the absence of the SUPER directive the default Mainfile format for a UHF calculation J K will apply While the above data structure appears the most straightforward way of accomplishing the com putation it relies on the initial trial eigenvector guess generated through the default ATOMS option providing the required open shell electronic configuration Such a situation is unlikely to hold in all cases as with open shell restricted Hartree Fock calculations a more reliab
113. arametrised by Wilson et al 27 25 HCTH The keyword HCTH selects the Hamprecht Cohen Tozer and Handy exchange correlation energy functional 26 11 5 Specification of Integration Grids While a large number of options are available in specifying possible integration grids see Part 4 the inexperienced user is strongly advised to use just the QUADRATURE directive for this purpose 11 DFT CALCULATIONS 35 11 5 1 The QUADRATURE Directive This directive may be used to select a quadrature grid that is designed to achieve a specified accuracy The resulting grids are constructed from the logarithmic radial grid 19 and Gauss Legendre angular grid using the SSF weighting scheme with screening 21 and MHL angular grid pruning 20 The directive consists of two data fields read to the variables TEXT ACCU using format 2A e TEXT should be set to the character string QUADRATURE e ACCU is a keyword used to define the required grid accuracy Valid keywords include LOW The LOW accuracy grid should only be used for preliminary studies it is designed to obtain the total number of electrons from the density integration with a relative error of 1 0e 4 per atom MEDIUM The MEDIUM accuracy grid is designed to obtain a relative error of less than 1 0e 6 in the number of electrons per atom HIGH The HIGH accuracy grid is designed to obtain a relative error of less than 1 0e 8 in the number of electrons per atom VE
114. asis functions 34 The sequence of integers specified on the MULLIKEN line specifies those MOs for which printed output is required RESTART TITLE H2CO 3 21G BASIS ANALYSIS OF VALENCE MOs ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE ANALYSE MULLIKEN ATOM ORBITAL 3 TO 8 END VECTORS 1 ENTER Note that it is also possible to define the groups of basis functions through user input Thus the following data would perform the same analysis as the ATOM specification above where the GROUP keyword on the MULLIK data line indicates that subsequent data lines will follow terminated by the END keyword that will assign the basis functions to user defined groups RESTART TITLE H2C0 3 21G BASIS INPUT GROUPS FOR ANALYSIS ZMATRIX ANGSTROM 0 0 1 1 203 13 ANALYSING THE WAVEFUNCTION 55 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE ANALYSE MULLIKEN GROUP 3 TO 8 END CATOM 1 TO 9 OATOM 10 TO 18 HiATOM 19 20 H2ATOM 21 22 END VECTORS 1 ENTER 13 7 Morokuma Energy Decomposition Analysis The following example illustrates how the Morokuma EDA is performed using a sequence of three separate GAMESS UK input decks one for each of the two fragments and an analysis job for the supermolecule The Class 2 MOROKUMA directive controls the job and may take one of two forms depending on whether a fragment SCF or an interaction calculations required The directive sequ
115. at the optimum geometry derived from an MP2 calculation First the data for the MP2 geometry optimisation where the spinfree natural orbitals at the optimised geometry are to be routed to section 20 TITLE H2CO X1iA1 MP2 DZ BASIS ZMATRIX ANGSTROM 0 0 1 c0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END BASIS DZ RUNTYPE OPTIMISE SCFTYPE MP2 NATORB 20 PRINT ENTER Having routed the spinfree natural orbitals to section 20 on the Dumpfile the properties calcu lation proceeds by nominating this section on the VECTORS line thus 13 ANALYSING THE WAVEFUNCTION 49 RESTART TITLE H2CO X1A1 MP2 DZ BASIS 1 E PROPERTIES ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END BASIS DZ RUNTYPE ANALYSE SCFTYPE MP2 PROPERTY 4c 40 END VECTORS 20 ENTER Note the use of RESTART in restoring the optimized geometry from the Dumpfile 13 2 Simplified Property Specification In the examples above we have assumed that property evaluation is to be conducted under con trol of RUNTYPE ANALYSE with explicit specification of the required one electron properties A simplified mechanism for property evaluation can be requested through presenting the data line PROPERTY ATOMS after RUNTYPE and SCFTYPE specification This will result in the default wavefunction anal ysis conducted after RUNTYPE processing being augmented with
116. ation using Coulomb fitting with explicit specification of the auxiliary basis the DGauss A1 set 29 TITLE H2CO 6 31G BLYP CLOSED SHELL DFT WITH COULOMB FITTING ZMATRIX ANGSTROM C 0 1 CO H 1 CH 2 121 8 H 1 CH 2 121 8 3 180 0 VARIABLES cO 1 203 CH 1 099 END BASIS 6 31G RUNTYPE OPTIMISE SCFTYPE DIRECT RHF DFT BLYP DFT JFIT JFITG DFT SCHWARZ 6 DFT JBAS DGauss A1 Coulomb fitting basis gamess basis set format SH 1 000000 45 000000000 SH 1 000000 7 500000000 SH 1 000000 1 500000000 SH 1 000000 0 300000000 sc 1 000000 1114 000000000 sc 1 000000 223 000000000 sc 1 000000 55 720000000 sc 1 000000 13 900000000 SP C 1 000000 4 400000000 1 00000000 SP C 1 000000 0 870000000 1 00000000 SP C 1 000000 0 220000000 1 00000000 11 DFT CALCULATIONS 37 DC 1 000000 4 400000000 DC 1 000000 0 870000000 DC 1 000000 0 220000000 So 1 000000 2000 000000000 So 1 000000 400 000000000 So 1 000000 100 000000000 So 1 000000 25 000000000 SP 0 1 000000 7 800000000 1 00000000 SP 0 1 000000 1 560000000 1 00000000 SP 0 1 000000 0 390000000 1 00000000 DO 1 000000 7 800000000 DO 1 000000 1 560000000 DO 1 000000 0 390000000 END ENTER The following points should be noted e Specification of the Auxiliary Fitting basis under control of the JBAS directive is based upon the same format as used in explicit specification under the BASIS directive As
117. automatic treatment of symmetry may breakdown leading to unreliable results in the subsequent Cl see Part 8 6 In default all molecular orbitals will be deemed active in the Cl calculation 23 1 Direct CI Single reference CISD Calculations A direct Cl calculation is to performed on the formaldehyde molecule using the SCF configu ration as the sole reference function A valid data sequence for performing such a calculation is shown below TITLE H2CO 3 21G CISD DIRECT CI CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 8 14 CONF 22222222 NATORB 11 O PRINT ENTER The following points should be noted e The DIRECT data line carries three integers defining in order NELEC the number of active electrons in the Cl 16 in this case NINT the number of orbitals in the internal space 8 in this example the doubly occupied SCF MOs NEXT the number of orbitals in the external space 14 in this example the total number of MOs the number of basis functions 22 as no orbitals have been frozen or discarded minus the number of internal orbitals 8 e Each reference function in the Cl is defined as a sequence of NINT integers specifying the orbital occupancy of each internal orbital in the function In the present case this corresponds to a single data line specified under the CONF directive containing 8 data fields e
118. ay now be applied on up to thirty roots of a given secular problem Semi direct Table Cl calculations are performed under control of the RUNTYPE CI specification with data input characterising the nature of the Cl introduced by a data line with the keyword MRDCI in the first data field and the keyword DIRECT in the second field Termination of this data is again accomplished by presenting a valid Class 2 directive such as VECTORS or ENTER Note that while the Conventional and Semi direct modules are based on the same Table Cl 24 TABLE CI CALCULATIONS 144 algorithm there are significant differences in both file utilisation and data requirements The most significant of these are highlighted below 1 In contrast to the conventional module the integral transformation is now performed under control of the conventional 4 index module of GAMESS rather than the ADAPT and TRAN Table Cl modules 2 The memory requirements of the semi direct module may be significantly greater than those associated with the conventional algorithm While the default memory allocations will prove adequate for small medium cases the user should use the MEMORY pre directive to request at least 8 MWords in calculations with say more than 20 active electrons 3 The Semi direct Table Cl module comprises a reduced set of 6 sub modules which may be user driven either implicitly or explicitly see below through data input These sub modules are as follows
119. below this data base will usually be available on a given machine but may be generated by the user SELECT performs configuration generation and subsequent selection based on a user specified set of reference configurations and appropriate thresholds Cl generates the Cl hamiltonian based on the set of selected configurations from SELECT and integrals from TRAN DIAG calculates one or more Cl eigenfunctions of the hamiltonian generated under Cl The remaining modules are optional and may be used to analyse one or more of the Cl eigenvectors NATORB generate the spin free natural orbitals for one or more of the calculated Cl eigenvectors PROP compute various 1 electron properties of the Cl wavefunctions Note that the natural orbitals generated above may be routed to the Dumpfile and examined by the other analysis modules of GAMESS UK in a subsequent job TM compute the transition moments between nominated Cl eigenvectors Note at this point that there may be additional data input associated with each of the sub modules e g for defining the reference configurations and selection attributes in SELECT 2 In the interests of efficiency the Table Cl module requires as input a data base of pattern symbolic matrix elements for use in both the selection process and in construction of the final Cl Hamiltonian over the selected configurations These pattern elements are assumed to reside on a data set with LFN TABLE The da
120. bove e Both Cl and NATORB may be omitted the default values being required 24 13 Semi direct Table CI Restarting Calculations In the examples considered above we have assumed that the Table Cl job completes in the time allocated This may not be the case and we need consider restarting the computation in a controlled fashion Such a requirement may be met in RUNTYPE CI processing when e the associated integral evaluation SCF or integral transformation has not completed due either to lack of time or to convergence problems in the SCF e Table Cl processing itself has not completed In the present implementation it is not possible to restart Table Cl processing within a given sub module in the event of job termination due to lack of time It is possible however to fragment the calculation into separate sub module runs through the use of the BYPASS directive on the sub module data lines In such usage restarting the computation is achieved under control of the RESTART directive which nominates the Cl task for restarting Consider the Table Cl job of 16 5 we show below the data files for fragmenting this Cl into e integral transformation e configuration selection e hamiltonian pre processing and Davidson diagonalisation The subset of interfaces to be saved between the various steps is given in Table 7 Integral Transformation RESTART CI TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM
121. bs will require a subset of interfaces to be saved see Table 8 in addition to the Dumpfile ED3 and Mainfile ED2 Extensive use is also made of scratch FORTRAN data sets with LFNs FTNOO1 002 003 004 008 009 and FTNO10 4 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM in the SCF run 24 TABLE CI CALCULATIONS 131 Table 8 FORTRAN Interfaces Used by the Conventional Table CI Module File Contents Generated by Required by Sub Module Sub Module FTNO022 Symmetry Adapted Integrals ADAPT TRAN FTNO31 Transformed Integrals TRAN SELECT CI FTNO033 Partial Matrix Elements SELECT CI FTN034 Partial Matrix Elements SELECT CI FTNO35 CI Hamiltonian CI DIAG FTN036 CI Vectors DIAG NATORB PROP TM 24 3 Conventional Table CI Single reference CISD Calculations A Conventional Table Cl calculation is to performed on the formaldehyde molecule using the SCF configuration as the sole reference function A valid data sequence for performing such a calculation is shown below TITLE H2CO 3 21G DEFAULT BASIS MRDCI 1M 1R ZMAT ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT TRAN TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES 1 CONF 012345 13 17 18 ROOTS 1 THRESH 30 10 CI DIAG EXTRAP 2 ENTER The following points should be noted 1 Th
122. calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS keyword on the data lines initiating each of the sub modules We illustrate this point in the sections below 24 TABLE CI CALCULATIONS 125 24 1 Table CI and Molecular Symmetry A crucial requirement in running the Table Cl modules is an understanding of the treatment of symmetry Unlike the SCF and direct Cl modules the molecular orbitals are automatically reordered at the outset of the Cl into groups belonging to the same irreducible representation with the ordering within each group dictated by the ordering encountered at orbital generation time i e at SCF time Note that each representation has an associated index number e g in a system of Co symmetry the four representations a1 bj b2 and ag have associated index numbers of 1 2 3 and 4 respectively Groups of orbitals of common representation are ordered by virtue of increasing representation sequence number so that in a Ca system all molecular orbitals of a symmetry would occur first in the list with the occupied orbitals preceding the virtual orbitals in the subset followed by the orbitals of bj symmetry again with the DOMOS preceding the VMOS followed by orbitals of b symmetry DOMOS before VMOS and finally orbitals of ag symmetry Any subsequent reference to the orbitals for example when specifying the reference functions must be
123. ch will be permitted variable occupancy in the MCSCF treatment e UOC orbitals in the active space which are formally unoccupied corresponding to SCF virtual MOs but which will be permitted variable occupancy in the MCSCF Other valid orbital TAGs used in characterising open shell configurations include ALP and BET see 4 3 2 The integer tag appended to each three character identifier specifies the symmetry of the active orbital and corresponds to the irreducible representation IRrep of the MO information generated through the symmetry adaption process Considering the output from the closed shell SCF calculation on H2CO in particular the symmetry adapted basis set information provided prior to generating the trial set of vectors IRREP NO OF SYMMETRY ADAPTED BASIS FUNCTIONS 1 12 4 3 6 1 1 20 48361193 2 0000000 2 1 11 28387037 2 0000000 3 1 1 42107323 2 0000000 4 1 0 86257503 2 0000000 5 3 0 69835324 2 0000000 6 1 0 63657557 2 0000000 7 2 0 52867413 2 0000000 8 3 0 43116746 2 0000000 10 MCSCF CALCULATION 30 9 2 0 14867301 0 0000000 10 1 0 27270470 0 0000000 11 3 0 36811563 0 0000000 12 1 0 45408083 0 0000000 13 2 0 93005840 0 0000000 14 3 1 01802548 0 0000000 15 1 1 04135899 0 0000000 16 1 1 15883011 0 0000000 17 3 1 26989260 0 0000000 18 1 1 56946779 0 0000000 19 2 1 86711355 0 0000000 20 1 1 90074847 0 0000000 21 3 1 98283110 0 0000000 22 1 3 32677642 0 0000000 The following ORBITAL specification O
124. cing with the character string CCSD In this case a singles doubles calculation is performed 42 43 Inclusion of the triples component to the correlation energy 44 45 is requested by presenting the character string CCSD T see below The additional three integers define in order NACT the number of active orbitals in the calculation 48 in this case 26 COUPLED CLUSTER CALCULATIONS 167 NALPHA the number of a electrons 6 in this example the four highest doubly occupied SCF MOs NBETA the number of electrons again 6 in the closed shell molecule example Note that the values of NACT NALPHA and NBETA reflect the impact of CORE and ACTIVE had we been considering an all electron calculation the integer values would have been 52 8 and 8 respectively e The set of molecular orbitals to be used in the transformation and subsequent CC cal culation are restored from the default section section 1 associated with the closed shell SCF module e Two additional directives CCIT and CCTH may be used to control convergence of the iterative CCSD procedure CCIT This directive consists of a single data line read to variables TEXT MXCCIT using format A 1 where TEXT should be set to the character string CCIT MXCCIT is an integer used to specify the maximum number of cycles required in the iterative CCSD procedure Note that this directive may be omitted when MXCCIT will be set to the default value of 20
125. constructed in such a way as to allow such changes to occur e The present implementation of both MCSCF and Cl capabilities assumes that the process of symmetry adaptation is in operation If for any reason the SCF MOs of differing irreducible representations become mixed the post Hartree Fock calculations may prove unreliable 1 2 The Role of the Dumpfile GAMESS UK makes extensive use of a number of files the most important of which is the so called Dumpfile that in default is routed to ED3 This file is crucial to the program and controls all restart activities The Dumpfile is organised into variable length sections with the user typically nominating a number of these for data storage e g for eigenvectors The sections are characterised by integers in the range 1 350 which are specified by the user through data input Routine usage of the code has normally involved such specification at two points or more in the data input through the VECTORS and ENTER directive In both cases the directive is used to control the reading and writing of eigenvectors with VECTORS used in restart jobs to specify the location of suitable vectors for input to some SCF process and ENTER used in both startup and restart jobs to specify where generated eigenvectors are to be stored In contrast to previous versions of GAMESS UK which required explicit specification of these section numbers the current release provides a set of default values so that the u
126. corrected wavefunction the second order correction to the wavefunction is not computed Therefore the only information obtained additional to the MP2 calculation is the MP3 correlation energy and the MP3 total energy which is printed as SESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S SESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S Multi reference MP3 Ecorr 0 1741698388 E 113 3964308158 SESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S SESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SS However for a consistent treatment of the perturbation theory one should optimise the orbitals for the state of interest In general that will involve an MCSCF calculation of some sort Suppose that we want to calculate an excited state of formaldehyde with the same symmetry as the ground state We start by building the guess orbitals with a simple RHF calculation TITLE H2CO 3 21G CLOSED SHELL SCF ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER Next we perform an MCSCF calculation for the excited of interest immediately followed by the MRMP calculation 23 DIRECT CI CALCULATIONS 120 RESTART NEW TITLE H2CO 3 21G CISD 12 REFERENCE MP2 EXCITED STATE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI SCFTYPE MCSCF MCSCF ORBITALS 4COR1 2COR3 DOC1 DOC2 U0C1 U0C2 END STATE 2 WEIGHT O 1 COPT 0 1 1 0
127. culation e discard certain virtual orbitals from the coupled cluster calculation typically the high energy inner shell complement orbitals The CORE and ACTIVE directives of the transformation module are provided for controlling the final subset of orbitals for inclusion in the CC The freezing of core or inner shell orbitals is achieved by nominating the sequence nos of those orbitals to be frozen under control of the CORE directive The discarding of orbitals is performed under control of the ACTIVE directive which specifies the sequence nos of the active set of orbitals to appear in the CC Turning to the H2CO calculation the following data sequence would be required to freeze the two inner shell and two lowest valence SCF MOs while retaining all virtual orbitals in the subsequent coupled cluster treatment TITLE H2CO TZVP VALENCE CCSD CCSD ENERGY 114 2600151982 SUPER OFF NOSYM NOPRINT ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ACTIVE 3 TO 50 END CORE 1 TO 2 END RUNTYPE CI CCSD 48 6 6 CCTH 10 CCIT 30 ENTER The following points should be noted e both ACTIVE and CORE are control directives of the integral transformation module As such they should be presented in the data stream prior to the specification of the coupled cluster data i e before the CCSD data line e The nature of the coupled cluster calculation is determined by the data line commen
128. described below The following points should be noted 1 DFT calculations on closed shell systems may be performed using either the conven tional SCFTYPE RHF or direct SCF SCFTYPE DIRECT RHF or SCFTYPE DIRECT modules 2 DFT calculations on open shell systems are only available using conventional UHF SCFTYPE UHF or direct UHF SCFTYPE DIRECT UHF modules Restricted ROHF calculations are not possible in the current release of the code 3 Only conventional 2 electron integral format is available when performing either closed or open shell DFT calculations Neither P supermatrix nor separate J and K Supermatrices are currently supported 11 2 DFT Basis Sets In addition to the standard basis sets available see Part 3 the polarized DFT orbital basis sets due to Godbout et al 29 may be requested through simple keyword specification on the BASIS directive Three such sets are available through this mechanism the DZVP DZVP2 and TZVP basis each is requested in straightforward fashion by a BASIS directive of the form BASIS DFT DZVP BASIS DFT DZVP2 BASIS DFT TZVP Omitting the third string and presenting the data line BASIS DFT will realise the DZVP basis 11 DFT CALCULATIONS 33 11 3 DFT Directive Options The role of the DFT directive is twofold i to trigger a DFT rather than HF calculation and ii to provide a mechanism for overriding the default DFT functional and quadrature settings The latter is achieved
129. e ADAPT data line specifies generation of a symmetry adapted list of 1 and 2 electron integrals 24 TABLE CI CALCULATIONS 132 2 Integral transformation requested through the TRAN directive will use the converged closed shell SCF vectors resident in section 1 see Table 1 the default closed shell section If section specification is made on the TRAN directive it should point to this section i e TRAN 1 3 In this example we are generating the TABLE data base as requested by the presence of the TABLE data line rather than restoring from the library file 4 The majority of the data input characterising the Cl calculation is presented under the SELECT keyword In the present case we are requesting Cl wavefunctions of Ay symmetry SYMMETRY 1 requesting singlet Cl wavefunctions SPIN 1 defining the number of active electrons in the Cl through the CNTRL directive requesting the inclusion of all singly excited configurations with respect to the ref erence configuration SINGLES 1 regardless of the computed energy lowerings defining the reference configuration under control of the CONF directive controlling the selection process through the ROOTS and THRESH directives In the Table Cl procedure this selection process involves construction of an explicit zero order Hamiltonian Ho over the nominated reference functions followed by perturbative selection of configurations with respect to the user nominated roots of Hp The ROOTS dir
130. e Initial Hessian In addition to specifying the starting geometry and internal coordinates the user need also consider defining an initial force constant matrix Hessian or second derivative matrix bearing in mind that a drastic reduction in the number of energy and gradient calculations required in the optimisation pathway can be realised through an accurate estimate of this Hessian This is particularly true in the location of transition states The following options are available 1 In default mode as in the example above the program provides an estimate of the diagonal force constant matrix based on a look up table of bond stretches bending angle etc involving the component nuclei of the molecule 2 These defaults are in most cases perfectly adequate in determining equilibrium geome tries They may however be overridden by providing additional information on the cor responding VARIABLE definition lines In the formaldehyde examples above the default value for the C H bond variable may be replaced by the data line 15 GEOMETRY OPTIMISATION 62 CH 1 099 HESSIAN 0 5 whereby the diagonal force constant for the CH variable is set to 0 5 3 A more accurate but clearly more expensive estimate of the initial force constant matrix may be generated through explicit computation either numerically or analytically of all or part of the trial hessian a NUMERICAL DETERMINATION of some subset of the hessian may be performed in s
131. e X A state of formaldehyde we mention some general points on conducting such calculations 1 RUNTYPE Cl represents a combination of tasks requesting integral generation SCF integral transformation and finally the Cl calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 2 The Full Cl procedure is of course exceedingly demanding in its memory requirements 40 Of the machines discussed in Parts 12 16 of the manual 3 Several direct access files will be generated under RUNTYPE CI processing For Full Cl calculations these include e the Mainfile ED2 and Dumpfile ED3 e the semi transformed ED4 and transformed ED6 integral files e the Scratch file ED7 e temporary files for sorting transformed integrals the Sortfile Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 25 FULL CI CALCULATIONS 161 4 In addition to the direct access files above the full Cl module uses conventional un formatted FORTRAN data sets Four such files will be used with LFNs FTNO02 FTN003 FTN004 and FTNOO8 Note that any restart jobs will rely on the availability of the latte
132. e data set containing the Dumpfile from the small calculation has been assigned to the extended calculation with the LFN ED4 commencing at block 1 This Hessian may be generated in a previous optimise run or in a separate analytical hessian calculation The data on the runtype card is read like in the FCMIN directive part4 This is a particularly attractive way of minimising overall CPU requirements given that the small basis eigenvectors may also be input to initiate the extended SCF calculation under control of the GETQ directive see section 4 8 Note that if this restoring of the Hessian is performed in an optimisation startup the identical RUNTYPE directive must be presented in any subsequent restarts failure to do so will lead to a PARAMETER ERROR diagnostic and job failure 15 GEOMETRY OPTIMISATION 64 15 3 Cartesian Coordinate Optimisation A second optimisation procedure is provided specifically for those cases where problems arise with the internal coordinate driven scheme or when direct input of cartesian coordinates e g from a data base is more convenient While the cartesian procedure is less flexible than the internal coordinate method in that e it is not possible to define the starting Hessian or to restore a Hessian from say a smaller basis calculation e the algorithm employed is only guaranteed to converge to a stationary point not neces sarily a minimum nevertheless the quasi Newt
133. e default VECTORS section for closed shell SCF orbitals that is written in the startup job now being used as the source of eigenvectors Use of this default section will be carried through into the Table Cl module so that explicit specification on the TRAN directive i e TRAN 1 in the above is not in fact required The calculation may be further subdivided by splitting Run above into separate integral trans formation and Cl runs using the BYPASS keyword on the data lines of the appropriate Table Cl sub modules to deactivate the computation accordingly Thus Run Ila The Transformation Job RESTART TITLE H2CO 3 21G TABLE CI 1M 1R TRANSFORMATION SUPER OFF NOSYM BYPASS SCF ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT TRAN SELECT BYPASS SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES 1 CONF 012345 13 17 18 ROOTS 1 THRESH 30 10 CI BYPASS DIAG BYPASS EXTRAP 2 ENTER Thus BYPASS is appended to the data lines requesting those Table Cl sub modules SELECT CI and DIAG to deactivate the associated processing Run IIb The Table CI Job RESTART TITLE H2C0 3 21G TABLE CI 1M 1R SELECTION AND CI 24 TABLE CI CALCULATIONS 136 SUPER OFF NOSYM BYPASS SCF ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT BYPASS TRAN BYPASS TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES 1 CONF
134. e excitation 1b12b1 to 2b23b2 This leads to the following occupation patterns for the 4 reference functions Reference la 2a 3a 4a Ib 5a 1by 2bo 2b 3b Function 1 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 0 2 2 0 3 2 2 2 2 2 2 2 0 0 2 4 2 2 2 2 2 2 1 1 1 1 Then each data line of the CONF directive will reflect the occupation patterns above CONF 012345 13 17 18 oe Ref 1 012345 14 17 18 am Ref 2 012345 13 17 19 ots Ref 3 413141819 1234517 Sc Ref 4 The full data input for the job would be as follows RESTART TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM 24 TABLE CI CALCULATIONS 140 ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT TRAN SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 ROOTS 1 THRESH 30 10 CI DIAG EXTRAP 2 ENTER 24 6 Conventional Table CI Default Sub module Attributes To simplify the data driven loading of sub modules the program assumes a default loading order so that assuming no additional data input is required by a given sub module i e the default attributes of that sub module are in effect the user may omit explicit specification of the module from the data input The assumed default is shown below MRDCI ADAPT TRAN SELECT CI DIAG In practice the SELECT module will always require input characterisin
135. e noted 1 the starting variables for the initial geometry in the CASSCF calculation have been taken from the output of the previous HF optimisation 2 the initial vectors in the CASSCF calculation will be the final set of HF 3 21G SCF orbitals restored from the default closed shell SCF vectors section 1 of the Dumpfile 3 the initial hessian is again constructed numerically Note that using the HF hessian through RUNTYPE SADDLE ED3 specification may not provide the optimal choice for post HF calculations With systems of fewer than 10 atoms it is often more efficient as above to utilise the TYPE 3 feature to compute the initial hessian numerically assuming the initial geometry is close to the final structure Using the HF 3 21G hessian would be accomplished with the following data where we are using the HF 3 21G TS geometry 16 TRANSITION STATE OPTIMISATION 79 RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 3 21G MCSCF TOTAL ENERGY 113 223061249 ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 m mb bd hd QO Se BOUNE VARIABLES co 1 1525832 CHH 1 2981078 XH 0 6596229 ANG1 43 4018534 ANG2 57 3815232 END RUNTYPE SADDLE ED3 SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC1 DOC1 DOC2 DOC1 VOC2 UOC1 UOC1 U0C1 END ENTER A total of 9 energy and gradient calculations are required in locating the transition state using the
136. e transition state initially in a small STO 3G basis e using the final STO 3G Hessian geometry and eigenvectors to instigate the larger 3 21G calculation Example 1 The H2CO to HCOH transition structure STO 3G Calculation TITLE HCOH lt gt H2CO 1A TS STO3G ZMAT ANGS 0 0 1 C0 H 1 CH1 2 OCH1 H 1 CH5 2 H5CO 3 180 0 VARIABLES OCH1 56 3 TYPE 3 co 1 27 TYPE 3 CH1 1 22 TYPE 3 CH5 1 10 TYPE 3 H5C0 115 8 TYPE 3 END BASIS STO3G RUNTYPE SADDLE ENTER 3 21G Calculation DUMPFILE ED3 350 TITLE H2CO lt gt HCOH 1A TS 3 21G BASIS ZMAT ANGS 16 TRANSITION STATE OPTIMISATION 73 0 0 1 C0 H 1 CH1 2 OCH1 H 1 CH5 2 H5CO 3 180 0 VARIABLES OCH1 57 236 TYPE CO 1 299456 TYPE CH1 1 201293 TYPE CH5 1 115436 TYPE H5C0 116 882 TYPE END RUNTYPE SADDLE ED3 1 VECTORS GETQ ED3 1 1 ENTER wuwwuwuw The following points should be noted 1 The Dumpfile for both calculations are sited on the same data set that for the extended basis calculation commencing at block 350 The initial Hessian for the STO 3G study is constructed numerically through the TYPE 3 specifications on the VARIABLE Definition lines The initial VARIABLE specifications in the 3 21G case are taken from the optimised STO 3G structure The Hessian in the 3 21G case is taken from the optimised STO 3G structure through the data line RUNTYPE SADDLE ED3 1 Note that such data overrides the TYPE
137. ect access files listed above the Table Cl module again makes extensive use of FORTRAN data sets hereafter referred to as interfaces Any restart jobs will require a subset of interfaces to be saved see Table 9 in addition to the Dumpfile ED3 Mainfile ED2 and Transformed Integral File ED6 Extensive use is also made of scratch FORTRAN data sets with LFNs FTNOO1 002 003 004 008 009 010 011 022 041 043 and FTN044 6 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM in the SCF run 24 9 Semi direct Table ClI Multi reference CI Calculations We would again point out that all semi direct Table Cl calculations require at least two reference configurations i e CISD calculations based on a single reference configuration are not possible with this module However we do not consider this to be a major disadvantage given that the process of configuration choice and specification has been simplified through the use of automated configuration generation see below 24 TABLE CI CALCULATIONS 146 Table 9 FORTRAN Interfaces Used by the Semi direct Table CI Module File Contents Generated by Required by Sub Module Sub Module FTNO31 Transformed Transformation SELECT CI Integrals module FTN033 Partial Matrix Elements SELECT CI FTN034 Partial Matrix Elements SELECT CI FTN042 Zero order vectors SELECT CI FTN012
138. ection 5 of the Dumpfile the default section associated with the energy ordered open shell SCF MOS having been placed in that Section by the SCF process Now let us consider performing the closed shell calculation above in a sequence of jobs where the first job carries out the SCF the second the transformation and Cl First the closed shell case valid data sequences for performing the calculation are shown below Run I The Scf Job TITLE H2CO 3 21G SCF PRIOR TO FULL CI CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER The only obvious point to note is the use of the SUPER directive in requesting full integral list generation required in the subsequent transformation Run II The Transformation and CI Job 25 FULL CI CALCULATIONS 164 RESTART TITLE H2CO 3 21G BASIS VALENCE FULL CI SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ACTIVE 5 TO 22 END CORE 1 TO 4 END RUNTYPE CI FULLCI 18 4 4 ENTER The following points should be noted e The SCF computation is BYPASS ed e The SCF vectors from the first run will be restored from Section 1 of the Dumpfile the default section associated with the closed shell SCF MOs The calculation may be further subdivided by splitting Run Il above into separate integral transformation and Cl runs using the RUNTYPE TRANSFORM specificatio
139. ective specifies these roots typically the nominated roots will exhibit a strong overlap with the final Cl wavefunctions with the dominant configurations in the final Cl wavefunction present in the vectors of the zero order Hamiltonian indeed the process of extrapolation based on selection assumes this to be true In the present case this specification is trivial the zero order Hamiltonian is simply a unit matrix comprising the SCF configuration The thresholds to be used in selection are specified on the THRESH data line The first integer specified is the minimum threshold to to be used Tmin in units of micro Hartree the second integer the increment to be used in defining higher threshold cases to be solved in the process of extrapolation 39 5 The Cl data line requests construction of the Cl Hamiltonian over the set of selected configurations 6 The DIAG directive requests diagonalisation of the Cl Hamiltonian with EXTRAP re questing two extrapolation passes to be performed in the process of extrapolation to the zero threshold limit T 0 The sequence of data lines defining the Conventional Table Cl calculation is terminated by the VECTORS directive Let us now consider a Conventional Table Cl calculation on the B state of H COt again using the SCF configuration as the sole reference function A valid data sequence for performing such a calculation is shown below where we are still performing all the computation in a sing
140. ed orbital case below Use of the default ENTER directive would result in the LMO over writing the closed shell SCF vectors TITLE H2C0 3 21G CLOSED SHELL SCF WITH ANALYSIS ZMATRIX ANGSTROM Cc 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER RUNTYPE ANALYSE Molecular Properties PROPERTY 4C 40 END VECTORS 1 ENTER RUNTYPE ANALYSE Localised Orbitals LOCAL 3 TO 8 END VECTORS 1 ENTER 2 RUNTYPE ANALYSE Distributed Multipole Analysis DMA VECTORS 1 ENTER RUNTYPE ANALYSE 33 MULTIPLE RUNTYPE CALCULATIONS 193 Graphical Analysis GRAPHICS GDEF TYPE 2D POINTS 99 TITLE SQUARE 2D GRID 99 99 CALC TYPE ATOM TITLE H2CO ATOM DIFFERENCE SECTION 150 PLOT TYPE LINE TITLE ATOM DIFFERENCE DENSITY LINEPRINTER PLOT CALC TYPE DENS SECTION 151 TITLE H2CO TOTAL DENSITY PLOT TYPE LINE TITLE DENSITY LINEPRINTER PLOT CALC TYPE MO 2 TITLE H2CO MO 2 AMPLITUDE SECTION 152 PLOT TYPE LINE TITLE MO 2 LINEPRINTER PLOT GDEF TYPE 2D POINTS 25 TITLE SQUARE 2D GRID 25 25 CALC TYPE POTE TITLE H2CO POTENTIAL SECTION 153 PLOT TYPE LINE TITLE POTENTIAL LINEPRINTER PLOT VECTORS 1 ENTER RUNTYPE ANALYSE Mulliken Analysis MULLIKEN ATOM ORBITAL 3 TO 8 END VECTORS 1 ENTER 33 MULTIPLE RUNTYPE CALCULATIONS 194 33 3 Initial Hessian and Transition State Location In this example we initially compute a trial hessian to be used in
141. elow the data for performing valence only molecular orbital treatments using both the semi local 6 and non local 7 formalisms Note that in the non local procedure the required library of pseudopotentials is held on a Library File which in default is assumed to be available on EDO commencing at block 1 Overriding this default is described under the PSEUDO directive No such file is required when performing semi local ECP calculations 7 1 Non Local Pseudopotential Calculation The following data sequence would be required in performing a non local ECP calculation TITLE H2CO 1Ai NON LOCAL ECP CALCULATION ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS ECPDZ PSEUDO NONLOCAL 00 cc ENTER The following points should be noted e The non local pseudopotential is requested on the PSEUDO directive the subsequent data lines of this directive allocate an ECP stored in the Library to the atoms specified in the z matrix through TAG specification This explains hopefully the somewhat confusing syntax above the library ECPs for carbon and oxygen are tagged as C and O respectively i e the same tags applied in the z matrix The first TAG on such a data line refers to the library TAG all subsequent fields to the unique nuclei tags specified in the z matrix e the ECPDZ tag on the BASIS line requests use of a double zeta contraction of the appropriate library of ECP basis sets 6 7 ECP C
142. ely Before detailing the Table Cl data we should mention that the revised numbering scheme used in the specification of for example the reference configurations is as in the conventional case that in effect after the freezing and discarding of orbitals Having effectively removed three orbitals of aj symmetry and one of b from the subsequent Cl the table below presents the final orbital numbering to be used in CONF specification IRrep IRrep SCF Sequence Table Cl Occupation No No Sequence No No ay 1 3 1 2 0 4 2 2 0 6 3 2 0 10 4 0 0 12 5 0 0 15 6 0 0 16 7 0 0 18 8 0 0 20 9 0 0 b 2 7 10 2 0 9 11 0 0 13 12 0 0 19 13 0 0 b 3 5 14 2 0 8 15 2 0 11 16 0 0 14 17 0 0 17 18 0 0 The data for performing the semi direct Table Cl calculation is shown below TITLE H2CO 3 21G BASIS valence direct MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 24 TABLE CI CALCULATIONS 156 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI CORE 1 2 END ACTIVE 3 TO 20 END MRDCI DIRECT TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 12 SINGLES ALL CONF 0123 10 14 15 0123 11 14 15 0123 10 14 16 410111516123 14 END ROOTS 1 THRESH 2 2 CI NATORB ENTER The following points should be noted e the number of active electrons in the Cl specified on the CNTRL data line is now 12 e the integers specified on the CONF data line now label the six doubly occupied orbitals in the r
143. ence MOROKUMA FRAG NUMBER TAG specifies the RHF calculation on one of the fragments NUMBER should be 1 or 2 indicating the position of the fragment in the supermolecule TAG is replaced with a string to identify the fragment the job will result in a file of this name containing the fragment basis and wavefunction information being written in the working directory of the job There is currently an 8 character limit on TAG The sequence MOROKUMA INTERACT TAG1 TAG2 requests that an interaction energy analysis be performed The geometry is assumed to be that of the supermolecule and the two tags denote the fragment files from two previous runs under control of MOROKUMA FRAG as above A number of restrictions should be noted when using the morokuma analysis module e The implementation is restricted to RHF calculations using the conventional non direct SCF module e The use of symmetry including symmetry adaption must be disabled for all component jobs The atoms in the supermolecule must be presented in the same order as that obtained by concatenating the two fragments and the basis sets specified for the separate tasks must correspond e The code is developmental although it is believed to work correctly within the above limits prospective users are advised to contact the authors 14 RESTARTING INTEGRAL AND SCF COMPUTATIONS 56 e Morokuma EDA jobs cannot be restarted TITLE MOROKUMA TEST FRAG2 ADAPT OFF NOSYM GEOMETR
144. envector source Assuming the fortran file FTN008 had been saved the following job would continue processing the above example assuming this had terminated cleanly during the iterative Davidson process RESTART CI TITLE H2CO 3 21G BASIS VALENCE FULL CI SUPER OFF NOSYM NOPRINT ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ACTIVE 5 TO 22 END CORE 1 TO 4 END RUNTYPE CI FULLCI 18 4 4 ENTER Let us now consider the corresponding calculation on the 7By state of HxCOT now using the open shell SCF orbitals A valid data sequence for performing such a calculation is shown below where we are still performing all the computation in a single job TITLE H2C0 2B2 3 21G VALENCE FULL CI SUPER OFF NOSYM CHARGE 1 25 FULL CI CALCULATIONS 163 MULT 2 ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END RUNTYPE CI OPEN 1 1 FULLCI 18 4 3 SYMMETRY 3 ENTER Considering the changes to the closed shell run the following points should be noted e Of the three integers on the FULLCI data line NACT and NALPHA remain unchanged while NBETA the number of electrons is now 3 e The OPEN directive is now present specified prior to the full Cl data e An additional directive is required in the full Cl data SYMMETRY defining the spatial symmetry index of the Cl wavefunction e The set of vectors used in the integral transformation will be restored from s
145. equested as follows MP2 RHF no additional files required MP2 UHF ED16 ED17 ED18 and ED19 MP3 RHF ED16 and ED17 MP3 UHF ED16 ED17 ED18 ED19 MTO and MT1 Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 3 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF in the SCF run Note that in contrast to CASSCF and MCSCF calculations MP processing is driven off the skeletonised list of 2 electron integrals so that the NOSYM parameter specification is not required on the SUPER directive 4 In default all molecular orbitals will be deemed active in the MP calculation 12 M LLER PLESSET MP2 AND MP3 CALCULATIONS Al 12 1 MP2 Calculations A closed shell MP2 calculation is to performed on the formaldehyde molecule A valid data sequence for performing such a calculation is shown below where we are performing all the computation in a single job TITLE H2CO 3 21G DEFAULT BASIS MP2 RHF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MP2 RHF ENTER Note that the SCFTYPE specification above may be simplified to just SCFTYPE MP2 with RHF the default level of underlying SCF for closed shell systems Now let us consider per forming the above calculation in two steps where the first carries out the SCF the second t
146. erated on termination of the MCSCF process Both sections contain information that is used internally within the MCSCF module and in contrast to the CASSCF module are not designed for reference by other modules within GAMESS UK Now the most obvious starting point for a post Hartree Fock computation are the MCSCF natural orbitals that are written to the section specified by the CANONICAL directive see above 11 DFT CALCULATIONS 31 e In default the non canonicalised MCSCF vectors will be written to section 8 of the Dump file while the restart information will be written to section 9 see Table 1 e Explicit specification of these sections thus requires two integers on the ENTER directive Presenting the data line ENTER 8 9 will result in the same eigenvector section storage as the default 11 DFT Calculations Background material on Density Functional Theory DFT and a description of the GAMESS UK implementation and issues relating to the choice of functionals integration grids and associated performance together with a full description of the available directives are given in Part 4 of the manual The user is advised to consult that material prior to using the code 11 1 The DFT Directive and Default Settings Input for a DFT calculation is essentially that for the closed shell RHF or UHF module with additional keywords that control the DFT specific features In the simplest case the user need just introduce a single data with t
147. erising the system They act for example to define the charge of the component nuclei and are used in establishing the effective point group symmetry of the system The program incorporates a number of built in basis sets with the split valence 3 21G basis due to Pople et al 4 as the default The following data sequence would be required in performing the SCF calculation using this default basis TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER Note that this data sequence assumes a number of default specifications the corresponding sequence specifying these defaults in line would be as follows DUMPFILE ED3 1 2 CLOSED SHELL SCF CALCULATION 5 MAINFILE ED2 MINBLOCK ED2 1 MAXBLOCK ED2 99999 ADAPT ON TITLE H2CO FULL DATA SPECIFICATION CHARGE 0 MULT 1 SUPER ON ZMATRIX ANGSTROM C 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS SV 3 21G RUNTYPE SCF SCFTYPE RHF LEVEL 1 0 5 0 3 DIIS ON VECTORS ATOMS ENTER 1 where the default specifications which apply in the present closed shell single point geometry calculation are indicated by a In particular 1 DUMPFILE MAINFILE MINBLOCK and MAXBLOCK specify the file attributes Dump file output is routed to ED3 commencing at block 1 while Mainfile output is to ED2 commencing at block 1 2 CHARGE
148. eta plus polarisation TZVP spherical harmonic basis is shown below TITLE H2CO EXTENDED TZVP SPHERICAL HARMONIC BASIS CLOSED SHELL SCF HARMONIC ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ENTER The following points should be noted e The HARMONIC directive if present should appear before the BASIS directive 3 CLOSED SHELL DIRECT SCF CALCULATION 9 e A primary use of spherical functions is to help to eliminate problems with linear depen dence e It is not possible in the present release of the code to employ the HARMONIC option in Table Cl calculations 3 Closed Shell Direct SCF Calculation We wish to perform a direct SCF calculation equivalent to that above A valid data sequence for performing such a calculation is shown below TITLE H2CO EXTENDED TZVP BASIS DIRECT SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP SCFTYPE DIRECT RHF ENTER Note that the SCFTYPE directive is now required in requesting the DIRECT option The third parameter on the data line RHF points to the particular category of wavefunction required i e closed shell SCF The options supported in direct mode include RHF UHF GVB and MP2 see below Omitting this parameter and presenting just the line SCFTYPE DIRECT will lead to the default option of a direct RHF calculation for closed shell systems Note that the default file ou
149. etry optimisation of H2CO followed by a direct Cl calculation at this optimised geometry The first occurrence of ENTER in the data stream terminates the input for the geometry optimisation step while the RUNTYPE CI data line initiates data input for the direct Cl calculation with the VECTORS directive pointing to section 1 as the source of molecular orbitals The Cl calculation will be performed at the geometry determined in the first step being restored from the Dumpfile TITLE H2CO DZ BASIS CLOSED SHELL SCF OPTIMISATION DIRECT CI ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 33 MULTIPLE RUNTYPE CALCULATIONS 192 END BASIS DZ RUNTYPE OPTIMIZE ENTER CI calculation RUNTYPE CI DIRECT 16 8 14 CONF 22222222 NATORB 10 O PRINT ENTER 33 2 SCF Calculation and Property Evaluation In this example we perform an initial SCF calculation on H2CO then analyse the associated SCF wavefunction through repeated RUNTYPE ANALYSE directives The first occurrence of EN TER in the data stream terminates the input for the SCF step while each RUNTYPE ANALYSE data line initiates data input for some different analysis option with the VECTORS directive pointing to section 1 as the source of molecular orbitals in each case Note that the ENTER directive should be specified in those cases where a new set of orbitals will be generated as a result of the requested analysis the localis
150. etry optimisations Generally to ensure that the rotational modes all have frequencies below 10 wavenumbers the XTOL directive should be employed in any preceding geometry optimisation to reduce all elements of the gradient to about 1075 a u Several files will be generated under RUNTYPE HESSIAN processing e For SCF force constants these include the Mainfile ED2 and Dumpfile ED3 the Scratch file ED7 the semi transformed ED4 and transformed ED6 integral files note that ED4 is also used as a scratch file in the solution of the coupled Hartree Fock equations the Hamiltonian file ED12 which acts to store the derivative Fock operators temporary files for sorting both transformed integrals the Sortfile and inter mediate matrices in the Hessian calculation e The generation of MP2 force constants is significantly more complex in addition to the files generated under SCF processing additional temporary files will be required including EDO ED11 ED16 ED17 ED18 ED18 ED19 MTO and MT1 Any restart jobs will require ED6 and ED12 being saved in addition to the Dumpfile ED3 and Mainfile ED2 The following examples demonstrate HESSIAN usage where in each case we show data files for performing the appropriate geometry optimisation together with data for determining the force constants under RUNTYPE HESSIAN processing 1 2 Optimisation of the geometry and calculation of the vibrational
151. evised numbering scheme outlined above 24 12 Semi direct Table CI Default Sub module Attributes To simplify the data driven loading of sub modules the program assumes a default loading order so that assuming no additional data input is required by a given sub module i e the default attributes of that sub module are in effect the user may omit explicit specification of the module from the data input The assumed default is shown below MRDCI DIRECT TABLE SELECT CI NATORB 24 TABLE CI CALCULATIONS 157 In practice the SELECT module will require input except in cases where the default configura tion generation described above is used characterising for example the nature of the reference configurations selection attributes etc but in many instances the defaults of the other sub modules will hold so that the associated data input may be omitted Clearly this omission of data requires a firm understanding of the defaults in effect which will only be apparent after the detailed description of directives presented in Part 6 For the moment we illustrate this by considering the simplified data file for the multi reference calculation on H2CO above RESTART TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI SELECT CNTRL 16 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 END
152. form an initial SCF and MCSCF at a previously optimised transition state geometry then compute the numerical force constants at this geometry GENERATE INITIAL GUESS ORBITALS FOR MCSCF TITLE H2 CO lt gt H2CO 1A 3 21G BASIS SCF MCSCF ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES CO 1 2034717 CHH 1 3040659 XH 0 7415189 ANG1 41 4927811 ANG2 56 6325324 END ENTER NOW PERFORM SINGLE POINT MCSCF CALCULATION USING SCF MOS TITLE H2 CO lt gt H2CO 1A 3 21G MCSCF AT OPT TS GEOMETRY SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC1 DOC1 DOC2 DOC1 VOC2 VOC1 UVOC1 UOC1 END ENTER NOW COMPUTE NUMERICAL FORCE CONSTANTS TITLE H2 CO lt gt H2CO 1A TS 3 21G MCSCF FORCE CONSTANTS FREQ 1825 4 767 8 900 3 1259 4 1720 5 3185 4 RUNTYPE FORCE SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC1 DOC1 DOC2 DOC1 VOC2 VOC1 UOC1 UOC1 END PRINT ORBITALS VIRTUALS NATORB CANONICAL 12 FOCK DENSITY FOCK ENTER m mM oh oe a nO RR RONE REFERENCES 196 References 1 M Dupuis and H F King Int J Quant Chem 11 1977 613 doi 10 1002 qua 560110408 M Dupuis and H F King J Chem Phys 68 1978 3998 doi 10 1063 1 436313 H F King and M Dupuis J Comp Phys 21 1976 144 doi 10 1016 0021 9991 76 90008 5 M Dupuis J Rys and H F King J Chem Phys 65 1976 111 doi 10 1063 1 432807 2 W
153. g for example the nature of the reference configurations selection attributes etc but in many instances the defaults of the other sub modules will hold so that the associated data input may be omitted Clearly this omission of data requires a firm understanding of the defaults in effect which will only be apparent after the detailed description of directives presented in section 5 For the moment we illustrate this by considering the simplified data file for the multi reference calculation on H2CO above 24 TABLE CI CALCULATIONS 141 RESTART TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI SELECT SINGLES 1 CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 4 13 14 18 19 1234517 ENTER The following points should be noted e t is assumed that the complete sequence of sub tasks is to be carried out If any task is to be BYPASS ed then the associated data line must be present e In the absence of the TRAN directive the transformation module will use the default section number corresponding to use of ENTER i e section 1 directive as the location of the molecular orbital coefficient array e The SYMMETRY SPIN CNTRL ROOTS and THRESH directives of the SELECT sub module may all be omitted since the required specification corresponds in each case to the default values e Both Cl and DIAG may be o
154. gorithm to determine whether sufficient central memory is available to house 9 CASSCF CALCULATIONS 24 the complete integral file if this memory is judged not to be available the conventional 1 O route will be followed with integrals routed to ED2 2 A more flexible option is to nominate a data set to receive any integrals that will not fit into local memory thus MFILE MEMORY ED4 whereby the data set assigned as ED4 will be used to store those integrals that exceed the local available memory capacity Note also the following e this capability is at present limited to UNIX implementations of the code e in core processing of the integral file is available within all SCFTYPEs RUNTYPEs and integral file formats e such jobs may not be restarted since the memory resident integral file is not at present routed to disk e the data set ED2 cannot be used as the memory backup file since the program uses the internal tables associated with this file to map memory resident integrals i e the data line MFILE MEMORY ED2 is invalid The following data sequence would be required in performing an in core SCF calculation on H CO TITLE H2C0 3 21G DEFAULT BASIS IN CORE SCF MFILE MEMORY ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER 9 CASSCF Calculations The present release of GAMESS UK contains two distinct modules for performing MCSCF calculations namely e
155. he transformation and MP2 calculation Assuming we wish to avoid recalculating the 2e integrals in the MP2 calculation then the SUPER OFF data line should be presented in the SCF job allowing bypassing of integral evaluation in the subsequent calculation First the closed shell case valid data sequences for performing the calculation are given below Closed shell SCF Data TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF SUPER OFF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER MP2 Data RESTART TITLE H2C0 X1iA1 3 21G DEFAULT BASIS MP2 RHF CALCULATION SUPER OFF BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 12 M LLER PLESSET MP2 AND MP3 CALCULATIONS 42 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MP2 ENTER Let us now consider a MP2 calculation on the B state of H COt now using the UHF formalism A valid data sequence for performing such a calculation is shown below where we are performing all the computation in a single job TITLE H2C0 2B2 3 21G DEFAULT BASIS MP2 UHF CALCULATION CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MP2 UHF ENTER Again the UHF flag may be omitted from the SCFTYPE data line given that UHF is the under lying SCF for open shell systems Consider performing the above calculation in two steps where the first carries out the UHF the second the t
156. he character string CDFT or DFT in the first data field to request a DFT rather than HF calculation thus input for a closed shell DFT calculation would appear as follows TITLE H2CO 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END DFT ENTER while the corresponding UHF data for performing an open shell unrestricted UKS calculation would appear thus TITLE H2C0 2B2 DEFAULT 3 21G BASIS UKS CALCULATION CHARGE 1 MULT 2 ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END 11 DFT CALCULATIONS 32 SCFTYPE UHF DFT ENTER The directive DFT thus switches on the DFT specific modifications to the Hartree Fock scheme omitting the directive would yield the corresponding Hartree Fock input If as in the above the DFT module is switched on without specifying any options then the following functional and quadrature settings will apply e the Becke 1988 exchange functional 17 e the Lee Yang and Parr LYP correlation functional 18 e quadrature grids designed to obtain a relative error of less than 1 0e 6 in the number of electrons per atom These grids are constructed from the logarithmic radial grid 19 and Gauss Legendre angular grid using the SSF weighting scheme with screening 21 and MHL angular grid pruning 20 Note that this choice corresponds to the QUADRATURE MEDIUM setting
157. he non canonicalised vectors will be written to section 6 of the Dumpfile while the canonicalised vectors will be written to section 7 see Table 1 Note that the latter section also contains the current Cl coefficients 9 CASSCF CALCULATIONS 27 Explicit specification of these sections thus requires two integers on the ENTER directive Presenting the data line ENTER 6 7 will result in the same eigenvector section storage as the default The present CASSCF module 16 incorporates several optimisation techniques each of which tends to be most effective at differing stages of the MCSCF procedure We note here that Super Cl 2 step Newton Raphson NR and 1 step Newton Raphson optimi sation may be requested In previous releases of GAMESS UK the user was responsible for determining just which of the possible optimisation methods was to apply at each CASSCF iteration and when to carry out explicit Hessian construction The optimisa tion techniques were controlled by the SUPERCI NEWTON and HESSIAN directives In the current release the appropriate method is chosen dynamically and the user need no longer drive this process however such control is still possible if the dynamic method runs into trouble Thus the following data sequence would be required to force Super Cl optimisation on cycles 1 7 of the iterative process and 2 step Newton Raphson on cycles 8 20 with Hessian construction conducted on each NR cycle RESTART TITLE H2CO
158. hes to compute a number of properties of the CASSCF wavefunction but no longer has access to the Dumpfile used above This may be accomplished using the following data sets the first to compute an initial SCF wavefunction at the optimised MCSCF ge ometry the second to re do a single point MCSCF calculation at this geometry using the PROPERTY ATOMS directive see 12 to obtain a variety of one electron properties Run I The Initial SCF Calculation TITLE H2CO 3 21G SCF AT MCSCF OPT GEOM ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES co 1 2406315 CH 1 1136940 HCO 123 1819948 END ENTER Run II The MCSCF Property Analysis RESTART NEW TITLE H2CO MCSCF PROPERTIES AT OPTIMISED GEOM 10E IN 9 M O ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES co 1 2406315 CH 1 1136940 HCO 123 1819948 END SCFTYPE MCSCF PROPERTY ATOMS MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC3 DOC1 DOC2 DOC3 UVOC2 UVOC1 UOC3 UVOC1 END ENTER 15 6 3 MP2 Geometry Optimisation MP2 RHF Optimisation Data TITLE H2CO 3 21G DEFAULT BASIS MP2 RHF OPTIMISATION ZMATRIX ANGSTROM 15 GEOMETRY OPTIMISATION co CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE MP2 XTOL 0 0001 ENTER Cc 0 1 H 1 The following points should be noted 70 e Use of the XTOL directive this is to converge the geometry optimisation m
159. ile for direct use in the CASSCF calculation requires the data line SUPER OFF NOSYM in the closed shell run hence allowing BYPASS ing in the MCSCF computation Closed shell SCF Data TITLE H2CO 3 21G CLOSED SHELL SCF SUPPRESS SKELETONISATION SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 ENTER CASSCF Data RESTART TITLE H2C0 CASSCF 3 21G BASIS 10E IN 9 M 0 BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE CASSCF CONFIG PRINT 9 CASSCF CALCULATIONS 26 FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END ENTER Note the additional CONFIG directive specified in the CASSCF data responsible for defining 1 the active orbital space for the calculation This involves classifying the input MOs as either primary or secondary in character with the primary orbitals classified by type 2 an initial reference configuration typically the Hartree Fock configuration to be used in generating the complete Cl expansion and hence the loop formulae tape This involves assigning occupation numbers through orbital TAGs to the primary orbitals The active orbital space and initial reference configuration are defined by CONFIG each orbital in the primary space MOs 1 12 is classified by type where the following types are introduced e FZC frozen core orbital an orbital which will remain doubly occupied in all configura
160. in this revised numbering scheme Let us consider an example to try and clarify this point Consider again the output from the closed shell SCF calculation on H2CO in particular the symmetry adapted basis set information IRREP NO OF SYMMETRY ADAPTED BASIS FUNCTIONS 1 12 2 4 3 6 1 1 20 48275080 2 0000000 2 1 11 28286952 2 0000000 3 1 1 40833443 2 0000000 4 1 0 86648626 2 0000000 5 3 0 69818828 2 0000000 6 1 0 63034883 2 0000000 7 2 0 52027278 2 0000000 8 3 0 43433094 2 0000000 9 2 0 14397469 0 0000000 10 1 0 27419771 0 0000000 11 3 0 36740523 0 0000000 12 1 0 45123743 0 0000000 13 2 0 93266602 0 0000000 14 3 1 02032602 0 0000000 15 1 1 02498516 0 0000000 16 1 1 14613786 0 0000000 17 3 1 27971217 0 0000000 18 1 1 57176247 0 0000000 19 2 1 86744709 0 0000000 24 TABLE CI CALCULATIONS 126 20 1 1 91087974 0 0000000 21 3 1 98262324 0 0000000 22 1 3 31460342 0 0000000 Based on the reordering scheme outlined above the table below outlines the sequence numbers of the MOs both prior to and after reordering Note that a list of irreducible representations IRreps and their associated indices for each of the abelian point groups are given in Table 7 With the molecular orbitals reordered thus the user must apply the revised numbering scheme in specification of for example the reference configurations Thus consider the SCF configuration for H2CO in terms of the doubly occupied SCF m o s m o la 2a 3a 4a 1b ba
161. ing e the Mainfile ED2 and Dumpfile ED3 e the semi transformed ED4 and transformed ED6 integral files e the Scratch file ED7 e temporary files for sorting both transformed integrals the Sortfile e In addition to the direct access files above use is made of the more conventional FORTRAN unformatted data sets These files allocated with the LFNs FTNO02 FTNO004 FTNO08 and FTNOO9 can become large Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 4 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM 29 GREEN S FUNCTION CALCULATIONS II THE TDA METHOD 178 in the SCF run 5 In TDA calculations the user must specify those valence shell molecular orbitals to be included in the valence ionisation computation These orbitals are defined by use of the BAND directive Any core orbitals may be removed from computation using the CORE directive of the integral transformation module 6 The user should note that the rate determining step in TDA calculations involves the diagonalisation of matrices whose order is a function of the square of the number of virtual orbitals included in the computation Although spatial symmetry considerations are used to reduce these large diagonalisation problems use of the ACTIVE directive in reducing the virtual manifold will often be required when
162. ion 0 1 2 3 4 6 13 17 18 ie 5a1 gt 6a1 double 2 5 6 1 2 3 4 13 17 18 s 5a1 gt 6al single 0 1 2 3 4 5 14 17 18 z 1bi gt 2b1 double 2 13 14 1 2 3 4 5 17 18 E 1bi gt 2b1 single 0 1 2 3 4 5 13 17 19 ne 2b2 gt 3b2 double 2 18 19 1 2 3 4 5 13 17 ans 2b2 gt 3b2 single 8 The default selection process subsequently undertaken is equivalent to the following ROOTS and THRESH directives THRESH 10 10 ROOTS 1 Thus this default selection process involves construction of an explicit zero order Hamilto nian Ho over the reference functions described above followed by perturbative selection of configurations with respect to the lowest root of Hp The minimum threshold to be used in selection Tmin is 10 micro Hartree with an increment of 10 uH to be used in defining the higher threshold case to be solved in the process of extrapolation 39 9 In default the module will having solved the secular problem for the lowest root of the Cl secular problem generate the spinfree natural orbitals from the associated Cl eigenfunction The sequence of data lines defining the Semi direct Table Cl calculation is terminated by the VECTORS directive Note at this stage that the full data specification corresponding to the defaults generated from the above data file is as follows TITLE H2CO 3 21G EXPLICIT DATA FOR DEFAULT MRDCI SETTINGS 113 43885803 SUPER OFF NOSYM ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 24 TABLE CI CALCULATI
163. ion is to performed on the formaldehyde molecule with estimates required of the ionisation energies of the six valence orbitals the 3a to 2b A valid data sequence for performing such a calculation is shown below TITLE H2CO DZ BASIS OVGF VALENCE I E S SUPER OFF NOSYM NOPRINT ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE GF ACTIVE 3 TO 22 END CORE 1 TO 2 END I P SECOND 3 TO 8 END THIRD 3 TO 8 END ENTER The following points should be noted e The ACTIVE and CORE directives are used to discard the two inner shell functions from the OVGF calculation Note that it is also possible to truncate the virtual manifold employed although this has not been done in the present case e The data lines associated with the l P directive are used to nominate the required valence orbital ionisation energies and the particular level of perturbation theory SECOND and THIRD to be employed in this computation 28 GREEN S FUNCTION CALCULATIONS I THE OVGF METHOD e The set of molecular orbitals to be used in the transformation and subsequent GF calcu lation will be restored from the default section associated with closed shell SCF module or from the section explicitly nominated on the ENTER directive Now let us consider performing the above calculation in two separate jobs where the first carries out the SCF the second the transformation and OVGF calculation First the closed shel
164. is available e g in an MP2 calculation In both cases the user may need to ensure that the associated set of spinfree natural orbitals and where relevant SPIN natural orbitals are generated by specification of the NATORB directive s used to route the NOs to a nominated section on the Dumpfile We illustrate this effect by first considering the data requirements when performing a UHF wavefunction The following data sequence would be required when evaluating the properties based on a direct UHF calculation with the computation based on the alpha and beta UHF MOs routed to the default sections 1 and 2 respectively under implicit control of the ENTER directive TITLE H2CO 3A2 UHF PROPERTIES 3 21G BASIS MULT 3 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT UHF PROPERTY ATOMS ENTER The same calculation may be performed based on the spinfree and spin natural orbitals of the UHF wavefunction in this case the NATORB data lines will be used to route the spinfree and spin natural orbitals to sections 10 and 11 of the Dumpfile respectively and these orbitals will be used in computing the 1 electron properties thus TITLE H2C0 3A2 UHF NO BASED PROPERTIES 3 21G BASIS MULT 3 ZMATRIX ANGSTROM 13 ANALYSING THE WAVEFUNCTION N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT UHF PROPERTY ATOMS NATORB 10 NATORB SPIN 11 ENTER 5
165. isation 2 the initial hessian is to be constructed numerically through the TYPE 3 specifications on the VARIABLE Definition lines Using that from the previous HF 3 21G calculation could have been achieved by specifying RUNTYPE SADDLE ED3 3 the initial vectors in the CASSCF calculation will be the final set of HF 3 21G closed shell SCF orbitals restored from the default section 1 of the Dumpfile 16 TRANSITION STATE OPTIMISATION 78 16 3 MCSCF Transition State Optimisation We again use the H2CO to H2 CO transition structure location to illustrate performing MCSCF optimisations First we follow the CASSCF example performing the calculation in two steps Having located the transition state at the HF SCF level we then use the resulting geometry and possibly the hessian as a starting point for the MCSCF calculation The data for the HF optimisation is as given above that for the MCSCF optimisation as follows RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 3 21G BASIS MCSCF TOTAL ENERGY 113 223061249 ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 mom he x x a O Be RMN E 4 XH 6 90 0 2 0 0 VARIABLES co 1 1525832 TYPE 3 CHH 1 2981078 TYPE 3 XH 0 6596229 TYPE 3 ANG1 43 4018534 TYPE 3 ANG2 57 3815232 TYPE 3 END RUNTYPE SADDLE SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC1 DOC1 DOC2 DOC1 VOC2 UVOC1 UOC1 VOC1 END ENTER The following points should b
166. itu prior to commencing the geometry optimisation This is requested through spec ification of the TYPE keyword on the VARIABLE definition lines In such cases the corresponding part of the Hessian will be evaluated numerically prior to commencing optimisation Two settings are possible e TYPE 2 requests calculation of the diagonal force constant and involves an additional energy calculation e TYPE 3 requests calculation of the diagonal force constant and all off diagonal elements involving the variable This requires an additional energy plus gradient calculation for each variable nominated Thus the following data sequence would lead to explicit calculation of the complete Hessian for formaldehyde ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 TYPE 3 CH 1 099 TYPE 3 HCO 121 8 TYPE 3 END ANALYTIC DETERMINATION of the complete trial force constant matrix may be performed under control of a separate RUNTYPE HESSIAN with the resulting Hessian matrix subsequently restored from the Dumpfile in the optimisation job This method of determination is considered in more detail below see for example 2 16 2 Example 3 it is rarely justified in equilibrium geometry determination but is probably the most efficient method in the more complex process of locating tran sition structures At this point we merely present an example where the Hessian is restored though the FCM specification on the RUNT
167. l The following data sequence would be required if the user wished to compute the properties of the annihilated UHF wavefunction TITLE H2C0 3A2 annihilated UHF properties 3 21G BASIS MULT 3 ZMATRIX ANGSTROM 6 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT UHF PROPERTY ATOMS NATORB 10 ANNIHILATE NATORB SPIN 11 ANNIHILATE ENTER Note again that the NOs of the UHF and AUHF wave function are in fact identical the only difference lying in the occupation numbers Now let us consider the date requirements when computing properties at the optimum geometry derived from an MP2 calculation TITLE H2CO X141 MP2 DZ BASIS PROPERTIES ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END BASIS DZ RUNTYPE OPTIMISE PROPERTY ATOMS SCFTYPE MP2 NATORB 20 ENTER Having generated the MP2 optimised geometry the spinfree natural orbitals will be routed to section 20 on the Dumpfile and used in the subsequent properties calculation 13 ANALYSING THE WAVEFUNCTION 52 13 3 Localised Orbitals The following data sequence would be required in localising the valence SCF MOs using the Foster Boys algorithm where the LOCAL directive specifies those orbitals deemed to be active in the localisation process RESTART TITLE H2CO 3 21G DEFAULT BASIS VALENCE LMOs ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099
168. l case valid data sequences for performing the calculation are shown below Run I The Scf Job TITLE H2CO 3 21G SCF PRIOR TO OVGF CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM N Cc 0 1 1 203 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER The only obvious point to note is the user of the SUPER directive in requesting full integral list generation required in the subsequent transformation Run II The Transformation and OVGF Job RESTART TITLE H2CO 3 21G OVGF CALCULATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END RUNTYPE GF ACTIVE 3 TO 22 END CORE 1 TO 2 END I P SECOND 3 TO 8 END THIRD 3 TO 8 END ENTER The following points should be noted e The SCF computation is BYPASS ed e The SCF vectors from the first run will be restored from Section 1 of the Dumpfile the default section associated with the closed shell SCF MOs 29 GREEN S FUNCTION CALCULATIONS II THE TDA METHOD 177 29 Green s Function Calculations II The TDA Method The second module designed to incorporate the effects of electron correlation in the computa tion of molecular ionisation potentials employs the so called two particle hole Tamm Dancoff approximation 2ph TDA for the one particle green s function 46 47 The TDA method provides at least a qualitative account of ionisation phenomena when the independent particle picture of ionisation no
169. lculation i e CNTRL 15 Singly excited configurations with respect to each of the default reference configurations SINGLES ALL will be included regardless of their computed energy lowerings The set of reference configurations to be employed will follow the same algorithm used in the closed shell case above i e the SCF configuration plus those generated from this configuration by including i for each symmetry IRREP the doubly excited configuration arising from excitation of the highest occupied DOMO of that symmetry to the lowest virtual orbital VMO of the same symmetry and ii the lowest singly excited configu ration again arising from the highest occupied DOMO to the lowest VMO of the same symmetry In the present example this will correspond to the SCF configuration the dou ble and single excitation arising from the DOMO 5a to VMO 6aj the double and single excitation arising from the DOMO 1b to VMO 2b and the double and single excitation arising from the DOMO 1b s to VMO 3b 2 Note that the DOMO involved in the latter configurations is now the lbg given that the 2b is now singly occupied and again the absence of excitations involving a2 MOs given the absence of such orbitals involved in the occupied manifold This again results in a total reference set of 7 functions as shown thus in the job output numbers of open shells and corresponding main configurations 1 18 1 2 3 4 5 13 17 ae SCF configuration 1 18 1 2 3 4 6 1
170. le below the structure of ethylene has been defined using a z matrix for two of the hydrogen atoms the remaining four atoms are input as cartesian coordinates Cartesian or internal coordinates can be defined as variables in the geometry optimisation Constructing molecules using mixed z matrix and cartesian input is discussed in greater detail in Part 3 TITLE ETHYLENE ZMATRIX ANGSTROM CARTESIANS 0 0 000 0 000 0 000 0 0 000 0 000 CC H WIDTH 0 000 DEPTH H WIDTH 0 000 DEPTH INTERNALS H 2 CH 1 CCH 3 TWIST H 2 CH 1 CCH 5 180 0 VARIABLES CC 1 4 CH 1 0 WIDTH 0 8 DEPTH 0 5 CCH 120 0 TWIST 10 0 END RUNTYPE OPTIMISE ENTER 15 5 Energy only Geometry Optimisation Finally an optimisation procedure is available which uses a modified Fletcher Powell method with numerical differentiation of energies to produce gradients This procedure is intended for use with methods for which analytic gradients are not available and is requested under RUNTYPE OPTIMIZE control through specification of and additional keyword FP on the RUNTYPE data line The following example demonstrates FP usage TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF OPTIMISATION ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE FP ENTER 15 GEOMETRY OPTIMISATION 66 15 6 Post Hartree Fock Geometry Optimisation While the examples above of internal coordinate car
171. le job 24 TABLE CI CALCULATIONS 133 TITLE H2CO 2B2 3 21G CISD TABLE CI CALCULATION CHARGE 1 MULT 2 ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT TRAN 5 SELECT SYMMETRY 3 SPIN 2 CNTRL 15 SINGLES 1 CONF 1 18 12345 13 17 ROOTS 1 THRESH 30 10 CI DIAG EXTRAP 2 ENTER Considering the changes to the closed shell run the following points should be noted e The OPEN directive is not explicitly required since it we are performing a default high spin RHF calculation If presented it should be specified prior to the Table Cl data e The set of vectors used in the Table Cl transformation will be restored from section 5 of the Dumpfile specified by the TRAN 5 data line having been placed in that Section by the SCF process Note again that this corresponds to the default section number of the energy ordered SCF eigenvectors generated by the open shell SCF module see Table 1 e The majority of data changes appear within the SELECT data Thus the SPIN directive now defines the spin multiplicity of the doublet Cl wavefunction SYMMETRY specifies the IRREP of the 2B state sequence number 3 while CNTRL defines the number of active electrons now 15 e The first integer of the CONF data line indicates a single open shell orbital the second the sequence number of that orbital the 2b2 no 16 in the reordered sequence with the remaining integers the
172. le way to proceed is to use an appropriate set of closed shell vectors as the starting guess Assuming again that the closed shell calculation of 2 has been successfully completed the following data sequence would be required in performing a UHF calculation on the cation using the J K supermatrix and eigenvectors from the closed shell run RESTART TITLE H2CO 2B2 3 21G DEFAULT BASIS UHF CALCULATION CHARGE 1 MULT 2 BYPASS ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE UHF ENTER Note that the default VECTOR and ENTER sections are still applicable in this example In deciding on an appropriate set of eigenvectors to initiate an open shell UHF calculation the program will first examine the Dumpfile to see if the default UHF VECTORS sections have been written to by a previous job If these sections exist the program will utilise the resident vectors as a starting point for the current UHF calculation If not as in the present example the closed shell default vectors section will be used to provide the starting guess for both a spin and 3 spin MOs as written to in Run I If this section is not present the calculation will revert to an atomic GUESS The UHF calculation will proceed to use the default open shell UHF vectors specification for output of the eigenvectors see Table 1 Thus the data sequence above is equivalent to presenting the data lines VECTORS 1 ENTER 2 3
173. les are quite distinct from the Direct Cl module described above 2 The aim of both modules is to calculate one or more roots of a given symmetry from a Multi Reference Cl calculation Both modules can also calculate transition moments TM between states of the same symmetry or states of different symmetry in addition to Cl Dipole and Quadrupole moments The modules are based on the Table Cl algorithm of R J Buenker 39 the main practical difference between this and the Direct Cl module being the use of configuration selection and energy extrapolation 3 The final list of selected configurations is derived from an initial list of configurations generated by single plus double excitations from a user specified list of reference functions Note that there is effectively no limit on this number of initial configurations The selection and extrapolation procedure may be applied to a number of roots of a given secular problem The Direct Cl module of course considers explicitly all configurations which are single and double excitations of a given set of reference configurations this module is typically limited to the lowest few roots of a given symmetry 4 RUNTYPE CI is in fact a combination of tasks requesting integral generation SCF and finally the various sub tasks associated with the Table Cl calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the
174. llows TITLE H2CO 3 21G CISD 3 REFERENCE CI SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 10 10 CONF 2222222200 2222220220 2222202202 ENTER 23 5 Direct CI Multi reference MP2 and MP3 Calculations As an alternative to the multi reference Cl calculations described in the previous section the user may also perform multi reference MP2 and MP3 calculations 49 50 51 52 The basic principle is that the program computes the wavefunction in the basis of those reference functions nominated by the user This wavefunction is then used as the reference function for generating the single and double excitations and the subsequent solving of the perturbation equations Data input when performing multi reference MP calculation is very similar to that required for a multi reference Cl calculation e g the following job is the multi reference MP2 equivalent of the multi reference Cl example of the previous section 23 DIRECT CI CALCULATIONS where the MP 2 directive switches the program to do the multi reference MP2 calculation TITLE H2CO 3 21G CISD 3 REFERENCE MP2 SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 10 10 MP 2 CONF 22222222 22222202 22222022 ENTER ONO NOOO The output shows a block like SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SESSS
175. locating the required tran sition state followed by the saddle point location itself where the FCM keyword on the RUNTYPE SADDLE line requests utilisation of the pre computed hessian Finally we derive the vibrational frequencies at the optimised geometry again under control of RUNTYPE HESSIAN Again note that this final step will be performed at the geometry determined in the preceding SADDLE run TITLE HCOH lt gt H2CO 1A TS 6 31G OPTIMIZE FREQUENCIES ZMAT ANGS C 0 1 C0 H 1 CH1 2 OCH1 H 1 CH5 2 H5C0 3 180 0 VARIABLES OCH1 56 3 CO 1 27 CH1 1 22 CH5 1 10 H5C0 115 8 END BASIS 6 31G Calculate initial hessian RUNTYPE HESSIAN ENTER Locate transition State restoring above hessian RUNTYPE SADDLE FCM MINMAX 10 10 XTOL 0 0001 ENTER Calculate Vibrational frequencies at TS geometry RUNTYPE HESSIAN ENTER 33 4 Geometry Optimisation and Raman Intensities In this example we initially optimise the geometry of H2CO followed by a computation of the Raman intensities at the optimised geometry TITLE H2C0 3 21G DEFAULT BASIS OPTIMISATION RAMAN INTENSITIES ZMATRIX ANGSTROM C 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END Optimise molecular geometry RUNTYPE OPTIMIZE XTOL 0 0001 ENTER 33 MULTIPLE RUNTYPE CALCULATIONS 195 Raman intensities at optimised geometry RUNTYPE RAMAN ENTER 33 5 MCSCF Force Constant Calculation In this example we per
176. lti reference MP2 and MP3 Calculations 23 6 Direct Cl Restarting Calculations 23 7 Direct Cl Property Calculations 24 Table Cl Calculations 24 1 Table Cl and Molecular Symmetry 24 2 Conventional Table Cl Calculations 0 a a eee eee 24 3 Conventional Table Cl Single reference CISD Calculations 24 4 Conventional Table Cl Freezing and Discarding Orbitals 24 5 Conventional Table Cl Multi refe rence CI Calculations 24 6 Conventional Table Cl Default Sub module Attributes 2 20 24 7 Conventional Table Cl Restarting Calculations 24 8 Semi direct Table Cl Calculations 24 9 Semi direct Table Cl Multi reference Cl Calculations 24 10Semi direct Table Cl Default MRDCI Calculations 24 11Semi direct Table Cl Freezing and Discarding Orbitals 24 12Semi direct Table Cl Default Sub module Attributes 24 13Semi direct Table Cl Restarting Calculations 25 Full Cl Calculations 26 Coupled Cluster Calculations 27 Cl Geometry Optimisation 27 1 Direct Cl Geometry Optimisation 27 2 Table Cl Geometry Optimisation 106 108 109 112 113 114 115 116 117 121 122 124 125 127 131 136 139 140 141 143 145 150 154 156 158 160 165 CONTENTS 27 3 CCSD Geometry Optimisation 0 0 000000 eee eee 28 Green s Function Calculations
177. minated on the VECTORS line RESTART NEW TITLE H2CO DZ 3A2 UHF SPIN DENSITIES MULT 3 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS DZ RUNTYPE ANALYSIS PROPERTY 19 C 19 0 19 H END 24 TABLE CI CALCULATIONS 124 VECTORS 12 ENTER 24 Table CI Calculations GAMESS UK now contains two separate modules for performing Table Cl calculations the original Conventional module that involves explicit storage of the Cl hamiltonian on disk and a new semi direct module that avoids explicit storage of the hamiltonian and is capable of handling significantly larger secular problems While the Conventional module will ultimately be phased out our intention at this stage is to support both so that the data requirements and file handling characteristics of both are described below Table Cl calculations are performed under control of the RUNTYPE Cl specification with data input characterising the nature of the Cl introduced by a data line with the keyword MRDCI in the first data field Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS or ENTER Before detailing example data files for performing both Conventional and Semi direct Table Cl calculations on the X A state of formaldehyde we mention some general points on conducting such calculations 1 The data requirements computational strategy and overall philosophy of the Table Cl modu
178. ming the calculation are shown below Run I The Scf Job TITLE H2CO 3 21G SCF PRIOR TO TDA CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END ENTER 179 The only obvious point to note is the user of the SUPER directive in requesting full integral list generation required in the subsequent transformation Run II The Transformation and TDA Job RESTART TITLE H2CO 3 21G TDA CALCULATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE TDA ACTIVE 3 TO 22 END CORE 1 TO 2 END I P BAND 3 TO 8 END ENTER The following points should be noted e The SCF computation is BYPASS ed e The SCF vectors from the first run will be restored from Section 1 of the Dumpfile the default section associated with the closed shell SCF MOs 30 Linear Response Calculations I The RPA Method GAMESS UK incorporates two modules designed to perform calculations of electronic transition energies and corresponding oscillator strengths using either the Random Phase Approximation RPA method or the Multiconfigurational Linear Response MCLR procedure The RPA 30 LINEAR RESPONSE CALCULATIONS I THE RPA METHOD 180 calculations may be performed either within the conventional approach where the two electron integrals are transformed or with a direct implementation The first of these methods
179. mitted the EXTRAP specification of DIAG corresponding to the default value 24 7 Conventional Table CI Restarting Calculations In the examples considered above we have assumed that the Table Cl job completes in the time allocated This may not be the case and we need consider restarting the computation in a controlled fashion Such a requirement may be met in RUNTYPE Cl processing when e the associated integral evaluation or SCF has not completed due either to lack of time or to convergence problems in the SCF e Table Cl processing itself has not completed In the present implementation it is not possible to restart Table Cl processing within a given sub module in the event of job termination due to lack of time It is possible however to fragment 24 TABLE CI CALCULATIONS 142 the calculation into separate sub module runs through the use of the BYPASS directive on the sub module data lines In such usage restarting the computation is achieved under control of the RESTART directive which nominates the Cl task for restarting Consider the Table Cl job of 16 5 we show below the data files for fragmenting this Cl into e symmetry adaptation and integral transformation e configuration selection and hamiltonian construction e Davidson diagonalisation The subset of interfaces to be saved between the various steps is given in Table 8 Adaptation and Transformation RESTART CI TITLE H2CO 3 21G DEFAULT BASIS MRDCI 4M 1R
180. mplete run the following points should be noted e The SCF computation is BYPASS ed e Note that the default VECTORS and ENTER data will still apply in the RESTART job with the default VECTORS section for closed shell SCF orbitals that is written in the startup job now being used as the source of eigenvectors The calculation may be further subdivided by splitting Run above into separate integral trans formation and Cl runs using the BYPASS keyword on the data lines of the appropriate Table Cl sub modules to deactivate the computation accordingly Thus Run Ila The Transformation Job RESTART TITLE H2CO 3 21G TABLE CI 4M 1R TRANSFORMATION SUPER OFF NOSYM BYPASS SCF ZMAT ANGSTROM 0 0 1 1 203 24 TABLE CI CALCULATIONS 149 H 11 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT TABLE BYPASS SELECT BYPASS SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES ALL CONF 012345 13 17 18 012345 14 17 18 012345 13 17 19 413141819 1234517 END ROOTS 1 THRESH 2 2 CI BYPASS NATORB BYPASS ENTER Thus BYPASS is appended to the data lines requesting those Table Cl sub modules SELECT Cl and NATORB to deactivate the associated processing Run IIb The Table CI Job RESTART TITLE H2CO 3 21G TABLE CI 4M 1R SELECTION AND CI SUPER OFF NOSYM BYPASS SCF TRAN ZMAT ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI DIRECT TABLE SELECT SYMMETRY
181. n with subsequent BYPASS ing of the transformation in the Cl job Thus Run Ila The Transformation Job RESTART TITLE H2CO 3 21G INTEGRAL TRANSFORMATION SUPER OFF NOSYM BYPASS SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE TRANSFORM ACTIVE 5 TO 22 END CORE 1 TO 4 END ENTER Run IIb The Full Ci Job RESTART TITLE H2CO 3 21G VALENCE FULL CI CALCULATION SUPER OFF NOSYM BYPASS TRANSFORM ZMATRIX ANGSTROM 0 26 COUPLED CLUSTER CALCULATIONS 165 1 203 099 2 121 8 0 1 H 1 H 1 099 2 121 8 3 180 0 t 1 END RUNTYPE CI ACTIVE 5 TO 22 END CORE 1 TO 4 END RUNTYPE CI FULLCI 18 4 4 ENTER 26 Coupled Cluster Calculations Coupled cluster CC calculations 41 are performed under control of the RUNTYPE CI spec ification with data input characterising the nature of the Cl introduced by a data line with the character string CCSD as the first four characters of the first data field Termination of this data is accomplished by presenting a valid Class 2 directive such as VECTORS Before detailing example data files for performing CC calculations on the X A state of formaldehyde we mention some general points on conducting such calculations 1 RUNTYPE Cl represents a combination of tasks requesting integral generation SCF integral transformation and finally the coupled cluster calculation itself While in simple cases it may be feasible to perform all ste
182. nd co workers 36 While we delay a detailed account of using this method until Part 4 we note here that e the algorithm may be invoked through the LSEARCH directive see Part 4 section 9 8 16 TRANSITION STATE OPTIMISATION 75 e additional data input is required in particular specification of the two minima in volved This is achieved through the VARIABLE definition lines of the ZMATRIX directive see for example 4 9 8 2 a modified variant of the hill walking algorithm due to Jorgensen and Simons 37 38 16 1 DFT Transition State Optimisation We again use the H2CO to H2 CO transition structure location to illustrate performing DFT optimisations We perform the calculation in two steps initially locating the transition state at the HF SCF level then using the resulting geometry and in some cases the hessian as a Starting point for the DFT calculation Note that it is not possible at present to use RUNTYPE HESSIAN in DFT calculations and the user should typically i restore the initial hessian in such a calculation from an initial HF transition state location or ii use the TYPE 3 VARIABLES specification to compute an initial DFT hessian HF STO 3G Optimisation TITLE H2 CO lt gt H2CO 1A TS STO3G SCF TOTAL ENERGY 112 1291164 AU ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES CO 1 134 TYPE 3 ANG1 43 7 TYPE 3
183. ng the reference configurations and selection attributes in SELECT 4 In the interests of efficiency the Table Cl module again requires as input a data base of pattern symbolic matrix elements for use in both the selection process and in construction of the final Cl Hamiltonian over the selected configurations These pattern elements are assumed to reside on a data set with LFN table ci The data base may be constructed in a given run of the Table Cl module by entering the TABLE sub module prior to SELECT and Cl Thus the following data driven loading of sub modules 24 TABLE CI CALCULATIONS 145 MRDCI DIRECT TABLE SELECT CI NATORB would be typical of that required when the user is explicitly constructing the TABLE data set in a given run of the program This is now the recommended route in semi direct calculations rather than the user allocating a pre generated version of the data set prior to executing the Table Cl modules Note that failure to correctly allocate table ci when using the above sequence will lead to an error condition 5 Several direct access files will be generated under RUNTYPE Cl processing For Semi direct Table Cl calculations these include e the Mainfile ED2 and Dumpfile ED3 e the Transformed Integral file ED6 e the Scratch file ED7 e temporary files for sorting both transformed integrals and intermediate matrices in the CI calculation the Sortfile e in addition to the standard dir
184. nge functional 17 and Lee Yang and Parr correlation LYP correlation energy functional 18 Over riding this default may be achieved through the following DFT keywords HFEX The keyword HFEX selects the Hartree Fock exchange term as the exchange functional BECKE88 The keyword BECKE88 selects the default Becke88 exchange functional This is a gradient corrected exchange energy functional with correct 1 r asymptotic behaviour of the exchange energy density LYP The keyword LYP selects the default Lee Yang and Parr correlation energy functional NOCORR The keyword directive NOCORR selects the null functional for the correlation energy i e it switches off all correlation energy functionals B3LYP The keyword B3LYP selects the hybrid exchange correlation energy functional due to Becke 22 S VWN or SVWN The keyword S VWN or SVWN selects the LDA exchange functional and the Vosko Wilk and Nusair VWN correlation functional 23 B P86 or BP86 The keyword B P86 or BP86 selects the Becke88 exchange energy func tional 17 and the Perdew 1986 gradient corrected correlation functional 24 B97 The keyword B97 selects the Becke97 hybrid exchange correlation energy functional 25 B97 1 The keyword B97 1 selects the Becke97 hybrid exchange correlation energy func tional as it was reparametrised by Hamprecht et al 26 25 B97 2 The keyword B97 2 selects the Becke97 hybrid exchange correlation energy func tional as it was rep
185. o used as a scratch file in the solution of the coupled Hartree Fock equations e temporary files for sorting both transformed integrals the Sortfile and intermediate matrices e MP2 polarisability calculations are more complex with more files required these include EDO ED16 and ED17 Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 5 It is possible to calculate frequency dependent polarisabilities at both real and imaginary frequencies and to obtain dispersion coefficients It is also possible to obtain excitation energies using the RPA method for closed shell SCF wavefunctions 18 POLARISABILITY CALCULATIONS 98 6 SCF convergence should be as a general rule be tightened under control of the THRESH directive when proceeding to any of the coupled Hartree Fock steps within the program Note that this is implemented automatically under control of the POLARISABILITY runtype and should only be considered when using the BYPASS directive to omit the associated SCF processing Example 1 Polarisability of HCO TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF POLARISABILITY ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES CO 1 203 CH 1 099 HCO 121 8 END RUNTYPE POLARISABILITY ENTER Example 2 Open shell RHF Polarisability Calculation In the example below we consider an open shell RHF polarisability calculation of the Ba state of H2COT o
186. ocessing when e the associated integral evaluation or SCF has not completed due either to lack of time or to convergence problems in the SCF e the integral transformation has not completed due to lack of time e Cl processing has not completed due invariably to lack of time or to convergence problems in the iterative processing associated with the Davidson diagonalisation Restarting the computation is achieved under control of the RESTART directive which nomi nates the Cl task for restarting Consider the multi reference Cl job described above and let us assume the job dumped during the Davidson diagonalisation The full data input for the restart job would be as follows RESTART CI TITLE H2CO 3 21G CISD 3 REFERENCE CI SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 10 10 CONF 22222222 22222202 22222022 ENTER ONO NOOO The only change to the startup job is the RESTART directive Note that the default VECTORS and ENTER data will still apply in the RESTART job with the default VECTORS section for closed shell SCF orbitals that is written in the startup job now being used as the source of eigenvectors The following points should be noted e Within the Direct Cl module itself restarts are only possible if the iterative diagonalisation has been initiated i e if the startup job runs out of time in the Cl Hamiltonian builder or in the post
187. odule loaded under RUNTYPE CI control so that the DIRECT directive is not required The division of the molecular orbital space into an internal and external space typically specified by the DIRECT directive is now handled automatically with the internal space comprising all doubly occupied SCF MOs orbitals the external space all SCF virtual MOs All electrons will be deemed active in the Cl The SYMMETRY and SPIN of the Cl wavefunction are taken to be those of the SCF wavefunction A single reference configuration will be employed just the SCF configuration the final configuration space will include all single and double excitations from this SCF reference configuration The spinfree natural orbitals will be written to section 11 of the Dumpfile The full data specification corresponding to the defaults generated from the above data file is as shown before namely TITLE H2CO 3 21G CISD DIRECT CI CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM 0 23 DIRECT CI CALCULATIONS 114 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI DIRECT 16 8 14 CONF 22222222 NATORB 11 O PRINT ENTER 23 2 2 Open shell Systems Let us now consider a Direct Cl calculation on the 7By state of H2CO again using default options available within the module A valid data sequence for performing such a calculation is shown below TITLE H2CO 2B2 3 21G DEFAULT CISD DIRECT CI OPTION MULT 2 CHA
188. on An examination of the input SCF orbitals the energy weighted orbitals from the Bo calculation reveals the following ordering of the doubly occupied orbitals DOMOs M O 1 2 3 4 5 6 7 8 symmetry la 2a 3a 4a I1bg 5a 1b 2b The input orbitals must be arranged such that the doubly occupied manifold precedes the open shell orbitals grouped according to shell In the present case with 7 DOMOS and 1 singly occupied orbital we must reorder the input MOs such that the 1b orbital occupies the 8th position in the input list Such a reordering is accomplished by the SWAP directive as in the following data sequence RESTART TITLE H2C0 2B1 3 21G DEFAULT BASIS OPEN SHELL RHF CHARGE 1 MULT 2 BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END 4 RHF OPEN SHELL CALCULATION 13 SWAP 7 8 END ENTER Note that the 7B eigenvectors will again be stored in the default open shell vectors sections 4 and 5 thus overwriting the Bz orbitals generated in Run II above To keep the orbitals from both open shell calculations will now require explicit specification of the sections to be used in storing the vectors this could be achieved as follows VECTORS 5 SWAP 7 8 END ENTER 6 7 where the initial vectors will be the energy ordered 7Bz MOS and the 7B vectors will be written to sections 6 non canonicalised and 7 energy ordered 4 1 Direct RHF Open Shell Calculation A valid da
189. on method driven under RUNTYPE OPTXYZ control has proved moderately robust and reliable The following data demonstrates OPTXYZ usage where the x y and z coordinates of the component atoms are input under control of the GEOMETRY directive here in atomic units TITLE H2CO GEOMETRY TEST GEOMETRY 0 0000000 0 0000000 0 9998722 6 C 0 0000000 0 0000000 1 2734689 8 0 0 0000000 1 7650653 2 0942591 1H 0 0000000 1 7650653 2 0942591 1H END RUNTYPE OPTXYZ ENTER The following points should be noted e It is now possible to freeze coordinates under OTPXYZ control This is achieved by appending the keyword NOOPT to the geometry definition lines of the appropriate centres as specified by the GEOMETRY directive Thus in the example above the H atoms may be held at their input geometry during optimisation using the following data TITLE H2CO GEOMETRY TEST GEOMETRY 0 0000000 0 0000000 0 9998722 6 C 0 0000000 0 0000000 1 2734689 8 0 0 0000000 1 7650653 2 0942591 1 H NOOPT 0 0000000 1 7650653 2 0942591 1 H NOOPT END RUNTYPE OPTXYZ ENTER e Note that is it is still possible to use the ZMATRIX to input the molecular geometry in such calculations although the starting variables provided will not be explicitly updated during the course of the subsequent optimisation 15 GEOMETRY OPTIMISATION 65 15 4 Mixed Z matrix and Cartesian Optimisation It is also possible to perform mixed z matrix cartesian optimisations In the examp
190. on of the coupled Hartree Fock equations calculation of analytic second derivatives and finally the calculation of the polarizability derivatives While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 2 Several files will be generated under RUNTYPE RAMAN processing These include e the Mainfile ED2 and Dumpfile ED3 22 CALCULATION OF RAMAN INTENSITIES 107 e the Scratch file ED7 e the semi transformed ED4 and transformed ED6 integral files note that ED4 is also used as a scratch file in the solution of the coupled Hartree Fock equations e the Hamiltonian file ED12 which acts to store the derivative Fock operators e temporary files for sorting both transformed integrals the Sortfile and intermediate matrices in the Hessian calculation Any restart jobs will require ED6 and ED12 being saved in addition to the Dumpfile ED3 and Mainfile ED2 Example Raman Intensities for HCO Run I Geometry Optimisation TITLE H2CO 3 21G DEFAULT BASIS GEOMETRY OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE XTOL 0 0001
191. ore orbitals are both of a1 symmetry and have sequence 24 TABLE CI CALCULATIONS 137 numbers 1 and 2 The virtual orbitals are of b SCF sequence no 21 and a SCF sequence no 22 symmetry and as the highest orbital of each IRrep correspond to the 6th orbital of b symmetry and the 12th orbital of a symmetry respectively The TRAN data will then appear as follows TRAN CORE DISCARD 2000 core MOs 12 1010 discarded MOs 12 6 where two additional data lines are associated with each category the first specifying the number of orbitals within each IRrep the second the sequence number of the orbitals in question Note again that the sequence numbers refer to the numbering within each IRrep Thus if we were to also freeze the 1b orbital the revised TRAN data would appear as follows TRAN CORE DISCARD 2010 core MOs 121 1010 discarded MOs 12 6 Before detailing the Table Cl data we should mention that the revised numbering scheme used in the specification of for example the reference configurations is that in effect after the freezing and discarding of orbitals Having effectively removed three orbitals of a symmetry and one of b from the subsequent Cl the table below presents the final orbital numbering to be used in CONF specification 24 TABLE CI CALCULATIONS 138 IRrep IRrep SCF Sequence Table Cl Occupation No No Sequence No No ay 1 3 1 2 0 4 2 2 0 6 3 2 0 10 4 0 0 12 5 0 0
192. ore stringently a typical tactic when subjecting the optimised geometry to a subsequent frequency anal ysis e It is NOT possible to either freeze or discard orbitals when performing M ller Plesset ge ometry optimisations Presenting the ACTIVE directive in such calculations will terminate the run MP3 RHF Optimisation Data TITLE H2CO 3 21G DEFAULT BASIS MP3 RHF OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE MP3 XTOL 0 0001 ENTER MP2 UHF Optimisation Data We consider performing the calculation in two steps where the first carries out a UHF calcu lation the second the MP2 UHF geometry optimisation Valid data sequences for performing the calculation are shown below where we again BYPASS initial integral evaluation in the MP2 job Note again that this BYPASS ing of the integral evaluation necessitates the introduction of SUPER OFF data line in the initial UHF job Run I The UHF Calculation 16 TRANSITION STATE OPTIMISATION TITLE H2C0 DEFAULT BASIS UHF CALCULATION CHARGE 1 MULT 2 SUPER OFF ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END SCFTYPE UHF ENTER Run II The MP2 UHF Calculation RESTART NEW TITLE H2CO 2B2 3 21G DEFAULT BASIS MP2 UHF OPTIMISATION CHARGE 1 MULT 2 BYPASS SUPER OFF ZMATRIX AN
193. perform the calculation from scratch using just the computed geometry from the optimisation Initially we show the data to re generate a set of MCSCF vectors at the transition state geometry followed by the force constant run MCSCF run at the transition state geometry RESTART NEW TITLE H2 CO lt gt H2CO 1A 3 21G MCSCF AT OPT TS GEOMETRY ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 VARIABLES co 1 2034717 CHH 1 3040659 XH 0 7415189 ANGI 41 4927811 ANG2 56 6325324 END SCFTYPE MCSCF MCSCF ORBITAL m om gt oe a nO BP PONE 17 FORCE CONSTANT CALCULATIONS 89 COR1 COR1 COR1 DOC1 DOC1 DOC1 DOC2 DOC1 VOC2 VOC1 UOC1 UOC1 END ENTER MCSCE force constants RESTART NEW TITLE H2 CO lt gt H2CO 1A TS 3 21G MCSCF FORCE CONSTANTS FREQ 1825 4 767 8 900 3 1259 4 1720 5 3185 4 ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 m oo oe aA Oo BR BONE VARIABLES co 1 2034717 CHH 1 3040659 XH 0 7415189 ANGI 41 4927811 ANG2 56 6325324 END RUNTYPE FORCE SCFTYPE MCSCF MCSCF ORBITAL COR1 COR1 COR1 DOC1 DOC1 DOC1 DOC2 DOC1 VOC2 VOC1 UOC1 U0OC1 END ENTER 17 2 Analytic Force Constants Analytic derivatives are available for closed shell SCF and RHF open shell wavefunctions to gether with MP2 closed shell wavefunctions At present UHF or pair GVB wavef
194. performing these calculations A 2ph TDA calculation is to performed on the formaldehyde molecule with estimates required of the ionisation energies of the six valence orbitals the 3a to 2b2 A valid data sequence for performing such a calculation is shown below TITLE H2C0 DZ BASIS TDA VALENCE I E S SUPER OFF NOSYM NOPRINT ZMATRIX ANGSTROM N Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END RUNTYPE TDA ACTIVE 3 TO 22 END CORE 1 TO 2 END I P BAND 3 TO 8 END ENTER The following points should be noted e The ACTIVE and CORE directives are used to discard the two inner shell functions from the TDA calculation Note that it is also possible to truncate the virtual manifold employed although this has not been done in the present case e The data lines associated with the l P directive are used to nominate the required valence orbital ionisation energies through the BAND data line e The set of molecular orbitals to be used in the transformation and subsequent TDA calculation are restored from the default section associated with the closed shell SCF module section 1 or from the section explicitly nominated on the ENTER directive Now let us consider performing the above calculation in two separate jobs where the first carries out the SCF the second the transformation and TDA calculation First the closed shell case 30 LINEAR RESPONSE CALCULATIONS I THE RPA METHOD valid data sequences for perfor
195. ps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 2 Several direct access files will be generated under RUNTYPE CI processing For coupled cluster calculations these include e the Mainfile ED2 and Dumpfile ED3 e the semi transformed ED4 and transformed ED6 integral files e the Scratch file ED7 e temporary files for sorting transformed integrals the Sortfile Any restart jobs will require ED6 being saved in addition to the Dumpfile ED3 and Mainfile ED2 3 In addition to the direct access files above the coupled cluster module uses a variety of conventional unformatted FORTRAN data sets 4 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM in the SCF run 26 COUPLED CLUSTER CALCULATIONS 166 A CC calculation is to to be performed on the Hy2CO molecule Before detailing the data requirements let us again consider the mechanisms for restricting the scale of the all electron computation since this will often be required in coupled cluster treatments The user will typically wish to e freeze inner shell orbitals performing a valence only coupled cluster cal
196. ptimising the molecular geometry in Run and calculating the polarisability at this geometry in Run II Run I Geometry Optimisation TITLE H2CO 2B2 DZP BASIS OPEN SHELL RHF CHARGE 1 MULT 2 SUPER OFF ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END BASIS DZP RUNTYPE OPTIMISE XTOL 0 0005 ENTER Run II Polarisability calculation 18 POLARISABILITY CALCULATIONS 99 Note the form of the RESTART directive below since the geometry optimisation has been conducted immediately prior to the POLARISABILITY run it is sufficient to use just RESTART when the optimised geometry will be read from the Dumpfile and override the ZMATRIX data in the input stream RESTART TITLE H2CO 2B2 DZP BASIS POLARISABILITY CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 O 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END BASIS DZP RUNTYPE POLARISABILITY ENTER Example 3 MP2 Polarisabilities The corresponding MP2 calculation to that of Example 1 above is given below where we now optimise the molecular geometry at the MP2 level and compute the MP2 polarisability at this optimised geometry Run I Geometry Optimisation TITLE H2C0 DZ BASIS MP2 RHF OPTIMISATION ZMATRIX ANGSTROM Cc 0 1 C0 H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END BASIS DZ RUNTYPE OPTIMISE SCF
197. r data set 5 As mentioned above generation of a valid Mainfile for subsequent use in the integral transformation routines requires the data line SUPER OFF NOSYM in the SCF run A Full Cl calculation is to performed on the H2CO molecule Before detailing the data re quirements let us again consider the mechanisms for restricting the scale of the all electron computation since this will often be required in full Cl treatments The user will typically wish to e freeze inner shell orbitals performing a valence only full Cl calculation e discard certain virtual orbitals from the Cl calculation typically the high energy inner shell complement orbitals The CORE and ACTIVE directives of the transformation module are provided for controlling the final subset of orbitals for inclusion in the Cl The freezing of core or inner shell orbitals is achieved by nominating the sequence nos of those orbitals to be frozen under control of the CORE directive The discarding of orbitals is performed under control of the ACTIVE directive which specifies the sequence nos of the active set of orbitals to appear in the Cl Turning to the H2CO calculation the following data sequence would be required to freeze the two inner shell and two lowest valence SCF MOs while retaining all virtual orbitals in the subsequent full Cl treatment TITLE H2CO 3 21G BASIS VALENCE FULL CI SUPER OFF NOSYM NOPRINT ZMATRIX ANGSTROM 0 0 1 1 20
198. r first in the final list of orbitals preceding the list of external orbitals In some cases this ordering will not be obeyed in the input set of MOs and the user must under control of the ACTIVE directive re order the input set to achieve the required ordering This highlights the underlying requirement of orbital occupancy specification under control of CONF namely that occupancy specification refers to the ordering of MOs as specified by the ACTIVE directive Consider initially an example where the ordering of the SCF MOs is consistent with the spec ification of the reference set and where reordering ACTIVE will not be required although it may still be required in the freezing discarding of MOs Assume that we wish to perform a 23 DIRECT CI CALCULATIONS 117 3 reference Cl calculation for H2CO comprising the SCF configuration that arising from the double excitation 1b to 2b and that from the double excitation 5a to 6a This leads to the following occupation patterns for the 3 reference functions Reference la 2a 3a 4a lbo 5a 1b 2b 2b 6a Function 1 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 0 2 2 0 3 2 2 2 2 2 0 2 2 0 2 Then the internal space must in addition to the ground state doubly occupied SCF MOs include the 2b and 5a virtual orbitals i e NINT 10 Then each data line of the CONF directive will comprise ten integers reflecting the occupation pattern above The full data input for the job would be as fo
199. ral MCSCF 2 electron integral 2 electron integral Thus for example attempting to use the integral file produced in default during a closed shell SCF calculation P supermatrix in a subsequent open shell computation must be considered an invalid operation and will lead to an error condition 5 RUNTYPE and SCFTYPE define the computation to be carried out RUNTYPE defines the particular task to be undertaken while SCFTYPE specifies the form of wavefunction calculation to be employed throughout the task RUNTYPE options are given in Table 3 while the categories of wavefunction that may be requested under control of the SCFTYPE directive are shown in Table 4 Note that additional directives may be required in further characterising the SCFTYPE specification The default program options are RUNTYPE SCF SCFTYPE RHF i e single point restricted Hartree Fock SCF computation 6 LEVEL and DIIS define the convergence aids to apply throughout the computation Note that the format of the LEVEL directive i e the number of level shifters to be specified is dependent on the SCFTYPE setting 7 The VECTORS directive determines the method to be used in generating a trial set of eigenvectors for the SCF calculation The program incorporates many options in default trial vectors are generated via the ATOMS option involving the superposition of atomic SCF densities 8 In default the final set of converged vectors will be written to Section
200. ransformation and MP2 calculation Valid data sequences for performing the calculation are shown below where we again BYPASS integral evaluation in the MP2 job Note again that this BYPASS ing of integral evaluation necessitates the introduction of the SUPER OFF data line in the initial UHF job UHF Data TITLE H2C0 2B2 3 21G DEFAULT BASIS UHF CALCULATION SUPER OFF CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE UHF ENTER MP2 Data RESTART TITLE H2C0 2B2 3 21G DEFAULT BASIS MP2 UHF CALCULATION 12 M LLER PLESSET MP2 AND MP3 CALCULATIONS 43 SUPER OFF BYPASS CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MP2 ENTER 12 2 MP3 Calculations The MP3 level of treatment is requested in equivalent fashion to the MP2 calculations detailed above with use of the MP3 keyword on the SCFTYPE data line Data sequences for performing a closed shell MP3 calculation on the formaldehyde molecule and an open shell calculation on the Bo state of H2CO are given below MP3 RHF Data TITLE H2CO 3 21G DEFAULT BASIS MP3 RHF ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE MP3 ENTER MP3 UHF Data TITLE H2C0 2B2 3 21G DEFAULT BASIS MP3 UHF CALCULATION CHARGE 1 MULT 2 ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 1
201. rective in the RPA module In particular it is not possible to calculate an interval ILOW IHIGH of roots with ILOW different from 1 A more through description of the role of the various MCLR directives is given in Part 7 32 ZORA RELATIVISTIC EFFECTS 189 32 ZORA relativistic effects Relativistic effects can be included through the ZORA formalism Zero Order Regular Approxi mation 53 In its simplest form this changes only the 1 electron terms in the Hamiltonian so that the relativistic effects once included can be carried over to all formalisms available This will be demonstrated based on a Hartree Fock calculation and a multi reference Cl calculation The relativistic equivalent of the very first closed shell Hartree Fock example is TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF ZORA ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER where the directive ZORA enables the relativistic effects Although it may seem overkill to use a relativistic approach with such light atoms the total energy of the relativistic calculation is about 0 0531500 au 1 4462 eV lower than that of the non relativistic calculation The relativistic HOMO LUMO gap is 0 00001615 au 0 0004395 eV smaller than its non relativistic counter part The relativistic version of the multi reference Cl example is TITLE H2CO 3 21G ZORA CISD 3 REFERENCE CI SUPER OFF NOSYM ZORA ZMATRIX ANGSTROM 0
202. rints the cartesian second derivative matrix in atomic units and the normal coordinates and vibrational frequencies All 3N normal coordinates are given The three translational modes will all have frequencies close to zero the degree to which they approach zero depending upon the degree of convergence of the SCF stage so that this SCF should be converged more stringently than usual this is done automatically by the FORCE and HESSIAN directives The three rotational modes will only be zero at a stationary point on the potential surface and consequently their values will depend upon the convergence of any preceding geometry optimisations Generally to ensure that the rotational modes all have frequencies below 10 wavenumbers the XTOL directive should be employed in any preceding geometry optimisation to reduce all elements of the gradient to about 1075 a u 2 Imaginary frequencies are printed as negative values The analysis at the end of both FORCE and HESSIAN runs will project out the rotations from the force constant matrix giving 6 5 for linear molecules very small frequencies 17 1 Numerical Force Constants Numerical force constant evaluation proceeds by taking finite differences of gradients using ei ther a 1 point forward difference or 2 point central difference formula The formula required default 1 point together with the step size to be used in differencing default 0 001 may be specified on the associated RUNTYPE directi
203. s Table 4 SCFTYPE Specification within GAMESS UK SCFTYPE RHF SCFTYPE DIRECT SCFTYPE UHF Restricted Hartree Fock Direct SCF Unrestricted Hartree Fock SCFTYPE DIRECT UHF Direct UHF SCFTYPE GVB Generalised Valence Bond SCFTYPE DIRECT GVB _ Direct GVB SCFTYPE MP2 SCFTYPE MP3 SCFTYPE CASSCF SCFTYPE MCSCF 2nd order Meller Plesset 3nd order Meller Plesset Complete Active Space SCF 2nd order MCSCF 2 CLOSED SHELL SCF CALCULATION 8 TITLE H2CO MINIMAL STO3G BASIS CLOSED SHELL SCF ZMATRIX ANGSTROM N Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END BASIS STO3G ENTER The corresponding data for performing an extended triple zeta plus polarisation TZVP basis is shown below TITLE H2CO EXTENDED TZVP BASIS CLOSED SHELL SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP ENTER 2 1 Spherical Harmonic Basis Sets The default Cartesian angular functions 6 d 10 f 15 g used throughout GAMESS UK may now be overridden under control of the HARMONIC directive This provides the option of using spherical harmonic 5 d 7 f 9g angular functions Note that such usage is implemented internally through appropriate transformations and not by computing integrals or derivative integrals over the spherical functions Typical usage will involve just presenting the string HARMONIC Thus the data for performing an extended triple z
204. s the hessian as a starting point for the CASSCF calculation Note that it is not possible at present to use RUNTYPE HESSIAN in CASSCF or MCSCF calculations and the user should typically i restore the initial hessian in such a calculation from an initial HF transition state location or ii use the TYPE 3 VARIABLES specification to compute an initial DFT CASSCF MCSCF hessian HF Optimisation TITLE H2 CO lt gt H2C0 1A TS 3 21G SCF TOTAL ENERGY 113 0500312 ZMAT ANGS 1 co 2 1 0 1 90 0 2 CHH 3 ANG1 1 180 0 41 0 2 90 0 3 0 0 4 1 0 5 ANG2 3 0 0 4 XH 6 90 0 2 180 0 T a a aO 16 TRANSITION STATE OPTIMISATION 77 H 4 XH 6 90 0 2 0 0 VARIABLES CO 1 134 TYPE 3 ANG1 43 7 TYPE 3 ANG2 57 8 TYPE 3 CHH 1 292 TYPE 3 XH 0 664 TYPE 3 END RUNTYPE SADDLE ENTER CASSCF Optimisation RESTART NEW TITLE H2 CO lt gt H2C0 1A TS 3 21G CASSCF TOTAL ENERGY 113 22306125 ZMAT ANGS co 1 0 1 90 0 CHH 3 ANG1 1 180 0 1 0 2 90 0 3 0 0 1 0 5 ANG2 3 0 0 XH 6 90 0 2 180 0 4 XH 6 90 0 2 0 0 Mm ob bo be a O BR PONE VARIABLES co 1 1525832 TYPE 3 CHH 1 2981078 TYPE 3 XH 0 6596229 TYPE 3 ANG1 43 4018534 TYPE 3 ANG2 57 3815232 TYPE 3 END RUNTYPE SADDLE SCFTYPE CASSCF CONFIG FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END ENTER The following points should be noted 1 the starting variables for the initial geometry in the CASSCF calculation have been taken from the output of the previous HF optim
205. s before result in a LANL ECP calculation with the DZ ECP basis set due to Hay and Wadt 8 In core SCF Calculations In all the conventional SCF calculations described above we have assumed that the 2 electron integral file is written to disk the Mainfile prior to repeated processing associated with the SCF iterations One alternative confined at present to closed shell SCF calculations is to use the direct SCF algorithm which removes the O processing associated with conventional SCF at the cost of an increased CPU requirement involved in recalculating the integrals on each SCF iteration In core SCF calculations provide a further alternative where the I O overhead associated with the conventional route is removed by mapping the two electron integral list directly to memory rather than disk storage While obviously limited to small medium sized molecules even on machines with sizable amounts of central memory i e 128 MBytes or more this technique can provide a significant increase in processing efficiency particularly on those machines with a poor I O subsystem In core SCF calculations are requested by modifications to the MFILE directive Two possible options are provided 1 The simplest option is to present the data line MFILE MEMORY requesting that the complete 2 electron integral file be routed to memory rather than disk Note that the program will in the presence of the above data line use a rather con servative al
206. sed shell calculation would result in a full J K super matrix of direct use in a subsequent GVB calculation although of course increasing the cost of the original SCF computation e An examination of the available integral options as a function of SCFTYPE Ta ble 2 reveals that the only option covering all possible wavefunction activities is the conventional two electron integral format If the use of symmetry is suppressed then such a file would also be suitable for direct input to the integral transforma tion program preceding MRD CI or DIRECT CI calculations This format may be requested in all SCF computations by presenting the data line SUPER OFF NOSYM Note that this directive must not only be specified in the run that generated the integrals but in a subsequent runs in which the file is used e Note that this suppressed symmetry integral file would not be usable in M ller Plesset or analytic derivative calculations The required format in such cases requires a skeletonised integral list and follows from presenting the data line SUPER OFF The following data sequences would perform the initial closed shell and subsequent GVB 1 PP calculation Note the form of the SCFTYPE directive in the GVB run the integer specified after the GVB keyword indicates the number of GVB pairs in the present case just 1 Closed shell SCF TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF SUPER FORCE NOSYM ZMATRIX ANGSTROM 0 0 1
207. sequence numbers of the doubly occupied MOs e The TABLE directive is omitted for we assume the data base generated in the closed shell run has been retained and allocated to the open shell calculation Now let us consider performing the closed shell calculation above in a sequence of jobs where the first job carries out the SCF the second the Table Cl calculation Valid data sequences for 24 TABLE CI CALCULATIONS 134 performing the calculation are shown below Run I The SCF Job TITLE H2CO 3 21G SCF PRIOR TO TABLE CI CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER The only obvious point to note is the use of the SUPER directive in requesting full integral list generation required in the subsequent symmetry adaption and integral transformation Run II The Table CI Job RESTART TITLE H2CO 3 21G TABLE CI 1M 1iR SUPER OFF NOSYM BYPASS SCF ZMAT ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE CI MRDCI ADAPT TRAN TABLE SELECT SYMMETRY 1 SPIN 1 CNTRL 16 SINGLES 1 CONF 012345 13 17 18 ROOTS 1 THRESH 30 10 CI DIAG EXTRAP 2 ENTER Considering the changes to the complete run the following points should be noted 24 TABLE CI CALCULATIONS 135 e The SCF computation is BYPASS ed e Note that the default VECTORS and ENTER data will still apply in the RESTART job with th
208. ser may avoid the task of nominating sections These defaults which are a function of SCFTYPE are summarised in Table 1 The following points should be noted e This default usage is not designed to completely remove the need for section specification and is intended primarily to cover simple operations e g a simple SCF or geometry optimisation 2 CLOSED SHELL SCF CALCULATION 4 Table 1 Default Vector Sections as a function of SCF TYPE SCFTYPE Number of Default Sections Section Numbers Closed shell SCF 1 1 UHF 2 2 3 Open shell RHF 2 4 5 GVB 2 4 5 CASSCF 2 6 T MCSCF 2 8 9 e While an expanded summary of section usage is now routinely printed on job termination the user should be aware of the attributes of the various vector sections before mixing default and input driven section specification e the contents of each of the sections specified in the table are described in detail at the appropriate point below 2 Closed Shell SCF Calculation We wish to perform an SCF calculation at the geometry r C H 1 099 A r C O 1 203 A and angle HCO 121 8 The geometry is specified through use of the z matrix 2 3 where each line of the ZMATRIX directive is responsible for specifying the nature and location of a given nucleus in terms of the position of those nuclei defined by previous lines Note at the outset that the z matrix TAGs used to characterise the component nuclei of the system play a vital role in charact
209. ses note that the present ATOMS implementation is much more likely to yield this configuration than the alternative VECTORS option EXTGUESS and a more reliable way to proceed is to use the closed shell vectors generated in section 2 as the starting guess Such a route requires e performing the calculations of 2 and 4 under control of the same Dumpfile e in the interests of efficiency we require the specification of a consistent format for the Mainfile thus allowing integral generation to be bypassed in section 4 with both closed and open shell calculations using the same integral file Taking these considerations into account the following data sequence for the examples of 2 and 4 should be presented where the Dumpfile created in the closed shell case is subsequently allocated as ED3 in the open shell calculation It is assumed of course that both Mainfile and Dumpfile produced in 2 have been saved Run I TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF SUPER FORCE ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER Run II RESTART TITLE H2C0 2B2 3 21G DEFAULT BASIS OPEN SHELL RHF CHARGE 1 MULT 2 BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER The closed shell data file now contains the SUPER directive and by virtue of the FORCE keyword instructs integral generation to proceed through J K Superma
210. ta base may be constructed in a given run of the Table Cl module by entering the TABLE sub module prior to SELECT and CI Thus the following data driven loading of sub modules MRDCI ADAPT TRAN TABLE 24 TABLE CI CALCULATIONS 130 SELECT CI DIAG would be typical of that required when the user is explicitly constructing the TABLE data set in a given run of the program Since TABLE generation is somewhat expensive it will be more usual for the user to allocate a pre generated version of the data set prior to executing the Table Cl modules This allocation process and detailed locations of TABLE are of course machine specific and will be outlined at the appropriate points in Parts 12 16 of the Manual In this case the TABLE data line is simply omitted from the data sequence shown above thus MRDCI ADAPT TRAN SELECT CI DIAG Note that failure to correctly allocate TABLE when using the above sequence will lead to an error condition 3 Several direct access files will be generated under RUNTYPE Cl processing For Conven tional Table Cl calculations these include e the Mainfile ED2 and Dumpfile ED3 e the Scratch file ED7 e temporary files for sorting both transformed integrals and intermediate matrices in the Cl calculation the Sortfile e in addition to the standard direct access files listed above the Table Cl module makes extensive use of FORTRAN data sets hereafter referred to as interfaces Any restart jo
211. ta sequence for performing a direct restricted Hartree Fock calculation on the formalde hyde cation is shown below TITLE H2CO 2B2 3 21G BASIS OPEN SHELL DIRECT RHF CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT ENTER Note that in contrast to the conventional open shell calculation the SCFTYPE directive must be presented to request the DIRECT requirement The third parameter on the SCFTYPE line is not required however given the default for an open shell system is to perform a restricted Hartree Fock calculation Equally the default high spin open shell occupancy means that the OPEN defaults apply so that the directive is not required The above data is thus equivalent to the following data sequence TITLE H2C0 2B2 3 21G BASIS OPEN SHELL DIRECT RHF CHARGE 1 MULT 2 4 RHF OPEN SHELL CALCULATION 14 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT RHF OPEN 1 1 ENTER In the absence of the RUNTYPE directive a single point Hartree Fock calculation will be performed Note that the SUPER directive is not relevant in a direct calculation given that the integrals are re computed on each iterative cycle of the SCF Equally use of the BYPASS directive in such calculations to avoid computation of some pre computed integral list has no real meaning and should not be used The following data seq
212. tains the dipole integrals useful for an investigation which mono excitations contribute to a large oscillator strength and the weights of the vectors y and z in the RPA eigenvectors y z e Note that files tda_table tex and rpa_table tex are generated containing the ATEX input for a list of the excited states computed by both methods comprising excitation energies oscillator strengths and most important single excitations e The set of molecular orbitals to be used in the transformation and subsequent RPA calculation are restored from the default section associated with the ENTER directive in this case section 1 Now let us consider performing the above calculation in two separate jobs where the first carries out the SCF the second the transformation and RPA calculation First the closed shell case valid data sequences for performing the calculation are shown below Run I The Scf Job TITLE H2CO TZVP R SP BASIS SCF PRIOR TO RPA CALCULATION SUPER OFF NOSYM ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END BASIS TZVP 0 TZVP C TZVP H Ss 0 1 0 0 02 PO 1 0 0 02 END ENTER The only obvious point to note is the user of the SUPER directive in requesting full integral list generation required in the subsequent transformation Run II The Transformation and RPA Job RESTART 30 LINEAR RESPONSE CALCULATIONS I THE RPA METHOD 183 TITLE H2CO TZVP R SP BASIS CONVENTIO
213. tation energies for the lowest 5 states of each irreducible representation A valid data sequence for performing such a calculation is shown below TITLE H2CO TZVP R SP BASIS RPA EXCITATION ENERGIES SUPER OFF NOSYM ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END BASIS TZVP 0 TZVP C TZVP H So 1 0 0 02 PO 1 0 0 02 END RUNTYPE RESPONSE RPA TDA SYMM 1 1 TO 5 SYMM 2 1 TO 5 SYMM 3 1 TO 5 SYMM 4 1 TO 5 ANALYSE ENTER The following points should be noted e By presenting the data line TDA an additional Tamm Dancoff TDA calculation may be requested for specified irreps and roots corresponding to a Cl in the space of single excitations Note that the line TDA ONLY can be used to suppress the RPA calculation performing a TDA calculation only 30 LINEAR RESPONSE CALCULATIONS I THE RPA METHOD 182 e The result table printed after successful completion of the iterative TDA RPA procedure contains the most important one electron excitations of the corresponding states If y z denotes an RPA eigenvector then all components of the vector y z with modulus larger than a certain threshold which may be specified in the THRESH directive see Part 7 are listed in this table With the help of the ANALYSE directive the user may in addition examine smaller components without having them listed in the result table The additional output generated by the ANALYSE directive also con
214. tesian coordinate and energy only optimi sation have used only the closed shell SCF case the user should note that such optimisations are also available for CASSCF MCSCF and MP2 MP3 wavefunctions in addition to UHF and GVB Energy only optimization capabilities for Direct Cl CCSD and Full Cl calculations are considered under the appropriate Cl section further in this chapter Data input requirements for the cases under consideration at this point follow straightforwardly from the preceding sec tions with appropriate SCFTYPE specification We illustrate such usage below for the cases of CASSCF MCSCF and MP2 RHF and MP2 UHF wavefunctions 15 6 1 CASSCF Geometry Optimisation When performing either CASSCF or MCSCF geometry optimisations the user should initially generate an appropriate set of trial MOS for input to the subsequent geometry optimisation using these orbitals as the basis for the CONFIG or ORBITAL data Run I The initial SCF Calculation TITLE H2CO 3 21G SCF STARTUP FOR CASSCF GEOM OPTIMISATION ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES c0 1 203 CH 1 099 HCO 121 8 END ENTER Run ITI The CASSCF Optimisation RESTART TITLE H2CO CASSCF GEOM OPT 10E IN 9 M O TOTAL ENERGY 113 359134855 ZMATRIX ANGSTROM 0 0 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 VARIABLES cO 1 203 CH 1 099 HCO 121 8 END RUNTYPE OPTIMIZE SCFTYPE CASSCF 15 GEOMETRY OPTIMISATION
215. the RESTART directive which now nominates the task to be restarted i e that in progress when the previous job dumped The following data files would be required in restarting the computation described in 2 86 and 9 above Closed Shell SCF Restart Data RESTART SCF TITLE H2CO 3 21G DEFAULT BASIS CLOSED SHELL SCF ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END VECTORS 1 ENTER 1 GVB 1 PP Restart Data RESTART SCF TITLE H2CO GVB 1 PP 3 21G BASIS 1B1 gt 2B1 BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE GVB 1 REST VECTORS 2 3 ENTER 2 3 CASSCF Restart Data RESTART SCF TITLE H2CO CASSCF 3 21G BASIS 10E IN 9 M 0 BYPASS ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 15 GEOMETRY OPTIMISATION 58 H 1 1 099 2 121 8 3 180 0 END SCFTYPE CASSCF CONFIG BYPASS FZC 1 TO 3 DOC 4 TO 8 UOC 9 TO 12 END VECTORS 2 3 ENTER 2 3 The following points should be noted 15 Given the default Dumpfile settings all examples commence with the data line RESTART SCF Note that the default VECTORS and ENTER attributes will in restart mode still apply Thus in the closed shell case the default VECTORS section section 1 will be examined at the outset of processing and if found to exist from a previous job i e the startup job will be used as a source of eigenvectors to restart the
216. the electron density associated with one or more molecular orbitals the amplitude of a molecular orbital a comparison of the density distribution in two or more molecular systems the interaction energy between a molecular distribution and a hypothetical point charge generating the so called electrostatic potential plot Two types of plot may be generated by the program to provide a pictorial representation of a given density or potential function in a specified molecular plane a contour plot with contours representing lines of constant value depicting the spatial characteristics of the given function a perspective plot with the values of the function in a given plane displayed as a 3 D perspective picture Both types of plot are generated from a grid of function values produced by the program e Perform a distributed multipole analysis DMA of an SCF wavefunction 32 e Perform a more detailed Mulliken analysis including both bond and orbital properties The user should note the following e While the various SCF modules provide default sections for eigenvector information it will be necessary in the ANALYSE modules to specify via the VECTORS directive the specific eigenvectors to be analysed 13 ANALYSING THE WAVEFUNCTION 46 e Each mode of analysis typically requires one or more directives to specify the particular tasks required At present we restrict ourselves to sample data files for property e
217. tomatically treat non Abelian groups by resorting to the optimum Abelian group when handing orbital symmetry The following points should be noted on the implementation and possible constraints inherent in the use of symmetry 1 INTRODUCTION 3 e The TAGs used to characterise the component nuclei of the system in either the GEOM ETRY or ZMATRIX directive play a vital role in symmetry determination They act for example to define the atomic number of the component nuclei and are used in establish ing the effective point group symmetry of the system Failure to appreciate the rules for TAG specification outlined in the description of these directives can lead to a considerable loss in efficiency e In RHF UHF and M ller Plesset calculations GAMESS UK will based on the molecular point group generate and retain only the unique integrals required for example in the process of constructing a skeletonised Fock matrix 1 Such a symmetry truncated integral list is however NOT usable at present in pair GVB CASSCF MCSCF RPA or Cl calculations and again considerable caution should be taken when using an integral file generated in an earlier SCF run directly in a subsequent post Hartree Fock calculation under control of the BYPASS directive e In geometry optimisations the point group deduced is based on the starting geometry and is not allowed to change during the subsequent optimisation This can lead to problems if the Z matrix is
218. tput in such calculations is confined to ED3 and ED7 the Dump and Scratch file respectively 4 RHF Open Shell Calculation A restricted Hartree Fock calculation is to be performed on the formaldehyde cation at the geometry specified above A valid data sequence for performing such a calculation is shown below TITLE H2C0 2B2 3 21G DEFAULT BASIS OPEN SHELL RHF CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END ENTER 4 RHF OPEN SHELL CALCULATION 10 In the absence of the RUNTYPE and SCFTYPE directives a single point restricted Hartree Fock calculation will be performed The following points should be noted 1 The CHARGE and MULT directives are now required to define the system attributes 2 In an open shell system the default SCF calculation uses the restricted Hartree Fock RHF method with the open shell occupancy assumed to correspond to the high spin configuration If the user wishes to modify this occupancy and define the shell structure characterising the wavefunction then the OPEN directive must be used to specify the electronic distribution in the open shell orbitals Using the OPEN directive in the present case would lead to the following data sequence TITLE H2C0 2B2 3 21G DEFAULT BASIS OPEN SHELL RHF CHARGE 1 MULT 2 ZMATRIX ANGSTROM Cc 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END OPEN 1 1 ENTER The current setting is self
219. trices rather than 4 RHF OPEN SHELL CALCULATION 12 through the default P supermatrix The following modifications to the data for the open shell calculation should be noted 1 The RESTART directive indicates that the calculation is to be driven from a known Dumpfile 2 The BYPASS directive indicates that the integral generation phase of the SCF processing is to be bypassed the file generated in Run I is to be used Again this bypassing is only made possible by virtue of requesting the appropriate integral format J K at generation time at the outset of the closed shell run 3 Note that the default VECTOR and ENTER sections are still applicable in this example In deciding on an appropriate set of eigenvectors to initiate an open shell calculation the program will in a RESTART job first examine the Dumpfile to see if the default open shell VECTORS section have been written to by a previous job If not as in the present example the closed shell default vectors section will be used to provide the starting guess as written to in Run I If this section is not present the calculation will revert to an atomic GUESS The open shell calculation will proceed to use the default open shell vectors specification for output of the eigenvectors see Table 1 Thus the data sequence above is equivalent to presenting the data lines VECTORS 1 ENTER 4 5 4 Assume that we now wish to perform a subsequent calculation on the 7B state of the cati
220. uence would be required to use the closed shell vectors as a starting guess for the open shell calculation where each phase of the calculation is conducted in DI RECT fashion cf the data sequences in section 2 and 4 Run I TITLE H2C0 3 21G BASIS CLOSED SHELL DIRECT SCF ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT ENTER Run II RESTART TITLE H2C0 2B2 3 21G BASIS OPEN SHELL DIRECT RHF CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT ENTER Assume that we now wish to perform a subsequent calculation on the 7B state of the cation Again the input orbitals must be arranged such that the doubly occupied manifold precedes the open shell orbitals In the present case with 7 DOMOS and 1 singly occupied orbital we 5 UHF CALCULATION ON THE FORMALDEHYDE CATION 15 must reorder the input MOs such that the 1b orbital occupies the 8th position in the input list through the SWAP directive thus RESTART TITLE H2CO 2B1 3 21G BASIS OPEN SHELL DIRECT RHF CHARGE 1 MULT 2 ZMATRIX ANGSTROM 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END SCFTYPE DIRECT SWAP 78 END ENTER 5 UHF Calculation on the formaldehyde cation The simplest way of conducting an unrestricted Hartree Fock UHF calculation is exemplified by the following data sequence for the form
221. unctions to gether with DFT CASSCF and MCSCF wavefunctions and ECP based calculations still have to employ finite differences of gradients under control of RUNTYPE FORCE The following points should be noted 1 RUNTYPE HESSIAN is in fact a combination of tasks requesting integral generation SCF gradient evaluation with additional evaluation of derivative Fock operators integral transformation solution of the coupled Hartree Fock CHF equations calculation of the two electron second derivative contribution and finally determination of the projected harmonic frequencies While in most cases it is feasible to perform all steps in a single calculation it may be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation We illustrate this point below 2 The degree to which the three translational modes of the cartesian second derivative matrix approach zero will depend upon the degree of convergence of the both the SCF 17 FORCE CONSTANT CALCULATIONS 90 3 and CHF stages and the SCF particularly should be converged more stringently than usual this is done automatically by the HESSIAN directive The three rotational modes will only be zero at a stationary point on the potential surface and consequently their values will depend upon the convergence of any preceding geom
222. using TYPE 3 specification on the variable definition lines of the ZMATRIX in numerically deriving the initial Hessian to be used in locating the required transition structure The final force constant matrix Run II at the optimised geometry is derived analytically under RUNTYPE HESSIAN control 17 FORCE CONSTANT CALCULATIONS 92 TITLE HCOH lt gt H2CO 1A TS 6 31G ZMAT ANGS 0 0 1 CO H 1 CH1 2 OCH1 H 1 CH5 2 H5C0 3 180 0 VARIABLES OCH1 56 3 TYPE 3 co 1 27 TYPE 3 CH1 1 22 TYPE 3 CHS 1 10 TYPE 3 H5CO 115 8 TYPE 3 END BASIS 6 31G RUNTYPE SADDLE XTOL 0 001 ENTER Run II Force Constant Evaluation RESTART TITLE HCOH lt gt H2CO 1A TS 6 31G OPT GEOM ZMAT ANGS Cc 0 1 CO H 1 CH1 2 OCH1 H 1 CH5 2 H5C0 3 180 0 VARIABLES OCH1 56 3 co 1 27 CH1 1 22 CH5 1 10 H5CO 115 8 END BASIS 6 31G RUNTYPE HESSIAN ENTER Example 3 The H2CO to t HCOH transition structure As described in the Geometry and Transition state optimisation sections above it is necessary to generate a trial force constant matrix for use in locating a transition structure Use of the HESSIAN runtype conducted at the starting geometry to be employed in locating the transition structure provides a powerful addition to the mechanisms outlined before This is illustrated in the example below where the hessian generated in Run I is subsequently restored in Run IT through specification of the FCM keyword on the RUNTYPE SADD
223. valuation localised orbital analysis graphical analysis DMA and extended Mulliken analysis In each case we assume that the closed shell SCF calculation on formaldehyde I has been successfully completed and perform the requested analysis based on the SCF MOs as written to the Section 1 of the Dumpfile 13 1 One electron Property Evaluation The following data sequence would be required in evaluating the electric field gradient at the carbon and oxygen nuclei RESTART TITLE H2CO 3 21G DEFAULT BASIS 1 E PROPERTIES ZMATRIX ANGSTROM N 0 0 1 1 203 H 1 1 099 2 121 8 H 1 1 099 2 121 8 3 180 0 END RUNTYPE ANALYSE PROPERTY 4c 40 END VECTORS 1 ENTER Each one electron operator is known to the user by an operator number a full list of the available operators and associated numbers in given in Table 6 The user specifies under control of the PROPERTY directive those properties to be be computed at any of the nuclei known to the system by virtue of the TAGs defined in the z matrix The example above typifies the case where a single set of MOs are associated with the particular SCFTYPE and as such may be input under control of the VECTORS directive to the properties package A somewhat different approach is required when computing the one electron properties derived from a wavefunction with more than one set of MOs e g a UHF wavefunction or in cases where only the total density matrix and not an associated set
224. ve Presenting the data line RUNTYPE FORCE will yield the default options Overriding may be achieved in obvious fashion thus RUNTYPE FORCE 2 0 003 with the integer specifying the required difference formula followed by the required step size The following points should be noted 1 A numerical force constant calculation is only meaningful when performed at an optimised equilibrium or transition state geometry 17 FORCE CONSTANT CALCULATIONS 84 2 Numerical force constant calculations may now be performed with DFT CASSCF and MCSCF wavefunctions but not with Cl wavefunctions 3 Specification of the optimised geometry in a FORCE run may be controlled by the form of the RESTART directive Using RESTART NEW will require the user entering the optimised variable values on the variable definition lines of the ZMATRIX directive Assuming however that geometry optimisation had been conducted immediately prior to the the FORCE run it would be sufficient to use just RESTART when the optimised geometry will be read from the Dumpfile and override the ZMATRIX data in the input stream Example 1 The H2CO to H CO transition structure Assuming the H2CO to H CO transition structure optimisation of Example 2 15 had successfully converged the following data file would be used in calculating the numerical force constants DUMPFILE ED3 350 RESTART TITLE H2 CO lt gt H2C0 1A TS 3 21G BASIS ZMAT ANGS co 1
225. we consider the format of the data required when carrying out such calculations using the quasi Newton optimisation procedures available in GAMESS UK The following points should be noted 15 GEOMETRY OPTIMISATION 59 1 Geometry optimisation may be conducted in either a framework of internal coordinates as defined by the ZMATRIX and VARIABLES specification lines or directly in a frame work of cartesian coordinates as generated from the ZMATRIX or defined through the GEOMETRY directive 2 Cartesian coordinate optimisation is requested by specifying the OPTXYZ option of the RUNTYPE directive Restarting such calculations after a controlled dump again involves the OPTXYZ specification on the RESTART directive 3 Internal coordinate optimisation is requested by specifying the OPTIMIZE option of the RUNTYPE directive Restarting such calculations after a controlled dump again involves the OPTIMIZE specification on the RESTART directive 15 1 Internal Coordinate Optimisation Under control of the RUNTYPE OPTIMIZE specification geometry optimisation is conducted in a system of internal coordinates bond lengths bond angles and dihedral angles defined by the z matrix This is controlled through the introduction of so called VARIABLES in the z matrix Any internal coordinate whose value is to be varied during optimisation must be specified as a VARIABLE and an initial value assigned to it through the VARIABLE definition lines of the ZMATRI
226. with the latter see Part 3 alternative formats in terms of atom orbital and coefficient exponent orderings are supported to provide compatibility with other packages and basis set libraries Thus the above JBAS data may also be presented through addition of the NWCHEM keyword as follows TITLE H2CO 6 31G BLYP CLOSED SHELL DFT WITH COULOMB FITTING ZMATRIX ANGSTROM 0 0 1 C0 H 1 CH 2 121 8 H 1 CH 2 121 8 3 180 0 VARIABLES cO 1 203 CH 1 099 END BASIS 6 31G RUNTYPE OPTIMISE SCFTYPE DIRECT RHF DFT BLYP 11 DFT CALCULATIONS DFT JFIT JFITG DFT SCHWARZ 6 DFT JBAS NWCHEM BASIS DGauss H H S 45 000000000 S 7 500000000 S 1 500000000 S 0 300000000 S 1114 000000000 S 223 000000000 S 55 720000000 S 13 900000000 SP 4 400000000 SP 0 870000000 SP 0 220000000 D 4 400000000 D 0 870000000 D 0 220000000 S 2000 000000000 END S 400 000000000 S 100 000000000 S 25 000000000 SP 7 800000000 SP 1 560000000 SP 0 390000000 D 7 800000000 D 1 560000000 D 0 390000000 ENTER A1 DFT Coulomb Fitting 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 1 00000000
227. y 1b 2be SCF ordering 1 2 3 4 5 6 7 8 Table ordering 1 2 3 4 17 5 13 18 Each reference function in the Cl is defined in terms of the reordered MOs under control of the CONF directive with the m o s in each representation presented in turn in order of increasing representation number Thus the following sequence 1 2 3 4 5 13 17 18 would define the SCF configuration for HCO Note that an additional integer is required in specifying the number of open shell orbitals NONO non identically coupled orbitals in each function This value is specified first in the CONF data sequence and would typically be followed by a sequence of NONO integers defining the orbitals in question In the present case NONO is zero as all m o s are doubly occupied so that the full CONF data line would be 0 1 2 3 4 5 13 17 18 24 TABLE CI CALCULATIONS 127 IRrep IRrep SCF Sequence Table Cl Occupation No No Sequence No No ay 1 1 1 2 0 2 2 2 0 3 3 2 0 4 4 2 0 6 5 2 0 10 6 0 0 12 7 0 0 15 8 0 0 16 9 0 0 18 10 0 0 20 11 0 0 22 12 0 0 b 2 7 13 2 0 9 14 0 0 13 15 0 0 19 16 0 0 b 3 5 17 2 0 8 18 2 0 11 19 0 0 14 20 0 0 17 21 0 0 21 22 0 0 Let us consider the specification for the following configuration 1a 2a 3a 4a 1b2 5a16a1 1b12b1 2b2 1 In this case there are two non identically spin coupled pairs i e 4 orbitals which must be specified first in the CONF data line This would then be 4 5 6 13 14 1 2 3 4 17 1

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