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GAMESS-UK USER'S GUIDE and REFERENCE MANUAL Version

1. 11 7 3 Angular integration Grid GAUSS LEGENDRE 11 7 4 Radial Integration Grid EULER MACLAURIN 11 7 5 Radial Integration Gtid LOG cc comen tae ds 11 7 6 Scaling Radial Grids SCALE o 11 7 7 Weighting scheme WEIGHT 0 11 7 8 Grid Point Screening SCREEN 0 11 7 9 Angular Grid Pruning ANGPRUNE 11 7 10 Atom Radii RADI 20 0 0 000 0 eee ee 11 7 11 Integration grids and BQ centers o 11 8 Energy Gradient Evaluation GRADQUAD ILO Coulomb INE s tea oaa 644 sd dd a dd 119 1 JRE and JFITG os ek eh eh ee aoe a Oe we ee we le hs TL92 AIBAS opo a ae ee e Se we we A 1193 SCHWARZ ooo as She ed Wos d aaa ee A aw Re i 12 Controlling the input Orbitals The VECTORS Directive 12 1 Mechanism Specification ooo 12 2 Section specification from the Parent Dumpfile 12 3 Using Default Sections under VECTORS and ENTER 2 12 4 Specification from a Foreign Dumpfile GETQ a EA IA A A a Sa a E 13 Controlling Geometry and Transition State Optimization 13 1 Geometry Optimisation and RUNTYPE Specification 13 2 Stopping an optimisation when molecule dissociates CHECK DISS or DIST 13 3 OPTIMIZE Data MINMAX XTOL STEPMAX and VALUE 13 3 1 OPTIMIZE Data MINMAX 00 000000 eee
2. OPEN STATE MULT 3 4 D 1 3 4 S 1 3 4 A 1 3 5 2 3 5 2 1 1 1 1 1 3 1 1 4 1 1 SIGP 2 1 1 SIGM 2 1 1 DELTA 2 1 1 1 1 1 3 2 1 SIGP 3 2 1 SIGM 3 2 1 DELTA 3 2 1 SIGP 1 2 1 SIGM 1 2 1 DELTA 1 2 3 SIGP 3 2 3 SIGM 3 2 3 DELTA 3 2 3 SIGP 1 2 3 SIGM 1 2 3 DELTA 1 2 3 SIGP 3 2 3 SIGM 3 2 3 DELTA 3 2 3 SIGP 1 2 3 SIGM 1 2 3 DELTA 1 4 DIRECTIVES DEFINING THE WAVEFUNCTION 10 4 2 GVB Wavefunctions While there are no additional directives required in characterising a GVB wavefunction we elaborate below on certain features of such calculations presenting a somewhat more complex example than that given previously section 2 6 In particular we consider the impact of using a set of localised orbitals see Part 8 to initiate the GVB calculation The following points on performing GVB pair calculations should again be noted 1 Remember that in the general case of a GVB 2 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 1 gt mtn open shell orbitals m n 1 gt m n 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 arrang
3. 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 94 13 8 4 SADDLE Data VALUE This directive may be used to control the accuracy of the search for a turning point during a line search and consists of a single data line read to the variables TEXT TURN using format A F e TEXT should be set to the character string VALUE e TURN should be set to a value between 0 0 and 1 0 that will control the accuracy of the line search procedure Note that the smaller TURN the more accurate the line search The VALUE directive may be omitted when TURN will be set to 0 3 The default thus corresponds to presenting the data line VALUE 0 3 13 9 Synchronous Transit Data The present implementation of the synchronous transit method is driven under specification of the LSEARCH directive Successful results from the method rely on the specification of not only a reasonable guess for the initial geometry but on presenting the equilibrium geometries as data for the two minima involved on the potential surface These minima are specified on the variable definition lines of the ZMATRIX and require that the form of the ZMATRIX has been constructed in such a way as to yield VARIABLES that transform smoothly from one minima though the transition state and onto the second minima This is shown below for the transition state involved in the HCN to HNC isomerisation process TITLE HCN SADDLE POINT SYNCHRONOUS TRANSIT ZMAT ANGS C X 11 0
4. In accordance to the other optimisers XTOL specifies the convergence criterion applied to the optimisation Note that XTOL has to be specified within the DLFIND block Default XTOL 0 003 15 1 10 MINMAX In accordance to the other optimisers MINMAX specifies the maximum number of energy evaluations Note that MINMAX has to be specified within the DLFIND block Default MINMAX 60 15 1 11 STEPMAX In accordance to the other optimisers STEPMAX specifies the maximum step in one coordinate component Note that STEPMAX has to be specified within the DLFIND block Default STEPMAX 0 5 15 2 Example 1 The following data file performs a simple minimisation of H2CO in redundant internal coordinates using the L BFGS algorithm TITLE H2C0 DZ DL FIND energy 113 8307609 ZMATRIX ANGSTROM C D 1 CO H 1 CH 2 HCO H 1 CH 2 HCO 3 180 0 15 OPTIMISATION USING DL FIND VARIAB c0 1 2 CH 1 0 HCO 12 END BASIS RUNTYPE OPTIMIZE DLFIND COORDINATES DLC END ENTER LES 03 99 1 8 DZ 15 3 Example 2 105 The following data files illustrate a NEB optimisation of part of the reaction path of HCO dissociation An additional file with the name neb_endpoint xyz is required It has the contents THORA TITLE H2C0 DZ DL FIND NEB energy 113 6497325 ZMATRIX ANGSTROM C D 1 CO H 1 L2 H 1 L3 2 42 3 0 0 VARIAB co 1 2 L2 1 5 L3 1 1 A1 120 A2 170 END BASIS RUNTYPE OPTIMIZE DLFIND NEB
5. 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 V R Saunders and I H Hillier Int J Quant Chem 7 1973 699 doi 10 1002 qua 560070407 R W Warren and B I Dunlap Fractional occupation numbers and density functional energy gradients with the linear combination of Gaussian type orbitals approach Chem Phys Lett 262 1996 384 392 doi 10 1016 0009 2614 96 01107 4 P J Stephens F J Devlin C F Chabalowski and M J Frisch Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields J Phys Chem 98 1994 11623 11627 doi 10 1021 j100096a001 R H Hertwig and W Koch On the parameterization of the local correlation functional What is Becke 3 LYP Chem Phys Lett 268 1997 345 351 doi 10 1016 S0009 2614 97 00207 8 REFERENCES 109 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Y Zhao B J Lynch and D G Truhlar Development and assessment of a new hybrid density functional model for thermochemical kinetics J Phys Chem A108 2004 2715 2719 doi 10 1021 jp049908s A D Becke Density functional thermochemistry IV A new dynamical correlation functional
6. 13 3 2 OPTIMIZE Data ATOL 2 2 2564 408 wets eee dea a Pee ws 1333 OPTIMIZE Data STEPMAX ecu s neo eee eA ee SHS 13 3 4 OPTIMIZE Data VALUE 2 2 24 465 446465444506 58 58 59 59 60 61 62 62 63 64 64 65 65 65 66 66 67 69 69 72 74 77 80 80 CONTENTS v 13 4 Modifying the Optimisation Pathway oaoa a e 2 85 13 5 OPTXYZ Data MINMAX XTOL and STEPMAX 88 13 5 1 OPTXYZ Data MINMAX 0 2 00000 ee 88 13 5 2 OPTAYZ Data XATOL ooo ec ee mal ee la 89 13 5 3 OPTAYZ Dita STEPMAX gt oc 440 oS e Dew ed 89 13 6 JORGENSEN Data Specification gt po ke beh ee eee bee bes 90 13 7 Transition State Location and RUNTYPE Specification 90 13 8 SADDLE Data Specification Trust Region 00 91 13 8 1 SADDLE Data MINMAX ooohh 00020050 91 13 8 2 SADDLE Dats lt AT L ceed ara a ees Sad A A wR i 93 13 8 3 SADDLE Data STEPMAX 0 200 000 004 93 13 8 4 SADDLE Data VALUE 0 2 00 00 50040 94 13 9 Synchronous Transit Data co e be ca s De Se wee Ree a rao oeit 94 13 9 1 Synchronous Transit Data LSEARCH 94 13 9 2 Synchronous Transit Data TOLMAX 95 13 9 3 Synchronous Transit Data TOLSTEP 95 13 9 4 Synchronous Transit Data TANSTEP 96 13 9 5 Synchronous Transit Data MINMAX 0 96 13 9 6 Synchronous Transit Data XTOL 0 4 9
7. A and CRITERIA I e DIRECTION should be either set to the character string ABOVE or BELOW to indicate the the change should happen when the number of cycles is greater than or less than the specified value e CRITERIA should be set to the number of SCF cycles within this phase 7 4 6 Total number of SCF cycles TOTCYC This directive consists of the keyword TOTCYC A followed by the parameters DIRECTION A and CRITERIA I 7 SCF CONVERGENCE ALTERNATE DRIVER 34 e DIRECTION should be either set to the character string ABOVE or BELOW to indicate the the change should happen when the number of cycles is greater than or less than the specified value e CRITERIA should be set to the total number of SCF cycles within this energy calculation This directive is most useful when used to trigger a phase change indicate convergence when used in conjunction with a slacker TESTER than the usual Often when performing geometry optimisations the wavefunction will not converge to the desired value of the tester at a paticular geometry regardless of the number of SCF cycles undertaken However the quality of the wavefunction may still be good enough to generate an energy profile that allows the optimiser to take a step towards a more favourable geometry where the wavefunction will converge with no problems The TOTCYC directive therefore allows a user to make this step after the SCF has been grinding away unsucces
8. VECTORS 1 ENTER 2 3 is permitted indicating that both a and P spin trial MOs are to be taken from the same Section Restarting the above computation would typically involve the sequence VECTORS 2 3 ENTER 2 3 Open shell RHF and GVB Calculations Again two Sections are involved The first is used to hold the internal non canonicalised MOs the orbital set used during the RHF or GVB iterations The second Section is used for output of the external canonicalised orbitals with energy weighting in the virtual manifold Again given a set of trial MOs in Section 1 we typically instigate the RHF GVB calculation with the data sequence 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 74 VECTORS 1 ENTER 4 5 and continue the processing with the sequence VECTORS 4 5 ENTER 4 5 4 CASSCF Calculations Again two Sections are required with both Sections containing information crucial to the internal running of the CASSCF module The first Section is assumed to contain just the orbital set while the second contains the canonicalised MOs relevant to subsequent Cl studies plus a set of Cl coefficients which may be used in assisting CASSCF restarts Given a trial set of MOs in Section 1 we would typically initiate the CASSCF calculation with the sequence VECTORS 1 ENTER 6 7 On completion of the job Section 6 will contain the CASSCF MOs while Section 7 will hold canonicalised orbitals plus the current set of Cl
9. can be used to specify how the Hessian should be updated CG Conjugate gradient method following Polak Ribi re SD Steepest descent DYN Damped molecular dynamics Four additional real parameters can be specified which determine 1 the time step in atomic units default 1 0 2 the start friction default 0 3 3 the factor to reduce the friction each time the energy decreases default 0 95 and the friction to apply if the energy increases default 0 3 The frictions are defined so that 0 corresponds to free undamped dynamics and 1 corresponds to steepest descent This variable friction facilitates convergence to an energy minimum 15 1 8 UPDATE The directive UPDATE specifies the Hessian update details in case an explicit Hessian is calcu lated i e for the PRFO optimiser Syntax UPDATE METHOD RECALC FD SOFT 15 OPTIMISATION USING DL FIND 104 Where RECALC is the integer number of updates before the Hessian is recalculated default 100 FD is 1 or 2 to use a one point or two point formula to calculate the finite difference Hessian default 2 SOFT is a positive real number default 0 003 Eigenmodes with an absolute eigenvalue below SOFT are ignored by the P RFO algorithm This avoids steps into the translation and rotation directions METHOD may be one of BOFILL Bofill update of the Hessian default POWELL Powell update of the Hessian NONE No update recalculate the Hessian in each step 15 1 9 XTOL
10. would require the following ORBITAL data ORBITAL DOC1 DOC1 DOC3 DOC1 DOC2 VOC1 UDC3 END Note that it is possible to abbreviate the data specification when successive orbitals of identical 9 DIRECTIVES CONTROLLING MCSCF CALCULATIONS 42 symmetry and type are involved This is achieved by preceding the orbital tag with an integer depicting the number of repeated orbitals Thus the data above may be presented thus ORBITAL 2D0C1 DOC3 DOC1 DOC2 VOC1 UODC3 END To freeze the Ols orbital as the SCF orbital we would present the sequence ORBITAL FZC1 DOC1 DOC3 DOC1 DOC2 UDCA UODC3 END and to maintain the double occupancy of the orbital while enabling it to relax would require the sequence ORBITAL COR1 DOC1 DOC3 DOC1 DOC2 UDCA UDC3 END The following sequence would be used to extend the space to include the 5a and 2b orbitals ORBITAL COR1 DOC1 DOC3 DOC1 DOC2 VOC1 VOC3 VOC1 UDC2 END Note that it is not required that all orbitals in the active space appear first in the input orbital set the specified sequence being derived automatically from the input MOs Based on an RHF calculation on the X B state of the H20 ion then a full valence calculation with frozen Ols would be performed under control of the following ORBITAL data ORBITAL 2D0C1 DOC3 DOC1 ALP2 UOC1 UODC3 END 9 2 2 ORBITAL Example 2 Assume the following set of input MOs from a TZVP RHF calculation on the X B state of methylene TOTAL ENERGY 38
11. Default value is 0 0 e MAXMAS Maximum allowed MASSCF iterations Default is 30 e NFRZ Number of frozen orbitals Default is 0 maximum is 20 e MOFRZ A list of NFRZ integers specifying the orbitals to be kept frozen throughout the MASSCF calculation e NOROT Number of frozen rotations Default is 0 maximum is 20 e NROTAB A list of NOROT integer pairs specifying the orbital rotations to be kept frozen throughout the MASSCF calculation e MXPN Maximum number of Davidson expansions Default is 10 e MXIT Maximum number of Davidson iterations Default is 30 e FCORE Option to freeze all core orbitals this is a flag no numerical parameter needed e SRSO Perform single reference second order SRSO calculation SRSO is useful in cases where an RHF or ROHF wavefunction is difficult to converge and the more pow erful Newton Raphson solver in MASSCF could be successful A single SCF iteration is executed to provide orbitals and the Cl step executes trivially only to provide the 1 and 2 particle densities necessary to form the orbital hessian matrix this is a flag no numerical parameter needed By themselves the above input specifications define the equivalent of a CASSCF calculation using the full NR method on the ground state In order to make full use of the capabilities of the ORMAS code the following input is required 10 2 ORMAS input keywords and their parameters There are no sensible defa
12. F The scale factor is used in the temperature updates going from the start to the final temperature To ensure that the final temperature has been reached at convergence the current temperature is updated as a linear function of the difference between the SCF tester and the SCF convergence criterion To Tstart 8 Tj41 max Tying min T SCALE_V ALUE tester convergence 9 A couple of points should be noted about the use of Fermi smearing 1 The Fermi Dirac smearing enforces strict Aufbau ordering of the orbitals through the occupations Thus it cannot be used together with options that may break the Aufbau ordering such as locking 2 The Fermi Dirac smearing breaks the strict distinction between occupied and virtual or bitals In practice there will be three categories occupied partially occupied and virtual orbitals This requires a modified definition of the tester The tester now becomes the absolute maximum off diagonal value of the Fock matrix excluding the occupied occupied and virtual virtual blocks 7 SCF CONVERGENCE ALTERNATE DRIVER 32 7 4 Changing Phase The change from one phase to another is controlled by a number blocks of commands each starting with a line with two data fields NEXT A and PHASE I e NEXT is set to the character string NEXT e PHASE is an integer identifying the phase to jump to once the relevant criteria described below have been met The block is terminated either by another
13. Including Empirical Corrections J Comp Chem 25 2004 1463 1473 doi 10 1002 jcc 20078 S Grimme Semi empirical GGA type density functional constructed with a long range dispersion correction J Comp Chem 27 2006 1787 1799 doi 10 1002 jcc 20495 J Antony S Grimme Density functional theory including dispersion corrections for intermolecular interactions in a large benchmark set of biologically relevant molecules Phys Chem Chem Phys 8 2006 5287 5293 doi 10 1039 b612585a The Construction and Interpretation of MCSCF wavefunctions M W Schmidt and M S Gordon Ann Rev Phys Chem 49 1998 233 266 doi 10 1146 annurev physchem 49 1 233 The Multiconfiguration SCF Method B O Roos in Methods in Computational Molecular Physics edited by G H F Diercksen and S Wilson D Reidel Publishing Dordrecht Netherlands 1983 pp 161 187 The Mul ticonfiguration SCF Method B O Roos in Lecture Notes in Quantum Chemistry edited by B O Roos Lecture Notes in Chemistry v58 Springer Verlag Berlin 1994 pp 177 254 Optimization and Characterization of a MCSCF State J Olsen D L Yeager P Jor gensen Adv Chem Phys 54 1983 1 176 doi 10 1002 9780470142783 ch1 Matrix For mulated Direct MCSCF and Multiconfiguration Reference Cl Methods H J Werner Adv Chem Phys 69 1987 1 62 doi 10 1002 9780470142943 ch1 The MCSCF Method R Shepard Adv Chem Phys 69 1987 63 200 doi 10 1002 97804
14. JORGENSEN there are a number of sub directives that may be used to control the search procedure These should be specified immediately following the RUNTYPE directive and are summarised below 14 2 POWELL The POWELL directive consists of a single data line comprising the keyword POWELL in the first data field The directive may be used to request updating of the Hessian using the Powell update procedure and should be specified in Transition state location 143 BFGS The BFGS directive consists of a single data line comprising the keyword BFGS in the first data field The directive may be used to request updating of the Hessian using the BFGS update procedure and should be specified in geometry optimisation 14 4 BFGSX The BFGSX directive may be used to request use of a modified BFGS update procedure in geometry optimisation calculations with safeguards to ensure retention of a positive definite hessian 145 RECALCULATE This directive consists of a single data line read to the variables TEXT NSTEP using format A I e TEXT should be set to the character string RECALCULATE e NSTEP is an integer used to specify the frequency of recalculation of the Hessian using the method dictated by the TYPE keywords of the Variables Definition line of the ZMATRIX directive 14 JORGENSEN AND SIMONS OPTIMISATION ALGORITHM 99 The directive may be omitted when the default of updating the hessian only will hold through out An alterna
15. LEVEL directive may be omitted when the program will assign the following default settings for most molecular systems Ei 1 0 E2 0 3 and IBRK 5 SCF calculations on transition metal complexes comprising first row metals are typically found to require higher values of level shifter for satisfactory convergence In such cases the above defaults are now modified by the code to the following E1 2 0 E2 2 0 and IBRK 999 The following points should be noted on the specification of level shifters e For the first three cycles a value of at least unity should be chosen to stabilise what are usually the most erratic cycles e If divergence is experienced with the DIIS procedure never instigated increasing the level shifter will force convergence to the onset of DIIS Increasing the level shifters through a data line of the form data line LEVEL 2 0 is usually sufficient to force convergence to this onset 6 1 2 Open shell RHF and GVB Calculations In the case of open shell RHF and GVB calculations the LEVEL directive consists of a single data line read to variables TEXT OCC1 V1 IBRK OCC2 V2 using format A 2F 1 2F e TEXT should be set to the character string LEVEL e OCC1 V1 are the doubly occupied partially occupied and occupied virtual level shifters up to the iterative cycle specified by IBRK e IBRK is an integer used to a specify the cycle number e OCC2 V2 are the doubly occupied partially occupied and occupie
16. N 1 CN 2 90 0 H 1 CH 2 90 0 3 HCN VARIABLES CN 1 1484 MINIMA 1 1371 1 1597 CH 1 5960 MINIMA 1 0502 2 1429 HCN 90 0 MINIMA 180 0 0 0 END BASIS SV 4 31G RUNTYPE SADDLE LSEARCH O 4 ENTER 13 9 1 Synchronous Transit Data LSEARCH The LSEARCH directive may be used to request and characterise the synchronous transit method overriding the default trust region and consists of a single data line read to the variables TEXT LINE IPOL using format A 21 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 95 e TEXT should be set to the character string LSEARCH e LINE is an integer used to identify the type of line search to be performed The two valid settings are LINE 0 requesting subsequent line searches be based on energy evaluation alone and LINE 1 when both the energy and gradient of the energy will be used at each point in each line search e IPOL is an integer used to specify the form of polynomial be employed for the princi pal direction of negative curvature 4 The two valid settings are LINE 2 quadratic polynomial or LINE 4 quartic polynomial The synchronous transit method is invoked by presenting the data line LSEARCH O 4 which must be presented after the RUNTYPE directive Note that the default trust region method corresponds to the specification LSEARCH O 5 The LSEARCH directive may also be used to influence OPTIMISE and OPTXYZ runs For an OPTIMISE run a LSEARCH 1 specification requests a
17. NEXT directive a PHASE directive or an END directive Within a NEXT block the criteria for when to change to phase 0 i e NEXT 0 is particularly important as this specifies when the calculation is determined to have converged If no NEXT 0 directive is specified for a phase then the calculation cannot converge from this phase and can only jump to other phases when it meets their jump criteria converging from them if it meets their NEXT 0 criteria If no NEXT 0 is specified in any phase the calculation will run until it runs out of cycles as specified by MAXCYC Multiple criteria can be specified within a NEXT block and the jump will only then occur when all of the criteria have been met i e a logical and test is used Users wishing to use an or test can specify multiple next blocks for the same phase The criteria for changing phases are as follows 7 4 1 TESTER This directive consists of the keyword TESTER A followed by the parameters DIRECTION A and CRITERIA F e DIRECTION should be either set to the character string ABOVE or BELOW to indicate the the change should happen when the tester is greater than or less than the specified value e CRITERIA should be set to the desired value of the TESTER The TESTER is defined as the maximum Fock matrix element in the MO basis for the occupied virtual block This value will tend to zero when the calculation has converged 7 4 2 Change in
18. R Sabin On some approximations in applications of Xa theory J Chem Phys 71 1979 3396 3402 doi 10 1063 1 438728 N Godbout D R Salahub J Andzelm and E Wimmer Can J Chem 70 1992 560 doi 10 1139 v92 079 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 V I Lebedev and D N Laikov A quadrature formula for the sphere of the 131st algebraic order of accuracy Doklady Mathematics 59 1999 477 481 REFERENCES 111 44 45 46 47 48 49 50 51 52 W Kohn and L J Sham Self Consistent Equations Including Exchange and Correla tion Effects Phys Rev 140 1965 A1133 A1138 doi 10 1103 PhysRev 140 A1133 P Hohenberg and W Kohn Inhomogeneous Electron Gas Phys Rev 136 1964 B864 doi 10 1103 PhysRev 136 B864 J C Slater Atomic Radii in Crystals J Chem Phys 41 1964 3199 3204 doi 10 1063 1 1725697 Note For some elements there are no Bragg Slater radii avail able In that case radii are taken from E Clementi D L Raimondi and W P Reinhardt Atomic Screening Constants from SCF Functions Il Atoms with 37 to 86 Electrons J Chem Phys 47 1967 1300 1307 doi 10 1063 1 1712084 S Grimme Accurate Description of van der Waals Complexes by Density Func tional Theory
19. TESTER DTESTER This directive consists of the keyword DTESTER A followed by the parameters DIRECTION A and CRITERIA F 7 SCF CONVERGENCE ALTERNATE DRIVER 33 e DIRECTION should be either set to the character string ABOVE or BELOW to indicate the the change should happen when the change in the tester is greater than or less than the specified value e CRITERIA should be set to the change in the tester within this phase 7 4 3 Change in energy DE This directive consists of the keyword DE A followed by the parameters DIRECTION A and CRITERIA F e DIRECTION should be either set to the character string ABOVE or BELOW to indicate the the change should happen when the change in energy is greater than or less than the specified value e CRITERIA should be set to the change in energy in Hartrees within this phase 7 4 4 Absolute change in energy DEABS This directive consists of the keyword DEABS A followed by the parameters DIRECTION A and CRITERIA F e DIRECTION should be either set to the character string ABOVE or BELOW to indicate the the change should happen when the change in energy is greater than or less than the specified value e CRITERIA should be set to the absolute change in energy i e from the starting Guess energy in Hartrees 7 4 5 Number of cycles in this phase NCYC This directive consists of the keyword NCYC A followed by the parameters DIRECTION
20. The keyword FT97A_X selects the Filatov Thiel exchange functional variant A 39 FT97B_X or FT97_X The keywords FT97B_X or FT97_X select the recommended Filatov Thiel exchange functional variant B 39 PBE_X The keyword PBE_X selects the Perdew Burke Ernzerhof exchange functional 20 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 54 PW91_X The keyword PW91_X selects the Perdew Wang 91 exchange functional 21 NULL_C The keyword NULL_C selects the NULL correlation functional B95 or B95_C The keyword B95 or B95_C select the Becke 95 meta correlation functional 15 EDF1_C The keyword EDF1_C selects the correlation part of the Empirical Density Func tional one 16 FT97_C The keyword FT97_C selects the Filatov Thiel correlation functional 38 LYP or LYP_C The keywords LYP or LYP_C select the default Lee Yang Parr correlation energy functional 34 P86 or P86_C The keywords P86 or P86_C select the Perdew 86 gradient corrected correlation functional 35 PBE_C The keyword PBE_C selects the Perdew Burke Ernzerhof correlation functional 20 PZ81 or PZ81_C The keywords PZ81 or PZ81_C select the Perdew Zunger local density correlation functional 36 PW91_C The keyword PW91_C selects the Perdew Wang 91 correlation functional 21 PW92 or PW92 C The keywords PW92 or PW92 C selects the Perdew Wang 92 local density correlation functional 22 VWN VWN5 or VWN_C The keywords VWN VWN5 or VWN_C select the reco
21. VARIABLE definition lines of the ZMATRIX see Part 3 section 8 2 the second internal coordinate driven method is that based on the hill walking algorithm due to Jorgensen and coworkers 6 A more detailed account of the method and associated data is given below in section 10 We note here that the procedure is driven through additional keyword specification on the RUNTYPE directive thus RUNTYPE SADDLE JORGENSEN The method is again reliant on a quality initial hessian for success 3 the third method perhaps less reliable and requiring additional input data than the others is the synchronous transit internal coordinate based method due to Bell and Crighton This is again requested through the RUNTYPE SADDLE specification together with appropriate usage of the LSEARCH directive see below We consider the data input requirements for the trust region and synchronous transit methods below and those for the Jorgenson algorithm in section 10 13 8 SADDLE Data Specification Trust Region Four directives are provided to control the trust region search procedure MINMAX XTOL STEPMAX and VALUE with specifications very similar to the corresponding directives described above for OPTIMIZE usage The user should note that the implementation is also based on maintaining a history of the optimisation pathway that will be worked through on each restart of the optimisation This appears on the output as a sequence of both old and
22. X21 1 90 3 0 F 2 R3 6 90 3 180 X41 1 90 30 F 4 R3 8 90 3 180 X31 1 90 4 0 F 3 R3 10 90 4 180 X51 1 90 4 0 F 5 R3 12 90 4 180 VARIABLES R1 1 2 R2 1 3 R3 1 313 END RUNTYPE OPTIMIZE LEVEL 2 0 40 1 0 ENTER Now let us assume we wish to tighten the convergence threshold using an XTOL setting of 0 001 Merely presenting a revised XTOL specification in a restart job will not have the desired effect for the job will merely work through the optimisation pathway reaching convergence before the revised XTOL setting will come into effect The user must inform the optimisation that the previous actions on the seventh line search are to be ignored and repeated with the revised XTOL setting by presenting the following data file RESTART OPTIMIZE TITLE xkk C4F4 3 21G 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 88 ZMAT ANGS X C 1 Ri C1 R2 2 90 C1 Ri 3 90 2 180 C1 R2 4 90 3 180 X21 1 90 30 F 2 R3 6 90 3 180 X41 1 90 3 0 F4R3 8 90 3 180 X31 1 90 40 F 3 R3 10 90 4 180 X51 1 90 40 F 5 R3 12 90 4 180 VARIABLES Ri 1 2 R2 1 3 R3 1 313 END RUNTYPE OPTIMIZE LEVEL 1 0 MINMAX REVISE 7 XTOL 0 001 ENTER 13 5 OPTXYZ Data MINMAX XTOL and STEPMAX Three directives are provided to control the OPTXYZ search procedure MINMAX XTOL and STEPMAX Note that directive specifications are similar but not identical to the descriptions above Note also that
23. a sequence of orbital TAGS whereby each orbital in the primary space is classified both by type and by symmetry with this sequence terminated by the character string END The following orbital types are used in this classification e FZC frozen orbital i e an orbital which will remain frozen as input throughout the MCSCF iterations e COR core orbital i e an orbital which will remain doubly occupied in all configurations e DOC doubly occupied i e an orbital which is doubly occupied in the reference configu ration and which will be permitted variable occupancy in the MCSCF treatment e ALP an unpaired orbital i e an orbital which is singly occupied with a spin in the principle reference configuration and which will be permitted variable occupancy in the MCSCF treatment e BET an unpaired orbital i e an orbital which is singly occupied with P spin in the principle reference configuration and which will be permitted variable occupancy in the MCSCF treatment e UOC formally unoccupied orbitals corresponding to SCF virtual MOs which will be permitted variable occupancy in the MCSCF Each of the core and active orbitals must be classified according to its type above and in addition its symmetry IRrep under the point group symmetry in use The integer flag char acterising the symmetry as produced for example in the SCF output is appended to the appropriate 3 character string above so that for a Co molecule a dou
24. algorithm employed only guarantees convergence to a stationary point not necessarily to a minimum 13 5 1 OPTXYZ Data MINMAX This directive may be used to control the number of energy evaluations and searches permitted in optimising a given structure and consists of a single data line read to the variables TEXT NPTS NSERCH using format A 21 e TEXT is set to the character string MINMAX e NPTS is an integer specifying the maximum number of energy evaluations allowed in the optimisation e NSERCH is an integer defining the maximum number of searches permitted in the BFGS update procedure The MINMAX directive may be omitted when both NPTS and NSERCH will be set to the maximum allowed value of 60 The following specification is thus equivalent to the default MINMAX 60 60 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 89 Example In some cases the user may wish to perform just the initial point on the optimisation pathway to gauge the quality of the starting geometry though the magnitude of the gradient at that point This may be achieved though use of MINMAX as shown below Start up Job TITLE H20 DZ OPTIMIZATION STARTUP ZMAT ANGSTROM O H 1 ROH H 1 ROH 2 THETA VARIABLES ROH 0 956 HESSIAN 0 7 THETA 104 5 HESSIAN 0 2 END BASIS DZ RUNTYPE OPTXYZ MINMAX 1 1 ENTER Here we are using the MINMAX directive to terminate the optimisation after the first point This may then be restarted as shown below where th
25. be used with the WEIGHT directive 11 7 8 Grid Point Screening SCREEN SCREEN PSI PSITOL P DENTOL RHO RHOTOL CONV The SCREEN Directive allows the user to activate the screening of grid points This may involve the optional specification of a number of tolerances and or a request to change dynamically the quadrature grid size according to the degree of convergence of the calculation Following the directive initiator SCREEN the following data fields may be presented e PSI PSITOL format A F This criterion is used in generating the radial grids for the atoms Based on this criterion a radius is computed for every atom beyond which the most diffuse basis function is assumed to be zero When building the radial grid all grid points that would end up outside this radius will be discarded e P DENTOL format A F The tolerance for the spin density matrix elements If an element in the spin density matrix has a value smaller than DENTOL the matrix element will be discarded in the electron density evaluation e RHO RHOTOL format A F The tolerance for the spin density in a batch of grid points If the maximal spin density in a batch of grid points is less than RHOTOL the whole batch will excluded from the functional integration CONV format A This option switches on the dynamic adaption of the quadrature precision with the convergence of the calculation The idea is that if the Kohn Sham orbitals are not ver
26. been constructed they have to be merged into a molecular grid To avoid artifacts from the finite size of the atomic grids it is essential that grid points be faded out if they get to close to another atom So called weighting functions were designed for this purpose So for proper integration the selection of angular grids radial grids and weighting functions have to be addressed 3 Improving integration efficiency Although the above approach properly defines the molecular integration grid the efficiency of applying this grid can be improved through 2 strategies a Screening This is based on removing grid points or functions at grid points that contribute little to the exchange correlation energy from the calculation at the ear liest opportunity b Pruning This is based on replacing 2 close grid points by 1 new grid point 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 51 11 2 The DFT Directive and Default Settings In common with most Density Functional programs the DFT module within GAMESS UK is implemented as a modified Hartree Fock program with the exchange term in the Hartree Fock equations replaced by the exchange correlation term 45 Thus 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 the character string CDFT or DFT in the first data field to
27. below Start up Job TITLE H20 DZ OPTIMIZATION STARTUP ZMAT ANGSTROM O H 1 ROH H 1 ROH 2 THETA VARIABLES ROH 0 956 HESSIAN 0 7 THETA 104 5 HESSIAN 0 2 END BASIS DZ RUNTYPE OPTIMIZE MINMAX 1 1 ENTER Here we are using the MINMAX directive to terminate the optimisation after the first point This may then be restarted as shown below where the default MINMAX settings will apply Restart Job RESTART OPTIMIZE TITLE H20 DZ OPTIMIZE ZMAT ANGSTROM O H 1 ROH H 1 ROH 2 THETA VARIABLES ROH 0 956 HESSIAN 0 7 THETA 104 5 HESSIAN 0 2 END BASIS DZ RUNTYPE OPTIMIZ ENTER 13 3 2 OPTIMIZE Data XTOL This directive may be used to define the convergence thresholds for the optimisation and consists of a single data line read to the variables TEXT TOL using format A F e TEXT should be set to the character string XTOL e TOL should be set to the value to be used in defining the four acceptance criteria for the convergence of the optimisation algorithm These criteria are maximum change in variables lt TOL average change in variables lt TOL 2 3 maximum gradient lt TOL 1 4 average gradient lt TOL 1 6 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 84 The XTOL directive may be omitted when TOL will be set to 0 003 The default thus corre sponds to presenting the data line XTOL 0 003 13 3 3 OPTIMIZE Data STEPMAX This directive may be used to define the the maximum allowed movement in any of the va
28. but in such cases often leads to a reliable set of MOs Note that the original MINGUESS implementation has been extended to handle nuclei up to and including Xenon VECTORS EXTGUESS Limited to split valence basis sets e g 3 21G 4 31G etc leading in general to a reliable set of orbitals Note that the original EXTGUESS implementation has been extended to handle polarisation basis sets such as 4 31G 4 31G etc and can now handle nuclei up to and including Xenon VECTORS ALPHAS Trial vectors are generated from a Fock matrix based on a Mulliken type approximation together with a set of input diagonal Fock elements Fol lowing the VECTORS line a sequence of NBASIS real numbers where NBASIS is the number of basis functions must be input with the l th such number set to the negative of the expected value of the l th diagonal Fock matrix in the basis representation Example the following ALPHAS data refers to a triple zeta TZV calculation on formaldehyde ALPHAS 8 9 11 6 5 5 2 7 1 2 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 72 0 2 0 0 0 2 0 1 0 4 0 8 0 0 0 1 0 4 15 5 15 1 6 6 3 6 1 7 0 3 0 1 0 1 0 0 0 1 0 5 0 0 0 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 Having generated the trial MOs and possibly manipulated them under control of the SWAP directive the resulting set of vectors is written to the Dumpfile Section s nom inated on the ENTER directive Thus a typical data sequence in a closed shell SCF calcula
29. cade yetka na CE AEDS BERR OS a RRR HS 9 2 1 ORBITAL Example I 0 0 00 00 000000 9 2 2 ORBITAL Example2 000 000 00 bri eee 93 CANONICAL o esos p par eee Sa de ow Oe BOE a ESE DA PRINT o e eee BO ee Bo sa REE Se eee 10 Directives Controlling MASSCF Calculations 11 10 1 Basic MASSCF input keywords and their parameters 10 2 ORMAS input keywords and their parameters 204 10 2 1 MASSCF Example Les c 4 044404 2694 444 4445 See ws 10 2 2 MASSCF Example2 0 0 000000 pee eee 10 2 3 MASSCF Example 3 306 cm gw o a eS 10 2 4 MASSCF Example4 0 0 0 000000 eee ee Directives Controlling DFT Calculations 11 1 Introductory remarks 2 2 2 11 2 The DFT Directive and Default Settings 20 11 3 DFT Directive Options sc s s osae cr waca ces eses asa aa 11 4 Specification of Fanctionals o o a oo e204 ee ed a ee ee S 11 5 Specification of Dispersion Corrections 2 2 o e ee 11 5 1 The DISPERSION directive os 4 5 0462 28 bee a ea E eo 11 6 Specification of Integration Grids 2 ee 11 6 1 The QUADRATURE Directive 0 2 00 iii 33 33 33 33 34 34 36 37 39 40 40 41 42 43 44 45 45 46 47 48 48 49 CONTENTS 11 7 Detailed Grid Specification s o ee s oco 44 08 eee creas ees 11 7 1 Grid Specification on a Per Atom Basis ELEMENT and LABEL 11 7 2 Angular Integration Grid LEBEDEV
30. configurations is required then the following data line CONFIG PRINT NOSORT should be presented in the startup job and the line CONFIG BYPASS NOSORT in a subsequent restart assuming that ED9 had been kept The user is recommended to take advantage of the BYPASS and NOSORT options where applicable since the space requirements and generation time of the loop formulae tape may often prove costly 5 Directives Controlling Wavefunction Convergence 5 1 MAXCYC This directive consists of a single data line read to variables TEXT MAXC using format A e TEXT should be set to the character string MAXCYC e MAXC is an integer used to specify the maximum number of iteration cycles required The directive may be omitted when MAXC will be set to the default value of 50 The following conditions cause termination of iteration e When the desired accuracy is reached iteration of the SCF or MCSCF process stops e f the job time remaining is insufficient to complete another iterative cycle or the max imum number of cycles as set by the MAXCYC directive or default has completed iteration will cease Example MAXCYC 100 Note that the maximum number of allowed cycles in CASSCF calculations is limited to 20 5 2 THRESHOLD This directive may be used to define a convergence threshold for SCF and MCSCF iterations and comprises a single data line read to the variables TEXT ISET using format A l 6 SCF CONVERGENCE DEF
31. lt lt 2r respectively The total grid size is specified through the number of grid points NTHETA in the 0 coordinate The number of points in the coordinate will be simply 2 x NTHETA so that the total angular grid size will be 2 x NTHETA In its simplest form the directive consists of two data fields read to the variables TEXT NTHETA using format A e TEXT should be set to the character string GAUSS LEGENDRE or more simply GAUSS e NTHETA is an integer specifying the required number of points In the same way as described above for LEBEDEV grids it is possible to specify different angular grids for different radii In the present case the GAUSS LEGENDRE directive comprises the following data fields e TEXT should be set to the character string GAUSS LEGENDRE e pairs of data fields are then presented each pair characterising a specific radial zone and read to the variables NTHETA RZ using format I F where NTHETA specifies the grid size in the th radial zone The floating point values of RZ subdivide the radial coordinate into different zones The values RZ are fractions of the Bragg Slater radius 46 of the atom Each zone runs from RZ _1 to RZ The first zone starts at 0 while the last zone runs up to infinity e NPT is again an integer specifying the required number of points in the outer most zone running up to infinity Examples GAUSSLEGENDRE 15 GAUSSLEGENDRE 11 0 1 15 0 5 17 GAUSSLEGE
32. of such an optimisation with the onset of the NR method specified to allow for possible large changes in wavefunction associated with large steps in the geometry optimisation Hessian construction must be performed on the first NR cycle The program currently requires in core treatment of the orbital hessian and as such NR usage is limited to cases with a rather modest number of orbital rotation parameters If memory requirements preclude such a treatment the user should present the data sequence SUPERCI 1 TO 20 THRESH 4 which will lead to satisfactory convergence in many cases In many instances the most rapid convergence is realised using the 1 step NR method featuring simultaneous optimisation of both Cl coefficients and orbital rotation param eters This technique may be requested under control of the SIMUL directive with a typical data sequence shown below SUPERCI 1 TO 5 NEWTON 6 TO 20 HESSIAN 6 TO 20 SIMUL 8 TO 20 The memory requirements are of course aggravated by the inclusion of the Cl terms in the Hessian When applicable this technique is highly effective in stable geometry optimisations SCF Convergence Alternate Driver A new SCF driver has has been developed within GAMESS UK that provides an alternative way of controlling SCF calculations The driver is orthogonal to the default driver and is currently still in the development stage and is therefore not included in the default build o
33. output and consists of a single data line with the character string PRINT in the first data field Subsequent data fields may comprise any combination of the following parameters NATORB 1 particle density matrix and natural orbitals ORBITALS Molecular orbital coefficient array CIVECTOR The Cl vector VIRTUALS Print virtual MOs in addition to core and active Note that the default PRINT settings Version 6 3 onwards correspond to presenting the data line PRINT ORBITALS VIRTUALS NATORB 10 DIRECTIVES CONTROLLING MASSCF CALCULATIONS 45 10 Directives Controlling MASSCF Calculations This section describes the parallel Multiple Active Space SCF MASSCF code in GAMESS UK The MASSCF method draws upon a mature body of literature covering techniques for constructing and optimizing MCSCF wavefunctions 50 MASSCF is shorthand for ORMAS MCSCF using the full Newton Raphson full NR orbital optimization technique 51 MASSCF proceeds via a two step decoupled approach in which the Cl and orbital update problems are solved separately ORMAS Occupation Restricted Multiple Active Space allows multiple active spaces to be defined governed by certain occupation rules or restrictions 52 The machinary of ORMAS then generates all possible determinants satisfying the occupation restrictions The usefulness of this approach is twofold Firstly a single compact notation generalizes to traditional Cl wave function types such as full Cl as
34. parameters controlling convergence of the ORMAS CI solver are as follows e KEEPVEC Number of Cl vectors to keep for next Cl step Default is 1 so the current solution provides the guess for the next Cl step e CIGUESS Dimension of Cl guess Hamiltonian Default is 300 e ITERCI Maximum number of Davidson iterations to solve Cl Default is 100 e CRIT Energy convergence criterion Default value is 1 0d 5 e MAXP Maximum number of Davidson expansions in Cl Default is 10 The following examples serve to illustrate the construction of Cl wave functions using ORMAS 10 2 1 MASSCF Example 1 TITLE H20 MASSCF 3 21G BASIS ZMATRIX ANGSTROM 0 H 1 OH H 1 OH 2 HOH VARIABLES OH 0 956 HOH 104 5 END SCFTYPE MASSCF MASSCF NCORE 1 NACT 8 NELS 8 END ENTER This is entirely equivalent to 10 DIRECTIVES CONTROLLING MASSCF CALCULATIONS 10 2 2 10 2 3 MASSCE Example 2 TITLE H20 MASSCF 3 21G BASIS ZMATRIX ANGSTROM 0 H 1 OH H 1 OH 2 HOH VARIABLES OH 0 956 HOH 104 5 END SCFTYPE MASSCF MASSCF NCORE NACT NELS NSPACE NORB MINE MAXE END ENTER OoAarOdr MASSCE Example 3 48 In this example up to double excitations CISD are allowed into a space containing eight virtual orbitals This case is difficult to converge so the maximum number of MASSCF iterations needs to be increased TITLE HCN 6 31G MASSCF RHF geometry GEOMETRY ANGSTROM 0 0 0 0 1 058995
35. polarisation basis set Again the symmetry adapted option may be different in the old and new calculation 4 The role of the EXTRA option see ATMOL3 9 is largely redundant given the availability of the revised GETQ and it is suggested that GETQ be used in such cases 5 The only major restriction in the use of GETQ is that the ordering of the nuclei presented in the z matrix definition lines be the same in both old and new calculation The syntax of the GETQ option is again dependent on the number of sets of vectors to be retrieved from foreign Dumpfiles 1 When restoring a single set of vectors as in closed and open shell restricted Hartree Fock calculations the VECTORS directive consists of a single data line as follows VECTORS GETQ fnvec iblkv isectv where e l nvec should be set to a valid character string EDO ED19 MT0 MT19 specifying the LFN of the data set on which the foreign Dumpfile resides e iblkv should be set to the starting block of the foreign Dumpfile e sectv is an integer used to specify the section where the required vectors are to be found on the foreign Dumpfile Note that isectv must be specified even if referring to the appropriate default section 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 79 2 When restoring two sets of eigenvectors from a foreign Dumpfile for example the a spin and 3 spin vectors in a UHF calculation th
36. the input set of localised orbitals e NOGEN assumes that the orbitals to be correlated are positioned at the top of the doubly occupied orbital input set see section 4 8 1 As only a subset of four of the LMOs are to be correlated we must ensure that the corresponding orbitals occupy the top four positions in the occupied set with sequence numbers 5 8 using the SWAP directive to reposition the two oxygen lone pair LMOs below the two C O and C H bonds i e with sequence numbers 3 and 4 e Note the presence of the ADAPT OFF data line This is now required when using the set of orbitals from the LMO analysis where the process of symmetry adaptation is automatically suppressed GVB PP Data RESTART NEW TITLE H2C0 3 21G 4PAIR GVB BYPASS SUPER OFF NOSYM ADAPT OFF ZMATRIX ANGSTROM C D 1 1 203 H 1 1 099 2 121 8 H 11 099 2 121 8 3 180 0 END SCFTYPE GVB 4 VECTORS NOGEN 2 SWAP 3 614 8 END ENTER 3 4 43 CASSCF wavefunctions The CONFIG Directive CONFIG The CONFIG directive must be presented in a CASSCF calculation and acts 1 to define the active space in the calculation by partitioning the orbitals into a primary and secondary set 3 4 DIRECTIVES DEFINING THE WAVEFUNCTION 13 2 to specify an initial reference configuration for example the associated SCF configuration that will be employed in generating the complete Cl space and the associated loop formulae tape CONFIG data comprises a sequence o
37. there will be three categories occupied partially occupied and virtual orbitals This requires a modified definition of the tester The tester now becomes the absolute maximum off diagonal value of the Fock matrix excluding the occupied occupied and virtual virtual blocks Finally with the IPRINT SMEAR directive more detailed information about the Fermi smearing can be obtained such as the actual orbital occupations used in every iteration and the chemical potential in Hartree 6 SCF CONVERGENCE DEFAULT 25 6 7 CASSCF Convergence Four directives are available for specifying the optimisation techniques to be used in the course of a CASSCF calculation The user nominates which techniques are to be employed on each iterative cycle of the computation through use of the SUPERCI NEWTON HESSIAN and SIMUL directives Thus the data sequence SUPERCI 1 TO 4 NEWTON 5 TO 20 HESSIAN 5 9 13 17 would specify super Cl optimisation for the first four cycles followed by subsequent 2 step Newton Raphson NR for the remainder of the computation with explicit construction of the orbital Hessian on cycles 5 9 13 and 17 The above sequence corresponds in fact to the default specification and will be used in the absence of controlling directives The following points should be noted 1 The optimum technique on a given cycle is very much dependent on the current degree of convergence At the outset of the calculation starting from say an SCF orbi
38. to the Lebedev grids the total number of grid points is set to 2ntheta and then truncated to the first smaller sized Lebedev grid Examples ANGPRUNE ANGPRUNE OFF ANGPRUNE AUTO ANGPRUNE LABEL C1 C2 ON ANGPRUNE LABEL C1 01 AUTO LABEL C2 H2 OFF 11 7 10 Atom Radii RADII This directive sets the atomic radii to be used in the grid generation The radii are to be specified in Bohr s This is not the same as the SCALE directive which affects only the spacing between the radial grid points Changing the atomic radii does the same thing as SCALE and affects the pruning of the angular grids and affects the atomic size adjustments in the weighting schemes The envisaged use of this directive is mainly to change the default grid on a BQ center which matches that of a Carbon atom to one that matches the grid of some other element Examples RADII 2 0 RADII LABEL BQ1 BQ2 3 0 RADII ELEMENT C 0 1 5 LABEL C2 BQ2 2 0 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 65 11 7 11 Integration grids and BQ centers Using the Becke approach for the numerical integration will result in each atom having an associated grid However in various calculations BQ centers will be included in the geometry to specify point charges additional basis functions or both Whether or not a BQ center should have a grid and what the grid parameters should be is not entirely clear yet The approach currently assumed is e A BQ center will be assigned a grid only if it has ba
39. 0 3 1b gt 2 0 8 5a 0 0 4 3a 2 0 9 2b 0 0 5 1b 2 0 To perform a full valence space calculation comprising 7 primary orbitals with the 4a and 2b virtual MOs included in the active space would require the following data lines CONFIG DOC 1 TO 5 UOC 6 7 END 4 DIRECTIVES DEFINING THE WAVEFUNCTION 14 To freeze the Ols orbital we would present the sequence CONFIG FZC 1 DOC 2 TO 5 UOC 6 7 END The following sequence would be used to extend the space to include the 5a and 2b orbitals CONFIG FZC 1 DOC 2 TO 5 UOC 6 TO 9 END Note that all orbitals in the active space must appear first in the input orbital set Thus if we wished to include the 2b MO but not the 5a we would present the sequence CONFIG FZC 1 DOC 2 TO 5 UOC 6 TO 8 END in conjunction with the SWAP data lines SWAP 8 9 END Assuming the same orbital ordering had been derived from an RHF calculation on the X B state of the H20 ion then a full valence calculation with frozen Ols would be performed under control of the following CONFIG data CONFIG FZC 1 DOC 2 TO 4 ALP 5 UOC 6 7 END Example 2 Assume the following set of input MOs from an RHF calculation on the X B4 state of methylene 4 DIRECTIVES DEFINING THE WAVEFUNCTION 15 MO Sequence Symmetry SCF MO Sequence Symmetry SCF number Occupation number Occupation 1 la 2 0 6 4a 0 0 2 2a1 2 0 7 2b 0 0 3 1b gt 2 0 4 3a1 1 0 5 1b 1 0 A full valence sp
40. 022645 29 Cu 0 924018 1 179405 2 034581 8 0 3 444799 0 046586 0 020112 13 Al 7 478471 0 371579 0 192578 8 0 5 043143 2 660967 1 071269 8 0 0 902242 1 249695 1 985263 8 0 5 027333 2 570596 1 047347 8 0 6 519617 3 214017 1 846467 1 H 0 954846 2 572273 3 214984 1 H 5 298164 0 243155 0 154613 7 N 0 874905 2 707837 3 083889 1 H 6 599492 3 284123 1 755577 1 H end basis dz runt scf Start newscf directives newscf print full diis frontier phase 1 level 2 0 2 0 next 2 info Changing to phase 2 as tester lt 0 01 tester below 0 01 phase 2 level 0 5 0 5 diis lock 8 SPECIFICATION OF DISPERSION CORRECTIONS 36 next 3 info Changing to phase 3 as tester lt 0 002 tester below 0 002 phase 3 lock diis next 0 info Converged form phase 3 as tester lt 5 0d 6 tester below 5 0d 6 end End newscf directives runtype optx scftype uhf cdft quad high cdft b3lyp screen vectors 3 4 enter 1 2 8 Specification of Dispersion Corrections A problem frequently encountered with effective one electron models is that long range corre lation effects such as dispersion or Van der Waals interactions are not properly described This leads to problems where these relatively weak dispersion forces are important such as in DNA base pair stacking or the interaction between aromatic molecules So far attempts to rigorously address these problems have had limited success In response to this empirical ap
41. 1 90 0 P2 180 0 P3 0 0 P5 0 0 P6 0 0 P7 0 0 END BASIS TZVP SCFTYPE DIRECT RHF DIIS ED4 1 ENTER Restart Job RESTART SCF TITLE C6H5 NO2 TZVP DIIS INFORMATION TO ED4 NOPRINT ZMAT ANGSTROM C N 1 RCN X 21 01 90 0 C 1 RCC1 2 T1 3 P1 C 1 RCC1 2 T1 3 P1 C 4 RCC2 1 T2 2 P2 C 5 RCC2 1 T2 2 P2 C 7 RCC3 5 T3 1 P3 0 2 RNO1 1 T5 3 90 0 0 2 RNO1 1 T5 3 90 0 H 4 RCH1 1 T6 2 P5 H 5 RCH1 1 T6 2 P5 H 6 RCH2 4 T7 11 P6 H 7 RCH2 5 T7 12 P6 H 8 RCH3 7 T8 14 P7 VARIABLES RCN 1 49 RCC1 1 37 RCC2 1 43 RCC3 1 37 RNO1 1 21 RCH1 1 084 RCH2 1 084 RCH3 1 084 6 SCF CONVERGENCE DEFAULT 23 T1 120 0 T2 120 0 T3 120 0 T5 120 0 T6 120 0 T7 120 0 T8 120 0 P1 90 0 P2 180 0 P3 0 0 P5 0 0 P6 0 0 P7 0 0 END BASIS TZVP SCFTYPE DIRECT RHF DIIS ED4 1 ENTER 6 4 CONV This directive may be used to override the default convergence techniques of level shifting and DIIS and consists of a single data line read to the variables TEXT INDEX using format A e TEXT should be set to the character string CONV e INDEX is an integer used to specify the particular technique s required The following options are available Obes Arsh use Pople s extrapolation Listas do NOT use damping extrapolation or level shifting Dala use damping and Pople s extrapolation diia use Davidson s damping A eee use level shifting and extrapolation Be agentes te use level shifting default Dreta use damping extrapolation and level shif
42. 1993 5612 5626 doi 10 1063 1 464906 C W Murray N C Handy and G J Laming Quadrature schemes for integrals of density functional theory Mol Phys 78 1993 997 doi 10 1080 00268979300100651 A D Becke Density functional exchange energy approximation with correct asymptotic behaviour Phys Rev A38 1988 3098 doi 10 1103 PhysRevA 38 3098 A D Becke A multicenter numerical integration scheme for polyatomic molecules J Chem Phys 88 1988 2547 doi 10 1063 1 454033 C Lee W Yang and R G Parr Development of the Colle Salvetti correlation energy formula into a functional of the density Phys Rev B37 1988 785 789 doi 10 1103 PhysRevB 37 785 John P Perdew Density functional approximation for the correlation en ergy of the inhomogeneous electron gas Phys Rev B33 1986 8822 8824 doi 10 1103 PhysRevB 33 8822 John P Perdew and Alex Zunger Self interaction correction to density functional approximations for many electron systems Phys Rev B23 1981 5048 5079 doi 10 1103 PhysRevB 23 5048 S J Vosko L Wilk and M Nusair Can J Phys 58 1980 1200 doi 10 1139 p80 159 M Filatov and W Thiel A nonlocal correlation energy density functional from a Coulomb hole model Int J Quant Chem 62 1997 603 616 M Filatov and W Thiel A new gradient corrected exchange correlation density func tional Mol Phys 91 1997 847 859 doi 10 1080 002689797170950 B I Dunlap J W D Connolly and J
43. 2 A1 LES 5 0 0 DZ 6 0 01 GEOMETRY neb_endpoint xyz END ENTER 4 0 3526549 0 1899991 1 3596765 0 7056650 0 4601460 0 6367263 1 1431771 1 4269885 0 0000000 0 0000000 0 0000000 0 0000000 16 THE ENTER DIRECTIVE 106 16 The ENTER Directive The ENTER directive should be the last directive specified since it initiates the calculation The directive may also be used to nominate the section s on the Dumpfile where eigenvectors generated by the processing requested through SCFTYPE during the present run of the program are to be written Since more than one set of vectors may be generated by several of the SCF options two for example in open shell RHF GVB UHF MCSCF and CASSCF calculations it follows that multiple section specification may feature on the ENTER directive The directive consists of a single data line read to variables TEXT ISECT1 and ISECT2 using format A 21 e TEXT should be set to the character string ENTER e ISECT1 may be used to specify the section number on the Dumpfile where the first set of vectors associated with the requested SCFTYPE are to be written e ISECT2 may be used to specify the section number on the Dumpfile where the second set of vectors associated with the requested SCFTYPE are to be written If both ISECT1 and ISECT are omitted it will be assumed that the default sections of Table 2 are in effect Note that if explicit section specification is used then I
44. 407 molecules 19 PBE The keyword PBE selects the Perdew Burke Enrzerhof gradient corrected exchange correlation functional 20 PW91 The keyword PW91 selects the Perdew Wang 91 gradient corrected exchange correlation functional 21 SVWN The keyword SVWN selects the LDA exchange functional and the Vosko Wilk Nusair local density correlation functional 37 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 56 11 5 Specification of Dispersion Corrections A problem frequently encountered with DFT calculations is that long range correlation effects such as dispersion or Van der Waals interactions are not properly described This leads to problems where these relatively weak dispersion forces are important such as in DNA base pair stacking or the interaction between aromatic molecules So far attempts to rigorously address these problems have had limited success In response to this empirical approaches to correct for the lack of dispersion have been suggested GAMESS UK supports two versions of one of these approaches named DFT D 47 48 49 Both these approaches are based on a simple model for the dispersion energy of two interacting atoms ij faam Ri j Dij Rij C8 R ij 15 The function fdamp is simply chosen such that it goes to zero when R goes to zero to prevent that atoms collapse onto eachother The above expression requires a Cg coefficient for every pair of chemical elements To reduce the number of these required pa
45. 5007 P J Wilson T J Bradley and D J Tozer Hybrid exchange correlation functional deter mined from thermochemical data and ab initio potentials J Chem Phys 115 2001 9233 9242 doi 10 1063 1 1412605 M E Mura and P J Knowles Improved radial grids for quadrature in molecular density functional calculations J Chem Phys 104 1996 9848 9858 doi 10 1063 1 471749 R E Stratmann G E Scuseria and M J Frisch Achieving linear scaling in exchange correlation density functional quadratures Chem Phys Lett 257 1996 213 223 doi 10 1016 0009 2614 96 00600 8 B G Johnson Development implementation and applications of efficient methodologies for density functional calculations pages 169 and further In J M Seminario and P Politzer Ed Modern Density Functional Theory A Tool for Chemistry Theoretical and Computational Chemistry Vol 2 Elsevier Science B V 1995 REFERENCES 110 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 A D Becke Density functional thermochemistry III The role of exact exchange J Chem Phys 98 1993 5648 doi 10 1063 1 464913 P M W Gill B G Johnson and J A Pople A standard grid for density functional cal culations Chem Phys Lett 209 1993 506 512 doi 10 1016 0009 2614 93 80125 9 B G Johnson P M W Gill J A Pople The performance of a family of density functional methods J Chem Phys 98
46. 6 13 9 7 Syrichronous Transit Datai coa s se we toca ye eee EOR 96 13 10Restoring the Force Constant Matrix FCM 0 4 96 14 Jorgensen and Simons Optimisation Algorithm 97 14 1 Invocation of The Algorithm and Associated Parameters 97 Ma POWELL do ani paan or p ee a ee ee ee 98 Be BPG ee es Sak e Ay a a Bae da A 98 14 4 BFGSA 2 2 o atata a Se a a ade ee A e yai 98 145 RECALCULATE x 66 enc awd d to AA E R E ao nd a As 98 IAG CUTOFFS o a e e a e ed do ada de a i 99 LAT GION AA EA 99 TAS BIGMA e a er Ea 22 Oe a 99 14 9 MAXJORGEN e 99 ls 6 4 a ay Soh Bee ee went A wk Ye ER R ES Rc eo Ee wl Arde 99 IAALTOPTPRINT coso ia RE Ee ads SE ek BS a me amp Bee aia 100 CONTENTS 14 Empleo oem bic ras oe Se A a eR 15 Optimisation using DL FIND 15 1 DL FIND directives 2 ma ora A E e ee es 15 1 1 COORDINATES os 2 a4 Gee ba MDE Meda hee 4 IA DIMER ain Se i be hoe ue a Oe ee oe ee a ee A Ae MMT eek cea det dee BR pa oe A a Ge te 1514 WER o he ia pua we a we eo ee de ed aiei 15 15 MEBMODE poses gow ee ao oe HO ed ee So ee me hos 151 6 GEOMETRY sac ndd paai h ai e aD a a ewe 154 7 OPTIMISER 00 idad Ore amp E we Be Eee A S IBAS URDA ME s 24 60 os em toe Re RS PGR RR EE 1519 ATL o ee ce go Gk ele we Qe bw Sree ee ence he we i IS LIO MINMAS oda 2 aw AR ek BO GR Se hee Bot ae IBATISTERMAR cd scesa ack aae ee a ee Sed E a a 152 Example o o 2 ce ach ote a ae SO ey ee we ee ee ee es 15 3 E
47. 6 1 0 H 0 0 0 0 0 0000000 6 0 C 0 00 0 1 1327718 7 0 N END BASIS 6 31Gx x SCFTYPE MASSCF MASSCF NCORE 2 NELS 10 NACT 13 NSPACE 2 NORB 5 8 MINE 8 0 MAXE 10 2 MAXMAS 100 END ENTER 10 DIRECTIVES CONTROLLING MASSCF CALCULATIONS 49 10 2 4 MASSCF Example 4 One need not be limited to conventional Cl wave function types as the following example serves to illustrate TITLE HCN 6 31G MASSCF RHF geometry GEOMETRY ANGSTROM 0 0 0 0 1 0589956 1 0 H 0 0 0 0 0 0000000 6 0 C 0 0 0 0 1 1327718 7 0 N END BASIS 6 31G SCFTYPE MASSCF MASSCF NCORE 2 NACT 11 NELS 10 NSPACE 3 NORB 5 4 2 MINE 4 0 0 MAXE 10 4 2 MAXMAS 1000 END ENTER In the above example up to quadruple excitations are allowed into the first virtual space and up to double excitations in the second virtual space Again this calculation is extremely slow to converge so the maximum number of MASSCF iterations must be increased to nearly 1000 to ensure convergence 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 50 11 Directives Controlling DFT Calculations 11 1 Introductory remarks Before describing the DFT specific input we briefly outline some background material that users should be aware of before attempting to use the Density Functional Theory module within GAMESS UK 1 The functionals An essential result from the paper by Hohenberg and Kohn 45 was that DFT would yield the exact ground state energy and electron density if the exchange
48. 70142943 ch2 The CASSCF Method and its Application in Electronic Structure Calculations B O Roos in Advances in Chemical Physics vol 69 edited by K P Lawley Wiley Interscience New York 1987 pp 339 445 doi 10 1002 9780470142943 ch7 General second order MCSCF theory A Density Matrix Directed Algorithm B H Lengsfield IIl J Chem Phys 73 1980 382 390 doi 10 1063 1 439885 The use of the Augmented Matrix in MCSCF Theory D R Yarkony Chem Phys Lett 77 634 635 1981 doi 10 1016 0009 2614 81 85223 2 M Dupuis P Mougenot J D Watts in Modern Techniques in Theoretical Chemistry E Clementi editor ESCOM Leiden 1989 chapter 7 Direct configuration interaction and multiconfigurational self consistent field method for multiple active spaces with variable occupations Method J Ivanic J Chem Phys 119 9364 9376 2003 doi 10 1063 1 1615954 REFERENCES 112 53 Direct configuration interaction and multiconfigurational self consistent field method for multiple active spaces with variable occupations II Application to oxoMn Salen and N204 J Ivanic J Chem Phys 119 9377 9385 2003 doi 10 1063 1 1615955
49. 9321296186 1 1 11 24483142 2 0000000 2 1 0 85646872 2 0000000 3 3 0 59962511 2 0000000 4 1 0 47810023 1 0000000 5 2 0 40348167 1 0000000 9 DIRECTIVES CONTROLLING MCSCF CALCULATIONS 6 1 0 16128671 7 3 0 24034249 8 3 0 28796496 9 1 0 30384049 10 2 0 32139063 ti 1 0 45957080 12 1 0 63630157 13 3 0 70724008 14 3 1 40064194 15 1 1 44828705 16 2 1 47979149 17 4 1 54845894 18 1 1 69050079 19 2 1 73938256 20 1 1 78688113 21 1 1 94167219 22 3 1 94783841 23 3 2 30755067 24 2 2 48250909 25 1 2 48720842 26 4 2 73866260 27 3 2 93545830 28 1 2 99931959 29 3 3 66924826 30 1 3 71124278 31 1 4 85256025 32 1 26 27807526 o00D0DO0O00O00000000000000000000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 43 A full valence space calculation on the X B state with frozen Cis would be controlled thus ORBITAL 2D0C1 DOC3 ALP1 ALP2 UOC1 U0C3 END The corresponding calculation on the 1B state featuring singlet coupling of the 3a and 1b MOs would require use of the ALP and BET tags thus ORBITAL 2D0C1 DOC3 ALP1 BET2 UOC1 UODC3 END remembering to change or remove the MULT 3 specification 93 CANONICAL The CANONICAL directive may be used to control the routing of MCSCF nat
50. AULT 17 e TEXT should be set to the character string THRESH e ISET is an integer parameter used in defining the threshold At SCF convergence the elements of the density matrix will be converged to within an absolute error 10 5 T_ The directive may be omitted when the default value 1075 will be used For CASSCF iterations values of the maximum Brillouin element super Cl or maximum first derivative Newton Raphson control the monitoring of convergence Note that in most CASSCF and MCSCF calculations setting ISET 4 will prove quite adequate 6 SCF Convergence Default Driver In default the RHF UHF and GVB modules of GAMESS UK iterate under control of a hybrid scheme of level shifting 10 and DIIS Direct inversion in the Iterated Subspace 1 A set of built in level shifters will when used in conjunction with DIIS lead in most cases to adequate convergence and the user need only consider providing data in troublesome cases A typical SCF calculation will when far from convergence proceed under control of level shifting alone and it is at this point of the calculation that overriding the default shifters under control of the LEVEL directive may be necessary Once convergence has set in the DIIS procedure is initiated corresponding to a TESTER of ca 0 1 experience to date suggests that rapid convergence proceeds once this point has been reached 6 1 LEVEL In its most general form the LEVEL directive may be used to nomi
51. BEL were introduced The keyword ELEMENT is followed by a list of one or more elements and the requested setting is applied to all atoms of that element The keyword LABEL works similarly to ELEMENT but uses the atom labels as specified in the geometry The various specifications are executed in order of appearance Example DFT LEBEDEV 302 ELEMENT C H 194 LABEL Ci H2 H4 266 This directive sets the angular grid for all atoms to the 302 point Lebedev grid then sets the grid for all carbon and hydrogen atoms to the 194 point grid and finally overrides the grid for all atoms with names C1 H2 and H4 giving them the 266 point grid 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 59 11 7 2 Angular Integration Grid LEBEDEV The LEBEDEV directive requests the grids of Lebedev for angular integration 43 These grids have been designed to integrate polynomials on a sphere exactly up to a specific order Grids with 6 14 26 38 50 74 86 110 146 170 194 234 266 302 350 434 590 770 974 and 1202 points are supported In its simplest form the directive consists of two data fields read to the variables TEXT NPT using format A 1 e TEXT should be set to the character string LEBEDEV e NPT is an integer specifying the required number of points It has been noted that close to the nucleus the density is more spherically symmetric than at larger distances so that a smaller angular grid can be used for smaller radii This capability is p
52. 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 4 DATA INPUT CLASS 2 Directives M F Guest H J J van Dam J Kendrick J H van Lenthe P Sherwood and G D Fletcher 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 2 RUNTYPE 1 2 1 Notes on RUNTYPE Specification c ss eos se ae m E 200200004 2 3 SCFTYPE 5 4 Directives defining the wavefunction 6 4 1 SCF Wavefunctions The OPEN Directive oaa aaa aa a 4 2 GVB Wavefunctions ccoo a a a 10 4 3 CASSCF wavefunctions The CONFIG Directive oaa aa aa 12 CONTENTS 5 Directives Controlling Wavefunction Convergence 54 MAXCYC sad a a BE eR Oe AAA ne 52 THRESHOLD orroa wie Ge Ae Oe O ee a EE e SCF Convergence Default Ol Pie Caca as SS EES SSeS ew eee OM a ey 6 1 1 Closed shell RHF Calculations 0200 6 1 2 Open shell RHF and GVB Calculations 6 1 3 Open shell UHF Calculations o e 6 2 Core Hole States Oo US o cada RE A tks 64 CONV AA 65 AVERAGE ss osp hs aoa Eee a be a eve eoh SS sk a i a DE ESR o RARAS REE A RRA e Be 6 7 CASSCF Convergence ss ee e a eR e SCF Convergence Alternate Driver TA Inp
53. DDLE XTOL 0 002 MINMAX 60 1 ENTER Here we are using the MINMAX directive to terminate the optimisation after the first line search Note that using the number of energy evaluations as the criterion may not be productive for this will cause termination at the first point in the evaluation of the 2nd derivative matrix re quested through the TYPE 3 specifications This may then be restarted as shown below where the default MINMAX settings will apply Restart Job RESTART SADDLE TITLE HCCH CCH2 RHF3 21G START UP JOB ZMAT ANGS C C 1 LI H 2 L2 1 Al X 21 0 1 90 0 3 180 01 H 2 L3 4 A2 1 180 0 VARIABLES Li 1 24054 TYPE 3 L2 1 65694 TYPE 3 L3 1 06318 TYPE 3 A1 60 3568 TYPE 3 A2 60 3568 TYPE 3 END RUNTYPE SADDLE XTOL 0 002 ENTER 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 93 13 8 2 SADDLE Data XTOL This directive may be used to define the convergence thresholds for the optimisation and consists of a single data line read to the variables TEXT TOL using format A F e TEXT should be set to the character string XTOL e TOL should be set to the value to be used in defining the four acceptance criteria for the convergence of the optimisation algorithm These criteria are maximum change in variables lt TOL average change in variables lt TOL 2 3 maximum gradient lt TOL 1 4 average gradient lt TOL 1 6 The XTOL directive may be omitted when TOL will be set to 0 001 The default thus c
54. E pre directive or ii use the IMEM parameter to control memory allocation in more detailed fashion e IMEM may be set to a number of words This should be used only with the MEMORY subdirective and only if the program runs out of memory With the MEMORY subdirective the program estimates the amount needed for the normal KS operations and reserves all other memory for the 3 center integral storage If the memory needed for the normal KS operations is underestimated IMEM may be set IMEM words of memory will then be added to the amount estimated for the normal KS operations i e the 3 center integral storage will be reduced by IMEM words To switch on Coulomb fitting for the energy gradient evaluation use the JFITG directive This comprises the single character string JFITG 11 9 2 JBAS To use Coulomb Fitting requires an auxiliary basis set to be specified for each atom of the molecule The JBAS directive should be used for this purpose It consists of 2 data fields read to variables TEXT TEXTOPT using format A A e TEXT should be set to the character string JBAS e TEXTOPT should be set to one of the following GAMESS to initiate explicit basis set specification from standard input in GAMESS UK format see Part 3 and Example 2 below NWCHEM to initiate explicit basis set specification from standard input in NWChem format 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 67 Setting TEXTOPT to one of the strings Al DGAU
55. ECTORS directive altogether The following points should be noted regarding use of these defaults 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 75 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 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 Table 2 have been described in some detail in Part 2 of the manual With the exception of RUNTYPE ANALYSE the choice of default section s is determined solely by the SCFTYPE that has been requested Given this the decision on the choice of input eigenvectors is made in three stages Thus when deciding on the section s to be used for these orbitals i e the VECTORS section s the default sections appropriate to the nominated SCFTYPE will be examined first If found to exist and in the absence of explicit section specification on the VECTORS directive the input eigenvectors will be taken from these default section s If these default sections have not been written to in some previous job or job step then the default closed shell eigenvector section section 1 will be examined and the input eigenvectors taken from this sec
56. INMAX XTOL STEPMAX and VALUE The user should note that the present implementation is based on maintaining a history of the optimisation pathway that will be worked through on each restart of the optimisation This appears on the output as a sequence of both old and new calculations with the history printed on each restart This printing may be suppressed through use of the NOPRINT directive with specification of the HISTORY keyword 13 3 1 OPTIMIZE Data MINMAX This directive may be used to control the number of energy evaluations and line searches per mitted in optimising a given structure and consists of a single data line read to the variables TEXT IVAL LINE using format A 21 e TEXT is set to the character string MINMAX e IVAL is an integer specifying the maximum number of energy evaluations allowed in the optimisation 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 83 e LINE is an integer defining the maximum number of line searches permitted in the opti misation The MINMAX directive may be omitted when both IVAL and LINE will be set to the maximum allowed value of 60 The following specification is thus equivalent to the default MINMAX 60 60 Example In some cases the user may wish to perform just the initial point on the optimisation pathway to gauge the quality of the starting geometry though the magnitude of the gradient at that point This may be achieved though use of MINMAX as shown
57. LLING DFT CALCULATIONS 53 TITLE H2C0 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE 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 DFT BECKE88 DFT LYP DFT QUADRATURE MEDIUM ENTER 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 exchange functional 32 and Lee Yang and Parr correlation LYP correlation energy functional 34 Over riding this default may be achieved through the following DFT keywords NULL_X The keyword NULL_X selects the null exchange functional Obviously this is useful only in very special cases HF_X The keyword HF_X selects the Hartree Fock exchange term as the exchange func tional LDA_X The keyword LDA selects the LDA exchange energy functional B88_X The keyword B88_X selects the default Becke 88 exchange functional This is a gradient corrected exchange energy functional with correct 1 r asymptotic behaviour of the exchange energy density 32 B3_X The keyword B3_X selects the Becke3 exchange functional This is the three param eter gradient corrected hybrid exchange energy functional with the Becke 88 functional as one of its components 28 B97_X The keyword B97_X selects the Becke97 exchange functional 23 EDF1_X The keyword EDF1_X selects the exchange functional of Empirical Density Func tional one 16 FT97A_X
58. NDRE LABEL Ci C2 11 0 1 15 0 5 17 ELEMENT CL 13 11 7 4 Radial Integration Grid EULER MACLAURIN The EULER MACLAURIN directive or shorter EULER selects the Euler MacLaurin radial in tegration grid 31 The grid size is specified through the number of grid points NPT The directive thus consists of two data field read to the variables TEXT NPT using format A e TEXT should be set to the character string EULER MACLAURIN or more simply EULER e NPT is an integer specifying the required number of points 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 61 The grid points will be located at 2 Ti n 1 2 i Xi wa NPT 1 where 1 lt i lt NPT In this expression a is an element dependent scale factor Note that all points with gt NPT 1 2 will have r gt a Moreover the most distant point will be at ri a x NPT In practice this means that relatively many points will be far from the nucleus Examples EULER 45 EULER LABEL Hi Hi 45 EULER ELEMENT C H 45 LABEL 01 20 11 7 5 Radial Integration Grid LOG The LOG directive selects the logarithmic radial integration grid 25 The grid size is specified through the number of grid points NPT In addition a power M must be specified which is defined below The directive thus consists of three data fields read to the variables TEXT NPT M using format A I F e TEXT should be set to the character string LOG e NPT is an integer specifying the required numbe
59. SECT2 should be omitted in those cases involving a single set of eigenvectors We illustrate below typical ENTER data lines as a function of SCFTYPE assuming the defaults of Table 2 are to be overwritten e For a closed shell SCF calculation the data line ENTER 10 will route the eigenvectors to section 10 of the Dumpfile e For a UHF calculation the data line ENTER 12 13 will route the a spin eigenvectors to section 12 of the Dumpfile G spin vectors to section 13 e For a GVB or open shell calculation the data line ENTER 16 17 will route the un canonicalised vectors to section 16 and the canonicalised orbitals to section 17 Omitting the second section in such calculations will result in the canoni calised set only appearing on the Dumpfile the un canonicalised set being overwritten on convergence of the SCF e For a CASSCF calculation the data line ENTER 18 19 will route the CASSCF orbitals to section 18 and the canonicalised CASSCF vectors to section 19 Note that the present set of Cl coefficients will be appended to this section 17 STOP 107 17 STOP The STOP directive may be presented as an alternative to ENTER and with the same syntax may be used simply as a check of the data input No modifications are made to the Dumpfile execution terminating once data processing is complete REFERENCES 108 References 1 2 3 4 5 6 7 8 9 10 11 12 13 P Pula
60. SERHF and GRHF options of ATMOL3 8 The STATE parameter is not required when no ambiguity in the required energy expression occurs Example When performing an open shell SERHF calculation on the 4 state of NHt characterised by the configuration 1072073011 tel ty 1 The data line OPEN 1 1 2 2 would be required together with a MULT 4 specification with the input orbitals ordered thus M O 1 2 3 4 5 Symmetry lo 20 30 lrx 11y where shell 1 comprises the closed shell orbitals lo 2c shell 2 the singly occupied 30 orbital and shell 3 the degenerate 17 orbital Calculations on the corresponding 7A state would require the directives MULT 2 and OPEN 1 1 2 2 DELTA 4 DIRECTIVES DEFINING THE WAVEFUNCTION Table 1 Energy Expressions Available and the OPEN Directive Configuration State Data Specification OPEN STATE MULT 2A 2 1 2 r 211 el 2E 92 35A De Y 3 2 35 e 3A 6 Ip 2 2 GAMMA 1 1 1A 2 2 DELTA 1 92 I5 t 2 2 SIGP 1 7 15 SIGP e LA A 53 2A 2 3 2 q 211 e3 2E p 2p 3 1 2 t 2T p 3P 3 2 3 t 3T p 1D 3 2 D 1 p Ig 3 2 S 1 t 1A 3 2 A 1 p 49 3 3 4 t 41A a 8 4 p 2D 3 3 D 2 t 2p 3 3 P 2 p 3P 3 4 3 4 DIRECTIVES DEFINING THE WAVEFUNCTION Configuration aoln OT olr aoln TT TT Rh e a ap TT TT TT Rh e a hop TT mm n n n n State 1p r5 1A 2P ep TI SII 35 Data Specification
61. SS A2 DGAUSS DEMON or AHLRICHS signals that the fitting basis set is not to be defined in the input stream but is to be loaded from the appropriate library of internal basis sets Al DGAUSS or A2 DGAUSS result in the A1 or A2 DGauss fitting sets 41 DEMON the DeMon fitting basis 41 and AHLRICHS the fitted basis sets tabulated by Ahlrichs and co workers 42 see Example 1 below TEXTOPT may be omitted in which case it is assumed that the basis set is to be specified in GAMESS UK format 11 93 SCHWARZ Finally to reduce the number of 3 center integrals small terms may be eliminated using the Schwarz inequality The SCHWARZ directive which is read to the variables TEXT ISCHWARZ using the format A l can be used to set the tolerance e TEXT should be set to the character string SCHWARZ e ISCHWARZ should be set to an integer value The Schwarz tolerance will then be set to 1Q ISCHWARZ Example 1 Coulomb Fitting Using the A1 DGAUSS Fitting Basis TITLE H2CO 6 31G BLYP DFT WITH A1 DGAUSS COULOMB FITTING ZMATRIX ANGSTROM C D 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 MEMORY DFT SCHWARZ 6 DFT JBAS A1i DGAUSS ENTER Example 2 Coulomb Fitting with Explicit Specification of the A1 DGAUSS Basis TITLE H2CO 6 31G BLYP DFT WITH A1 DGAUSS COULOMB FITTING ZMATRIX ANGSTROM 11 DIRECTIVES CONTROLLING DFT CALCULA
62. TIONS co CH 2 121 8 H 1 CH 2 121 8 3 180 0 VARIABLES c0 1 203 CH 1 099 END BASIS 6 31G RUNTYPE OPTIMISE SCFTYPE DIRECT RHF DFT BLYP DFT JFIT MEMORY DFT SCHWARZ 6 C 0 1 H 1 DFT JBAS DGauss A1 Coulomb fitting basis gamess basis set format S H 1 000000 45 000000000 SH 1 000000 7 500000000 S H 1 000000 1 500000000 S H 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 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 S 0 1 000000 25 000000000 SP 0 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 69 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 12 Controlling the input Orbitals The VECTORS Directive Each of the SCF modules requires one or more sets of trial molecular orbitals or eigenvectors to initiate the iterative process The analysis routines also require definition of the input set of orbitals to be analysed In both cases the origin of such a set is defined under control of the VECTORS direc
63. a block of directives of the following form newscf lt control directives gt end The lt control directives gt block can be empty in which case a default convergence scheme will be used or it can contain the control directives described in the following sections An input file with a set of example control directives is provided at the end of this section for readers who wish to gain an overview of how things are structured before before becoming bogged down in the details of each directive 7 2 Overall Control Flags 7 2 1 Controlling Printed Output PRINT This directive controls which data from the calculation will be included in the output The format of the directive is a single line containing the keyword PRINT A followed by any combination of the following parameters to the PRINT command all in A format 7 SCF CONVERGENCE ALTERNATE DRIVER 28 FOCK requests printing of the Fock matrix at SCF convergence GUESS Print out the trail vectors DENSITY Print out the density matrix VECTORS Print out the eigenvectors FULL Print everything WARNING this may produce a lot of output FRONTIER Print the frontier orbitals DIIS Monitoring of the solution of the DIIS equations TIME Print the cycle and total wallclock and cpu times each cycle So for example the line PRINT FOCK would cause the entire Fock matrix to be printed on SCF convergence 7 2 2 SCF exit status SOFTFAIL This directive consists of the th
64. ace calculation on the X B state with frozen Cls would be controlled thus CONFIG FZC 1 DOC 2 3 ALP 4 5 UOC 6 7 END The corresponding calculation on the tB state featuring singlet coupling of the 3a and 1b MOs would require use of the AOS and BOS tags thus CONFIG FZC 1 DOC 2 3 AOS 4 BOS 5 UOC 6 END 7 remembering to change or remove the MULT 3 specification Note Additional keywords may be specified on the directive initiator line as follows e PRINT to obtain a complete list of the CASSCF configurations characterised by oc cupation pattern e BYPASS at the outset of a CASSCF calculation the loop formulae tape written in default to ED9 must be generated The BYPASS keyword allows this step to be bypassed in a subsequent restart job assuming of course that the data set had been retained between jobs note that the PRINT option is not effective in BYPASS mode e NOSORT if the 1 step Newton Raphson optimisation technique is to be used during CASSCF iteration under control of the SIMUL directive see 5 4 2 then the loop for mulae tape is reordered in the interests of efficiency This reordered file is written in default to ED10 with the reordering process carried out automatically unless suppressed by presenting the NOSORT keyword on the CONFIG data line 5 DIRECTIVES CONTROLLING WAVEFUNCTION CONVERGENCE 16 Example Assuming that simultaneous optimisation is not to be performed and that a list of
65. ain a relative error of less than 1 0e 8 in the number of electrons per atom VERYHIGH The VERYHIGH accuracy grid is meant only for benchmark calcu lations It is designed to be significantly more accurate than the high accuracy grid 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 58 The directive may be omitted when ACCU will be set to the default MEDIUM quadrature setting Example TITLE H2C0 6 31G CLOSED SHELL DFT B3LYP HIGH QUADRATURE ZMATRIX ANGSTROM C 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END BASIS 6 31G DFT B3LYP DFT QUADRATURE HIGH ENTER Note that the LABEL and ELEMENT keywords discussed in the next subsection may also be used with the QUADRATURE sub directive 11 7 Detailed Grid Specification A number of sub directives of DFT are available to control the grids to be used although it is not expected that these would be routinely invoked when running the DFT module These sub directives include those for i specifying both the angular integration grid LEBEDEV or GAUSS LEGENDRE and radial grid EULER MACLAURIN or LOGARITHMIC ii the screening of grid points SCREEN iii an appropriate weighting scheme WEIGHT and iv activating angular grid pruning ANGPRUNE 11 7 1 Grid Specification on a Per Atom Basis ELEMENT and LABEL For optimal control over the integration it is required that the grid may be modified for each atom separately For this purpose the keywords ELEMENT and LA
66. al and final MOs then the single data line of the form ENTER 10 would be required with the final set of MOS being written to section 10 Note that usage of this set in some subsequent job would require explicit introduction of the data line VECTORS 10 to avoid use of the default section 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 76 2 UHF SCF Two sets of eigenvectors are generated in an open shell unrestricted Hartree Fock UHF calculation the a spin SCF MOs and 3 spin orbitals In default the a spin MOs will be written to section 2 of the Dumpfile and the 3 spin MOs to section 3 see Table 2 Thus presenting the single data line ENTER in a startup job would act to request an atomic GUESS for generating a set of SCF eigen vectors that would be be used to initiate the UHF process with the a and G3 spin MOs subsequently updated and written to sections 2 and 3 of the Dumpfile see Table 2 during the SCF process Presenting the same data line in a subsequent RESTART job would result in the eigenvectors of section 2 and 3 being used as the trial vector set and subsequently updated during the UHF process In practice these default sections would be exam ined for content at job outset and the contents used for the SCF process assuming the sections had been written to by a previous job If the sections are not present on the Dumpfile then either i the closed shell MOS if present in section 1 will be used as t
67. and implications for exact erchange mixing J Chem Phys 104 1996 1040 1046 doi 10 1063 1 470829 R D Adamson P M W Gill and J A Pople Empirical density functionals Chem Phys Lett 284 1998 6 11 doi 10 1016 S0009 2614 97 01282 7 F A Hamprecht A J Cohen D J Tozer and N C Handy Development and assess ment of new exchange correlation functionals J Chem Phys 109 1998 6264 6271 doi 10 1063 1 477267 A D Boese N L Doltsinis N C Handy and M Sprik New generalized gradient approx imation functionals J Chem Phys 112 2000 1670 1678 doi 10 1063 1 480732 A D Boese and N C Handy A new parametriztion of exchange correlation gener alized gradient approximation functionals J Chem Phys 114 2001 5497 5503 doi 10 1063 1 1347371 J P Perdew K Burke and M Ernzerhof Generalized gradient approximation made simple Phys Rev Lett 77 1996 3865 3868 doi 10 1103 PhysRevLett 77 3865 J P Perdew J A Chevary S H Vosko K A Jackson M R Pederson D J Singh and C Fiolhais Atoms molecules solids and surfaces Applications of the generalized gra dient approximation for exchange and correlation Phys Rev B46 1992 6671 6687 doi 10 1103 PhysRevB 46 6671 J P Perdew and Y Wang Accurate and simple analytic representation of the electron gas correlation energy Phys Rev B45 1992 13244 13249 doi 10 1103 PhysRevB 45 13244 A D Becke J Chem Phys 107 1997 8554 doi 10 1063 1 47
68. ant internal coordinates and hybrid delocalised in ternal coordinates L BFGS is the recommended method for minimum search Transition state search may be done by P RFO an improved version of the dimer method or nudged elastic band using a climbing image DL FIND is invoked by the runtype optimize or saddle and the directive DLFIND DL FIND directives END 15 1 DL FIND directives 15 1 1 COORDINATES The directive COORDINATES TEXT specifies the coordinate system in which the optimisation should be performed Possible choices for TEXT are CART Cartesian coordinates default MASS Mass weighted Cartesian coordinates DLC Delocalised internal coordinates A redundant set of bonds angles torsions and some times inversions is created A non redundant combination of them is found by diagonal ising the spectroscopic G matrix The optimisation is performed in this non redundant set TC Same as DLC but the redundant set consists only of bonds all atoms in the system are connected HDLC Hybrid delocalised internal coordinates The system is partitioned into fragments Delocalised coordinates as in DLC are used within each fragment The fragments are coupled via Cartesian coordinates This version is recommended for large systems as the coordinate transformation scales linearly with the number of atoms 15 OPTIMISATION USING DL FIND 102 15 1 2 DIMER The directive DIMER is used to start a transition state search using t
69. ault specification corresponding to TXTRFO 0N results in the RFO or P RFO steps only see 7 Specifying OFF will result in the taking of Newton Raphson steps where appropriate instead of RFO or P RFO steps 14 11 OPTPRINT This directive may be used to control diagnostic output during optimisation A data line of the form OPTPRINT ON may be used to increase diagnostic output 14 12 Example 1 The following data file may be used to perform the search for the FCN FNC transition state using an STO 3G basis set The initial Hessian is computed through TYPE 3 specification with the Powell update requested throughout Jorgensen optimisation TITLE FCN FNC TS SEARCH STO3G BASIS ZMAT ANGS Cc N 1 Li F 1 L2 2 Al VARIABLES L1 1 2 TYPE 3 L2 1 3 TYPE 3 A1 135 0 TYPE 3 END BASIS STO3G RUNTYPE SADDLE JORGENSEN POWELL MAXJOR 55 RECALC OFF RFO OFF CUTOFFS OPTPRINT ON XTOL 0 0018 ENTER 15 OPTIMISATION USING DL FIND 101 15 Optimisation using DL FIND DL FIND is a self contained module that is included into GAMESS UK Additional information on DL FIND as well as the developmental version of the code can be found on the DL FIND website at http ccpforge cse rl ac uk projects dl find DL FIND offers several methods for geometry optimisation and transition state search The ge ometry can be optimised in a range of coordinate systems Cartesian coordinates Mass weighted Cartesian coordinates delocalised redund
70. bly occupied orbital of az symmetry would be tagged DOC1 an unoccupied orbital of bg symmetry UOC3 9 DIRECTIVES CONTROLLING MCSCF CALCULATIONS Al 9 2 1 ORBITAL Example 1 Let us consider initially various calculations on the water molecule to illustrate ORBITAL spec ification The example is based on a TZVP basis with the following set of input MOs derived from a closed shell SCF calculation TOTAL ENERGY 76 0553958459 1 1 20 55996277 2 0000000 2 1 1 35317135 2 0000000 3 3 0 71806974 2 0000000 4 1 0 58054044 2 0000000 5 2 0 50734492 2 0000000 6 1 0 13628400 0 0000000 7 3 0 19133694 0 0000000 8 3 0 52235466 0 0000000 9 1 0 52876578 0 0000000 10 2 0 55149622 0 0000000 11 1 0 62397742 0 0000000 12 3 0 73116091 0 0000000 13 1 1 04616882 0 0000000 14 1 1 88402305 0 0000000 15 4 1 92286966 0 0000000 16 2 2 12532394 0 0000000 17 3 2 18404917 0 0000000 18 1 2 28261839 0 0000000 19 3 2 37902858 0 0000000 20 3 2 69431254 0 0000000 21 1 2 70971740 0 0000000 22 2 2 71654746 0 0000000 23 1 3 05834268 0 0000000 24 3 3 25415102 0 0000000 25 2 3 54107441 0 0000000 26 1 3 55600364 0 0000000 27 4 3 59173828 0 0000000 28 1 3 83258378 0 0000000 29 1 4 79289351 0 0000000 30 3 5 12382812 0 0000000 31 1 7 71922625 0 0000000 32 1 47 55358026 0 0000000 To perform a full valence space calculation comprising 7 primary orbitals with the 4a and 2b2 virtual MOs with sequence numbers 6 and 7 respectively included in the active space
71. ccupied orbitals in the previous SCF cycle and the current is calculated and the electrons remain in the orbital that overlaps most closely with the one they were in previously regardless of whether there is an unoccupied orbital lower in energy Locking can therefore be used to maintain an excited state configuration during a calculation 7 SCF CONVERGENCE ALTERNATE DRIVER 31 7 3 9 SMEAR The SMEAR directive implements Fermi smearing 11 for filling up the molecular orbitals Normally orbitals are either fully occupied or empty Fermi smearing allows orbitals to be fractionally filled according to a step function that depends on the Fermi temperature employed Fermi smearing can be useful in certain problematic convergence cases where degenerecies in the orbital energies mean that it is uncertain which state the SCF should converge on Smearing may alleviate the problem by using an average state thereby removing the need to make a discrete choice The format of the directive is SMEAR lt START_TEMP gt lt FINAL_TEMP gt lt UNITS gt SCALE lt SCALE_VALUE gt where e START_TEMP F is the starting Fermi Temperature e FINAL_TEMP F is the final Fermi Temperature e UNITS A specifies the units to be used for the final and starting tempratures By default the units are Hartrees but setting UNITS to EV changes the units to Electron Volts e SCALE A is the keyword SCALE followed by the scale factor SCALE_VALUE
72. ce of a RUNTYPE directive the default of a single point SCF calculation is assumed e When restoring a Hessian Matrix for use in OPTIMISE and SADDLE computations the source of this Hessian must be specified on the RUNTYPE directive This may take two forms 1 When the initial Hessian has been computed under control of the RUNTYPE HES SIAN directive the additional keyword FCM should be specified on the OPTIMISE or SADDLE data line thus RUNTYPE SADDLE FCM 2 When the Hessian is to be restored from some smaller basis set calculation i e from a Dumpfile separate to that of the present calculation this foreign Dumpfile must be specified on the RUNTYPE directive so the data line 2 RUNTYPE RUNTYPE SADDLE ED4 150 requests the initial Hessian to be restored from the Dumpfile commencing at block 150 on the data set assigned with the LFN ED4 RUNTYPE INTEGRAL RUNTYPE SCF RUNTYPE OPTIMISE RUNTYPE OPTXYZ RUNTYPE SADDLE RUNTYPE FORCE RUNTYPE HESSIAN RUNTYPE POLARISABILITY RUNTYPE HYPER RUNTYPE MAGNET RUNTYPE RAMAN RUNTYPE INFRARED RUNTYPE TRANSFORM RUNTYPE Cl RUNTYPE GF RUNTYPE TDA RUNTYPE RESPONSE RUNTYPE ANALYSE single point le and 2e Integral evaluation single point Integrals SCF calculation search for a local minimum on the potential energy surface using an internal coordinate quasi Newton rank 2 update method search for a local minimum on the potential energy surface using a cartesian based quasi Ne
73. coefficients In a subsequent restart we would specify VECTORS 6 7 ENTER 6 7 when the orbitals will be read from Section 6 and the Cl coefficients from Section 7 Note that the program assumes given two Sections on the VECTORS line that the second may be used as a source of Cl coefficients if that Sections contains no such data or coefficients from some different CASSCF calculation with a different Cl space an error condition will result There are times when it is useful to see the starting vectors in which case the character string PRINT may be specified on the VECTORS directive line eg VECTORS ATOMS PRINT If the vectors are read from a section one may forego the orthogonalisation of these vectors by specifying the keyword NOORTH e g VECTORS 19 NOORTH This may be used for example in calculating coulomb energies where the non orthogonal vectors are combined by the SERVEC subprogram 12 3 Using Default Sections under VECTORS and ENTER In all the examples above we have assumed that the User is explicitly defining the sections of the Dumpfile to be used for vector retrieval under control of the VECTORS directive and vector storage under control of the ENTER directive While this mechanism provides an additional degree of user control it is now possible to use a set of default sections that avoids the need for explicit specification on both VECTORS and ENTER directives and in most cases removes the need for presenting the V
74. correlation functional was known In practice the exact functional is unknown but one may try some approximate form This has led to a extensive search for functionals with new variations being published on a regular basis Because the quality of the results depends critically on the functional selecting a suitable form will be a vital factor in using the module 2 The integration grids Another issue related to the functionals stems from their form most functionals are such that they can not be integrated analytically over all space Therefore the exchange correlation energy can be evaluated only through numer ical integration It was found that this numerical integration could only be successful if the integration grid is adapted to the particular features of the molecular density These features are that the density is high and nearly spherically symmetric near the nuclei Between the nuclei the density has less symmetry and is smaller However because most of the chemistry depends on the density between the nuclei accurate integration in that region is essential To devise integration grids adapted to these features the atoms of a molecule were taken as the central points Each nucleus would be the center of a set of spherical grids with ever larger radii The simplest way to obtain such a grid would be to take the Cartesian product of a radial grid with a spherical grid But more advanced schemes can be engineered Once the atomic grids have
75. cussion of the data requirements for use when invoking the Simons and Jorgensen algorithm is given in section 10 For completeness we include here the data file required in optimising the geometry of H2CO noting that in most cases the default settings will prove satisfactory TITLE H2C0 DZ BASIS JORGENSEN OPTIMISATION ZMATRIX ANGSTROM C D 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 BASIS DZ RUNTYPE OPTIMIZE JORGENSEN ENTER 13 7 Transition State Location and RUNTYPE Specification Three methods are available to search for a transition state on a potential Surface each driven through SADDLE specification on the RUNTYPE directive and each relying on internal coor dinate specification through the ZMATRIX directive 1 the recommended method a modification to the Cerjan and Miller trust region algo rithm is driven through the specification RUNTYPE SADDLE This method performs optimisation in internal coordinates and thus requires initial ZMA TRIX and VARIABLES specification of the molecular geometry or ZMATRIX construction from an initial set of cartesian coordinates supplied under control of the GEOMETRY di rective Note that the success of the method is dependent on the quality of the initial 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 91 Hessian and the user is reminded of the need to address this issue through appropri ate TYPE specifications on the
76. d 5 being used as the trial vector set and subsequently updated and overwritten during the open shell SCF In practice these default sections would be examined for content at job outset and the contents used for the SCF process assuming the sections had been written to by a previous job If the sections are not present on the Dumpfile then either i the closed shell MOS if present in 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 77 section 1 will be used as the trial orbitals ii with no closed shell section a trial set will be generated using the VECTORS ATOMS mechanism If the User wished to keep copies of both sets of initial and final open shell MOS then a single data line of the form ENTER 10 11 would be required with the final set of internal MOS being written to section 10 and the canonicalised orbitals to section 11 Note that usage of this set in some subsequent job would require explicit introduction of the data line VECTORS 10 11 to avoid use of the default section 4 CASSCF Calculations Again two Sections are required the first housing the non canonicalised CASSCF MOs that are used during the CASSCF process and the second set the canonicalised vectors that are generated on termination of the CASSCF process In default the non canonicalised vectors will be written to section 6 of the Dumpfile while the canonicalised vectors will be written to section 7 see Table 2 Note that the latter sectio
77. d to define e the number of orbitals in each open shell e the number of electrons in each open shell The general syntax of the directive is OPEN N01 NE1 NO2 NE2 STATE where NO1 NE1 correspond to the number of orbitals and electrons respectively in the first open shell NO2 NE2 to the number of orbitals and electrons in the second open shell and so on until all open shells have been specified As outlined in Section 3 1l certain assumptions are made concerning the ordering of the input orbitals within RHF and GVB modules and this ordering ties in with the OPEN definition Specifically it is assumed that the orbitals are ordered thus e all doubly occupied orbitals occur first in the list the complete set defining Shell 1 the closed shell e following the closed shell manifold comes the open shells with the number of orbitals and electrons in each open shell defined by the OPEN directive e the GVB pair orbitals 4 DIRECTIVES DEFINING THE WAVEFUNCTION 7 In many cases the specification of the number of component orbitals and electrons associated with each open shell provides together with the MULT directive a unique definition of the associated electronic state When this is not the case and ambiguity remains in the definition the character string STATE may be used to nominate the required state A full list of the possible STATEs available is shown in Table 1 below Note they include all those possible under the
78. d virtual level shifters after the iterative cycle specified by IBRK An alternative form of LEVEL is permitted consisting of only three parameters read to variables TEXT OCC1 V1 using format A 2F In this form TEXT OCC1 and V1 have their usual meanings whilst the program will set IBRK 999 and OCC2 V2 to zero The LEVEL directive may be omitted when the program will assign the following default settings 6 SCF CONVERGENCE DEFAULT 19 occi 0 05 Vi 1 0 IBRK 5 DCC2 0 01 V2 0 5 The following points should be noted on using level shifters to proceed to the onset of DIIS e Note that the value of the doubly occupied partially occupied level shifter is typically far smaller than that involving the virtual interaction e lt can be shown that convergence to a stationary point on the energy surface can be guaranteed if sufficiently large and positive level shifters are used Thus if divergence is experienced the user may repeat the job but with increased level shifters The data line e As with closed shell systems the default shifters above are doubled in value for systems containing first row transition metal atom s LEVEL 0 3 1 5 is usually sufficient to force convergence to the onset of DIIS 6 1 3 Open shell UHF Calculations In the case of an open shell UHF calculation the LEVEL directive consists of a single data line read to variables TEXT EA1 EB1 IBRK EA2 EB2 using format A 2F 1 2F e TEXT should be
79. default GEOMETRIC to select the geometric mean Cg coefficient pair model The following three examples all result in using the dispersion corrections in accordance with the default settings Examples DFT DISPERSION DFT DISPERSION ON DFT DISPERSION AVERAGE 11 6 Specification of Integration Grids While a large number of options are available in specifying possible integration grids see below the inexperienced user is strongly advised to use just the QUADRATURE directive for this purpose 11 6 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 25 and Lebedev angular grids 43 using the SSF weighting scheme with screening 26 and MHL angular grid pruning 31 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 obt
80. e configura tion used for certain atoms this is useful for pseudopotentials when the user supplies the pseudopotentials under control of the CARDS option or if the user does not like the configuration chosen by the atomscf program The configuration s are specified for each atom on subsequent lines following the VECTORS directive with the data terminated by END ATOM subdirectives x CONF specify the required configuration to be used in the atomic scf for the ATOM as e g d5s1 It is worthwhile checking that the required effect is obtained x DCONF or DENS specify the configuration to be used in calculating the final atomic density matrix x CHARGE A F specify the charge for the ATOM The extra charge is prefer ably added to the highest open shell Otherwise it is spread over the closed shells Example Na charge 1 0 CL charge 1 0 x SPIN A A I 1 Specify the division of the electrons over the alpha and beta density matrices for the specified s p d f shell This directive is only allowed and then really required if UHF is specified on the VECTORS card More spin directives may given to specify the division for different shells This directive overrides specification by the DENS or CHARGE sub directives Example 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 71 Fe1 CONF d5s1 DENS d5si SPIN d 5 0 Fe2 CONF d5s1 DENS d5si SPIN d 0 5 NORE or NONREL Specifies that this atom is to be treated non relativist
81. e default MINMAX settings will apply Restart Job RESTART OPTXYZ TITLE H20 DZ OPTIMIZE ZMAT ANGSTROM O H 1 ROH H 1 ROH 2 THETA VARIABLES ROH 0 956 HESSIAN 0 7 THETA 104 5 HESSIAN 0 2 END BASIS DZ RUNTYPE OPTXYZ ENTER 13 5 2 OPTXYZ Data XTOL This directive may be used to define the convergence threshold for the optimisation and consists of a single data line read to the variables TEXT TOL using format A F e TEXT should be set to the character string XTOL e TOL should be set to the value to be used in defining the criteria for convergence of the optimisation algorithm the maximum component of the gradient The XTOL directive may be omitted when TOL will be set to 0 001 The default thus corre sponds to presenting the data line XTOL 0 001 13 5 3 OPTXYZ Data STEPMAX This directive may be used to define the the maximum allowed movement in any of the cartesian coordinates in a single step of the geometry optimisation in units of bohr The directive consists of a single data line read to the variables TEXT STEP using format A F 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 90 e TEXT should be set to the character string STEPMAX e STEP should be set to the maximum permitted movement in any coordinate The STEPMAX directive may be omitted when STEP will be set to 0 2 The default thus corresponds to presenting the data line STEPMAX 0 2 13 6 JORGENSEN Data Specification An extended dis
82. e endpoints of the NEB path will be freely minimised frozen or only free to move perpendicular to the path respectively FROZEN is the default If CART is specified only the initialisation of the path will be done in the coordinate system specified by COORDINATES The following minimisation will be done in Cartesian coordinates 15 OPTIMISATION USING DL FIND 103 15 1 6 GEOMETRY The directive GEOMETRY specifies the endpoint of an initial NEB path The other endpoint is specified by the normal input geometry The directive GEOMETRY can also be used to specify an initial dimer direction GEOMETRY TEXT TEXT is the name of a file in xyz format It has to contain the same atoms as the GAMESS input geometry 15 1 7 OPTIMISER The directive OPTIMISER TEXT specifies the optimisation algorithm Possible choices for TEXT are LBFGS Limited memory Broyden Fletcher Goldfarb Shanno optimisation Recommended for minimum search NEB and the dimer method The time and memory requirements spent for determining the search direction and step length scale linearly with the system size And additional integer parameter can be specified which determines the number of steps kept in memory Default is the number of degrees of freedom PRFO The partitioned rational function optimisation method Recommended for transition state search unless done by the dimer or NEB methods It requires the calculation of the Hessian The UPDATE directive see below
83. e single character string SOFTFAIL A and will prevent the code from generating an error if MAXCYC SCF cycles are reached without convergence 7 3 Controlling the convergence of a calculation Convergence is controlled by providing parameters for a series of phases each becoming active depending on particular criteria and employing various convergence controls If convergence control directives are omitted a default scheme is adopted otherwise the user will need to provide the control information for a number of phases including the criteria that are used to switch from one phase to another The control information is provided in a phase block which is started by a line with two data fields PHASE A and IPHASE I e PHASE is set to the character string PHASE e IPHASE is an integer greater than zero identifying the phase A phase block is terminated by a subsequent PHASE directive or an END directive indi cating the end of the newscf control directives Within a phase block the criteria for when to jump to a subsequent phase is determined by the NEXT directive An individual phase block is arranged as shown below PHASE lt N gt lt convergence controls gt NEXT lt M gt lt convergence criteria gt 7 SCF CONVERGENCE ALTERNATE DRIVER 29 where lt N gt is an integer denoting the phase in questions and lt M gt an integer denoting the next phase to jump to Within a phase bloc
84. ed 2 In default GAMESS UK will automatically based on the z matrix geometry specification deduce the molecular point group and hence generate and retain only the unique integrals required in the process of constructing a skeletonised Fock matrix 9 Such a symmetry truncated integral list is however NOT usable in pair GVB calculations and considerable caution should be exercised when considering use of an integral file generated in an earlier SCF run directly in a subsequent pair GVB calculation under control of the BYPASS directive The way to proceed in such cases has been outlined in section 2 6 Assume we wish to perform a 4 pair GVB PP calculation on H2CO treating the C H bonds and two C O orbitals within the perfect pairing approximation In such cases little progress is possible using the set of SCF MOs directly in the GVB it will be necessary to generate a trial set of GVB vectors based on a localised orbital set using the VECTORS option NOGEN to generate the set of secondary GVB pair orbitals based on the set of LMO Thus the sequence of calculations required is e perform the closed shell SCF calculation e localise the set of valence SCF orbitals 4 DIRECTIVES DEFINING THE WAVEFUNCTION 11 e perform the GVB calculation using the set of LMO input under control of the VECTORS option NOGEN First we show the data sequences for performing the initial closed shell calculation and the subsequent Boys localisation in which t
85. el does not affect those of the geometric mean model and vice versa 8 0 1 1 The ON directive The ON directive may be used to explicitly turn the dispersion corrections on The directive is read to the variable TEXT using the format A where TEXT should be set to the character string ON 8 0 1 2 The OFF directive The OFF directive may be used to explicitly turn the dis persion corrections off The directive is read to the variable TEXT using the format A where TEXT should be set to the character string OFF 8 0 1 3 The C6MODEL directive The C6MODEL directive may be used to choose the Ce coefficient pair model to be used The directive consists of two data fields read to the variables TEXT and TEXTA using the format A A e TEXT should be set to the character string COMODEL e TEXTA may be set to either AVERAGE to select the average Cg coefficient pair model according to equation 13 GEOMETRIC to select the geometric mean Cg coefficient pair model according to equation 14 8 0 1 4 The SCALE directive The SCALE directive may be used to change the overall scale factor sg for the dispersion correction The directive consists of two data fields read to the variables TEXT and SCALE using the format A F e TEXT should be set to the character string SCALE e SCALE should be set to the scale factor for the current Cg coefficient pair model which has to be a non negative floating point value 8 0 1 5 The ALPHA directive The ALPHA direc
86. ely The SPIN parameter may be omitted thus the directive is the same as that above and will cause a spin vectors to be interchanged 13 Controlling Geometry and Transition State Optimization There are a variety of methods available for controlling the search for a stationary point on a potential energy surface Each may be requested through appropriate keyword specification on the RUNTYPE directive and in the following section we detail subsequent data requirements of each method In most cases adequate control of the optimisation pathways is provided through a set of built in parameters and the user need only consider overriding these defaults in troublesome cases through use of the directives described below An introduction to the various methods and their usage has already been presented in Part 2 and should be used in conjunction with the notes below 13 1 Geometry Optimisation and RUNTYPE Specification Three methods are available to search for a minimum on a potential Surface 1 the recommended method a quasi Newton rank 2 update procedure is driven through the specification RUNTYPE OPTIMIZE This method performs optimisation in internal coordinates and thus requires initial ZMA TRIX and VARIABLES specification of the molecular geometry or ZMATRIX construction from a set of cartesian coordinates supplied under control of the GEOMETRY directive 2 the second internal coordinate driven method is that based on the h
87. en the VECTORS directive is a straightforward extension of the single vector case with the location of each set specified Thus the data line is as follows VECTORS GETQ fnveca iblka isecta Ifnvecb blkb isectb where e fnveca iblka and isecta The trial a spin vectors are to be restored from the Section specified by isecta on a foreign Dumpfile commencing at the block specified by blka with the Dumpfile residing on the data set assigned using the LFN fnveca e fnvecb iblkb and isectb The trial 3 spin vectors are to be restored from isectb on a foreign Dumpfile residing on a data set assigned using the LFN fnvecb commencing at block ib kb Note that e the trial G spin orbitals will be set equal to the trial a spin orbitals if fnvecb iblkb and isectb are omitted from the data line e there is currently no provision for restoring the Cl Vector Section in a CASSCF calculation under control of the GETQ option In such cases it is only possible to restore a single set of vectors the CASSCF orbitals Example 1 A geometry optimisation has been performed with a closed shell SCF calculation in a 3 21G basis set A single point calculation in a TZVP basis set is to be performed at the optimised geometry Assuming that the Dumpfile from the optimisation run is located on a data set assigned to the present calculation as ED4 starting at block 1 and that the converged 3 21G vectors are stored in Section 2 of this Dumpfile t
88. ent to providing a separate FCM directive The directive consists of a single line containing 14 JORGENSEN AND SIMONS OPTIMISATION ALGORITHM 97 FCM DD IBLOCK TYPE where DD is the name of the dumfile containing the Hessian and IBLOCK is its starting block TYPE is the type of Hessian requested and can be any of MP2 SCF or OPTIMISE where the former denote analytical hessians generated using MP2 or SCF respectively and OPTIMISE requests the Hessian produced during an OPTIMISE or SADDLE run If the TYPE is omitted the dumpfile is searched for hessian sections in the order given above The Dumpfile specification may be omitted in which case the current dumpfile is searched For example the next sets of input lines are equivalent assuming the default dumpfile RUNTYPE OPTIMISE FCM ED3 1 RUNTYPE OPTIMISE ED3 1 The FCM directive may also read FCM UNIT7 in which case the Force Constant Matrix is read from the punchfile 14 Jorgensen and Simons Optimisation Algorithm An alternative stationary point optimisation procedure code named JORGENSEN is avail able within GAMESS UK An efficient quasi Newton Raphson algorithm for locating transition states this procedure is based on a modification to the Newton Raphson step first proposed by Cerjan and Miller 5 although the major part of the algorithm is founded on the later develop ments of Simons Jorgensen and coworkers 6 The algorithm is capable of locating transition states eve
89. enting the LOCK directive in the closed shell case may act to minimise this occurrence 13 3 4 OPTIMIZE Data VALUE This directive may be used to control the accuracy of the search for a turning point during a line search and consists of a single data line read to the variables TEXT TURN using format A F e TEXT should be set to the character string VALUE 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 85 e TURN should be set to a value between 0 0 and 1 0 that will control the accuracy of the line search procedure Note that the smaller TURN the more accurate the line search The VALUE directive may be omitted when TURN will be set to 0 6 The default thus corresponds to presenting the data line VALUE 0 6 13 4 Modifying the Optimisation Pathway In some cases the user may wish to modify the parameters controlling geometry optimisation though XTOL VALUE and STEPMAX specification during the course of the optimisation Note that these parameters may only be modified between line searches and not between indi vidual energy or gradient evaluations The most straightforward example would be initialising the optimisation with stringent controls then relaxing these controls as the optimisation pro ceeds in some subsequent restart job The startup job may either be interrupted under control of the MINMAX directive or through time specification on the TIME pre directive see Parts 12 16 of the manual Consider the exa
90. es in the orbital energies mean that it is uncertain which state the SCF should converge on Smearing may alleviate the problem by using an average state thereby removing the need to make a discrete choice The format of the directive is SMEAR lt START_TEMP gt lt FINAL_TEMP gt lt UNITS gt SCALE lt SCALE_VALUE gt where e START_TEMP F is the starting Fermi Temperature e FINAL_TEMP F is the final Fermi Temperature e UNITS A specifies the units to be used for the final and starting tempratures By default the units are Hartrees but setting UNITS to EV changes the units to Electron Volts e SCALE A is the keyword SCALE followed by the scale factor SCALE VALUE F The scale factor is used in the temperature updates going from the start to the final temperature To ensure that the final temperature has been reached at convergence the current temperature is updated as a linear function of the difference between the SCF tester and the SCF convergence criterion To T start 2 Tia max T final min T SCALE_V ALUE x tester convergence 3 A couple of points should be noted about the use of Fermi smearing 1 The Fermi Dirac smearing enforces strict Aufbau ordering of the orbitals through the occupations Thus it cannot be used together with options that may break the Aufbau ordering such as locking 2 The Fermi Dirac smearing breaks the strict distinction between occupied and virtual or bitals In practice
91. exchange functional 58 and the Becke 95 meta correlation functional 14 BB95 The keyword BB95 selects the Becke 88 exchange functional and the Becke 95 meta correlation functional 15 BLYP The keyword BLYP selects the Becke88 exchange energy functional 32 and the Lee Yang and Parr correlation energy functional 34 BP86 The keyword BP86 selects the Becke88 exchange energy functional 32 and the Perdew 1986 gradient corrected correlation functional 35 EDF1 The keyword EDF1 selects Empirical Density Functional One as proposed by Adam son et al 16 FT97 The keyword FT97 selects the Filatov Thiel gradient corrected exchange correlation energy functional 38 39 This functional comprises the Filatov Thiel correlation energy functional and the exchange energy functional variant B HCTH or HCTH93 The keywords HCTH or HTCH93 select the Hamprecht Cohen Tozer Handy exchange correlation energy functional fitted against a training set of 93 molecules 17 HCTH120 The keyword HCTH120 selects the Hamprecht Cohen Tozer Handy exchange correlation energy functional fitted against a training set of 120 molecules 18 HCTH147 The keyword HCTH147 selects the Hamprecht Cohen Tozer Handy exchange correlation energy functional fitted against a training set of 147 molecules 18 HCTH407 The keyword HCTH407 selects the Hamprecht Cohen Tozer Handy exchange correlation energy functional fitted against a training set of
92. f GAMESS UK Users who have access to the source code and wish to include the driver in their build should add the newscf_f90 keyword as an option when configuring the code There were a number of motives for developing the new driver These included 7 SCF CONVERGENCE ALTERNATE DRIVER 27 e to allow more flexible control of convergence schemes for cases that were proving difficult to converge with the default driver e to reduce lO activity to the dumpfile scratchfile by holding more structures in memory thereby reducing a bottleneck for parallel calculations The consequence of more structures being held in memory has enabled the development of a parallel version of the driver in which these data structures can be distributed across all the nodes of a parallel machine allowing the code to take advantage of the large aggregate memory on these machines see the parallel ScaLAPACK version described in chapter 14 However a consequence of this is that the code is rather memory hungry when run in serial or on small processor counts As the driver is still relatively new it does not have support for all of the features within GAMESS UK such as ZORA DRF etc As of the writing of the manual the driver supports e RHF and UHF but not ROHF SCF Calculations both direct and conventional e RHF and UHF but not ROHF DFT Calculations both direct and conventional 7 1 Input Control Use of the module is requested by including
93. f orbital classification lines in which each orbital in the primary space is classified by type with the following orbital TAGs used in this classification e FZC frozen core orbital i e an orbital which will remain doubly occupied in all configu rations e DOC doubly occupied i e an orbital which is doubly occupied in the reference configu ration and which will be permitted variable occupancy in the CASSCF treatment e ALP an unpaired orbital i e an orbital which is singly occupied in the reference config uration and which will be permitted variable occupancy in the MCSCF treatment e AOS BOS those singly occupied orbitals in the reference configuration belonging to non identical singlet coupled pairs Again such orbitals will be permitted variable occupancy e UOC formally unoccupied orbitals corresponding to SCF virtual MOs which will be permitted variable occupancy in the MCSCF Each orbital definition line comprises an orbital TAG in the first data field followed by the sequence numbers of the input orbitals as restored under control of the VECTORS directive of the nominated type Example 1 Let us consider initially various calculations on the water molecule to illustrate CONFIG speci fication and assume the following set of input MOs derived from a closed shell SCF calculation MO Sequence Symmetry SCF MO Sequence Symmetry SCF number Occupation number Occupation 1 la 2 0 6 4a 0 0 2 2a1 2 0 7 2b 0
94. fault values so that the user may avoid the task of nominating sections These defaults which are a function of SCFTYPE are summarised in Table 2 Clearly a discussion of the VECTORS directive where we define Sections containing input MOs should now be linked to that of the ENTER directive where Sections for orbital output are nominated We also consider Section specification as a function of SCFTYPE in the notes below focusing attention initially on the use of orbitals resident on the parent Dumpfile 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 73 Table 2 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 7 MCSCF 2 8 9 1 Closed Shell SCF Here we are only involved in nominating a single Section on the Dumpfile to contain the closed shell SCF eigenvectors Thus given the data sequence VECTORS ATOMS ENTER 1 or just ENTER 1 in a startup job the sequence VECTORS 1 ENTER 1 would be specified in a subsequent SCF restart in which case the MOs in Section 1 would be updated or perhaps the sequence VECTORS 1 ENTER 10 if the User wished to keep copies of both initial and final MOs UHF SCF Now two Sections are required the first referring to the a spin orbitals the second to the B spin orbitals When initiating a UHF calculation the data sequence
95. fficients 47 i Od C 9 26 Co 13 Ch C4 This is presently the default The Geometric Mean Cg pair model In this model the pair Cg coefficient is approxi mated as the geometric mean of the elemental Ce coefficients 48 49 CS C5 Ci 14 This is currently considered as the most accurate model It also supports the most chemical elements through published atomic Ce coefficients 48 8 0 1 VDWAALS Directives controlling the dispersion corrections Detailed control of the dispersion corrections is available through a special input block for use with DFT calculations a simplified input is available see 11 5 This input block starts with the VDWAALS directive and terminates with the END directive In between these two directives any number of directives to fine tune the dispersion corrections may be presented So the input block is of the form Example VDWAALS END Within the above structure the directives ON OFF C6MODEL SCALE ALPHA RADIUS and C6 may be used as described below Note that the directives SCALE ALPHA RADIUS and C6 set values independently for the active Ce pair model l e VDWAALS C6MODEL AVERAGE SCALE 1 3 EXPONENT 30 0 C6MODEL GEOMETRIC END 8 SPECIFICATION OF DISPERSION CORRECTIONS 38 results in using the geometric mean Cg pair model with the default settings and NOT with the scale factor and exponent from the input The reason is that changing the parameters for the average C pair mod
96. he LOCAL directive is used to exclude the inner shell and virtual orbitals from the unitary transformation Note the SUPER OFF NOSYM specification in the closed shell calculation enabling subsequent use of the BYPASS directive in the GVB calculation itself Closed shell SCF TITLE H2C0 3 21G CLOSED SHELL SCF SUPER OFF NOSYM ZMATRIX ANGSTROM C 0 1 1 203 H 11 099 2 121 8 H 11 099 2 121 8 3 180 0 END ENTER Localised Orbital Analysis RESTART NEW TITLE H2C0 3 21G DEFAULT BASIS VALENCE LMOS 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 RUNTYPE ANALYSE LOCAL 3 TO 8 END ENTER 2 An examination of the closed shell SCF MOs and localised MOs reveals the ordering shown below MO Sequence Symmetry LMO Sequence Type Number Number 1 la 1 la 2 2a1 2 2a1 3 3a1 3 C O 4 4a 4 C H1 5 1b2 5 C H2 6 5a1 6 Ip O 7 1b 7 C O 8 2b 8 Ip20 4 DIRECTIVES DEFINING THE WAVEFUNCTION 12 The following points should be noted regarding the data sequence shown below for performing the GVB PP calculation e Note the form of the SCFTYPE directive the integer specified after the GVB keyword indicates the number of GVB pairs in the present case just 4 e Taking the localised orbitals as the starting point the trial vectors for the GVB calculation are obtained through use of the NOGEN directive where the specified integer identifies the Dumpfile section containing
97. he dimer method Two images of the system their distance is specified by the DELTA directive are calculated They are optimised along the force in all directions perpendicular to the dimer axis and against the force along the dimer axis Thus the system converges to a first order saddle point After a rotation step the gradient can be interpolated default or recalculated In this case specify the directive as DIMER NOINTERPOLATION 15 1 3 DELTA DELTA specifies the dimer distance and the elongation for finite difference Hessian evaluation The units are atomic units if Cartesian coordinates are used and undefined if delocalised internals are used Default DELTA 0 01 15 1 4 NEB The directive NEB specifies a nudged elastic band calculations The improved tangent NEB algorithm with a climbing image is implemented The L BFGS optimiser is recommended with NEB although other optimisers may as well be tried The syntax is NEB NIMAGE K Where NIMAGE is an integer specifying the number of images default 10 and K is a real number specifying the NEB force constant default 0 01 Two structures have to be provided for an NEB calculation One endpoint will be the geometry provided in the normal GAMESS input The other structure will be provided by the directive GEOMETRY 15 1 5 NEBMODE The directive NEBMODE specifies details of an NEB calculation NEBMODE MODE CART Where MODE can be FREE FROZEN or PERP It specifies if th
98. he trial orbitals for both a and 3 spin or ii with no closed shell section a trial set will be generated using the VECTORS ATOMS mechanism If the User wished to keep copies of both initial and final UHF MOs then the single data line of the form ENTER 10 11 would be required with the final set of a spin MOs MOS being written to section 10 and 3 spin orbitals to section 11 Note that usage of this set in some subsequent job would require explicit introduction of the data line VECTORS 10 11 to avoid use of the default section 3 Open shell RHF and GVB Calculations Again two Sections are involved the first holding the internal non canonicalised MOs the orbital set used during the RHF or GVB iterations while the second is used for output of the external canonicalised orbitals on termination of the SCF process In default the internal MO set will be written to section 4 and the canonicalised orbital set to section 5 of the Dumpfile see Table 2 Thus presenting the single data line ENTER in a startup job would act to request an atomic GUESS for generating a set of SCF eigen vectors that would be be used to initiate the open shell SCF with the internal non canonicalised MOs subsequently updated and written to section 4 of the Dumpfile and the canonicalised orbital set written to section 5 Presenting the same data line in a subsequent RESTART job would result in the eigenvectors of section 4 an
99. hen these vectors will provide a satisfactory starting point for the TZVP study and may be restored using a directive of the form VECTORS GETQ ED4 1 2 where the data set used to hold the foreign Dumpfile is assigned to the program using the LFN ED4 Example 2 The Dumpfile for the TZVP calculation above is to be located on the same data set used for performing the the 3 21G calculation Assume that on completion of the original optimisation the total length of the Dumpfile was found to be smaller than 250 blocks Siting the TZVP calculation at block 250 on this data set by means of the directive 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 80 DUMPFILE ED3 250 permits use of the following GETQ directive VECTORS GETQ ED3 1 2 in making the 3 21G vectors available to the present calculation Example 3 A UHF calculation has been performed in a 3 21G basis with the converged a and P spin orbitals stored in Sections 8 and 9 of the Dumpfile which had started at block 50 We now wish to perform the same calculation using a TZV basis set Assigning the data set containing this Dumpfile from the previous calculation as ED4 we may commence the TZV UHF calculation by means of a directive of the form VECTORS GETQ ED4 50 8 ED4 50 9 125 LOCK This directive consists of one data line with the character string LOCK in the first data field In the presence of the LOCK directive the program will seek a stationary value for
100. ic in an ATOMIC ZORA calculation FORCE Normally the changes specified in these subdirectives are only used to generate a start and are not included when calculating the atomic ZORA corrections Specifying FORCE will cause the program to use them always So one might have ZORA corrections for a charged atom Example The following specifies explicitly the configuration for the iron atoms in Fe203 where the two iron d shells are either completely alpha or beta and the s open shell is divided For fun the oxygens are made slightly negative VECTORS ATOMS CONF UHF Fel CONF d5si DENS dbs1 SPIN d 5 0 Fe2 CONF d5si DENS d5s1 SPIN d O 5 0 CHARGE 0 6 END VECTORS ATORBS Construct starting orbitals as a concatenation of the atomic orbitals of the atoms not generally recommended This is useful however for subsequent VB calculations and for calculations on atoms The SECTION keyword is recognised as input on the same line followed by the section number If given the atomic orbitals are written to the section specified and the density matrices are used as in the ATOMS option VECTORS HCORE Diagonalise the 1 electron core Hamiltonian This is the most general mechanism available but is also the least reliable in that the resulting MOs may often not exhibit the required ordering We return to this point below VECTORS MINGUESS Construct and diagonalise a Huckel type matrix This option is limited to minimal basis sets e g BASIS STO3G
101. ill walking algorithm due to Simons and Jorgensen 6 While primarily intended for transition state usage it may also be employed in geometry optimisation A more detailed account of the method and associated data is given below in section 10 We note here that the procedure is driven through additional keyword specification on the RUNTYPE directive thus RUNTYPE OPTIMIZE JORGENSEN 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 82 3 the third method perhaps less robust and flexible than the others is a cartesian driven update method This is requested through the following RUNTYPE specification RUNTYPE OPTXYZ We shall use the RUNTYPE keywords OPTIMIZE JORGENSEN and OPTXYZ to subse quently refer to the the three methods 13 2 Stopping an optimisation when molecule dissociates CHECK DISS or DIST Appending the keywords CHECK DISS or DIST in A format to any of the following runtypes e OPTIMIZE e SADDLE e OPTX Will cause a check to be carried out as to whether the number of bonds within the molecule changes defined as the distance between two bonded atoms changing by more than 15 over the course of the optimisation If the number of bonds changes then the optimisation will abort This can often be useful to halt a geometry optimisation when a molecule appears to be dissociating 13 3 OPTIMIZE Data Specification Four directives are provided to control the OPTIMIZE search procedure M
102. imisation with predictable consequences on the convergence of the geometry optimization 3 SCFTYPE The SCFTYPE directive specifies the category of self consistent field wavefunction to be used in conducting the task nominated by the RUNTYPE directive Valid data lines include the following SCFTYPE RHF perform a restricted Hartree Fock calculation SCFTYPE DIRECT RHF perform a restricted Hartree Fock Direct SCF calculation SCFTYPE UHF perform an unrestricted Hartree Fock calculation SCFTYPE DIRECT UHF perform an unrestricted Direct SCF calculation SCFTYPE GVB n perform a GVB n PP calculation i e involving n GVB pairs SCFTYPE DIRECT GVB n perform a direct GVB n PP calculation SCFTYPE MP2 perform a second order M oller Plesset MP2 calculation SCFTYPE DIRECT MP2 perform a M oller Plesset Direct MP2 calculation SCFTYPE MP3 perform a third order M oller Plesset MP3 calculation SCFTYPE CASSCF perform a complete active space SCF calculation SCFTYPE MCSCF perform a second order MCSCF calculation SCFTYPE MASSCF perform an ORMAS MCSCF calculation The following points should be noted e in the absence of a SCFTYPE directive a restricted Hartree Fock calculation is assumed for both closed and open shell systems e performing RHF calculations on open shell systems will assume the appropriate high spin configuration in default If this is not the required configuration then the OPEN directive must also be specified to define the required orbita
103. k the user can determine which convergence controls are to be used under what conditions to switch to another phase block and when the SCF will be deemed to have converged 7 3 1 CONVERGENCE CONTROLS The convergence controls available together with the default values are 7 3 2 Level Shifters LEVEL The format of the LEVEL directive is the same as that for the Default SCF driver described in section 6 1 The default value for the NEWSCF driver is 0 5 7 3 3 DIIS The single keyword DIIS in format A indicates that DIIS should be active for this phase 7 3 4 NEWDIIS This directive consists of the single keyword NEWDIIS in format A and resets the DIIS space for the phase as explained below DIIS works by taking a linear combination of the previous Fock matricies to determine the subsequent set of vectors DIIS therefore has a memory of the previous Fock matrices that it uses to generate the next solution The NEWDIIS keyword causes the memory from subsequent phases to be wiped and for DIIS to start afresh NB DIIS requires a memory of at least 3 cycles to be able to function so resetting DIIS means that it will only become active again on the 4th cycle of the phase 7 3 5 EXTRAPOLATION The format of this directive is a line with three data fields the first being the character EXTRAP A followed by the two values TEST F and COEF F The TEST and COEF variables are used as explained below When two succes
104. l occupancies e when performing CASSCF calculations the CONFIG directive must be specified e when performing MCSCF calculations the MCSCF and ORBITAL directives must be specified e when performing MASSCF calculations a MASSCF section must be present in the input that specifies values for at least the following directives NCORE NACT and NELS 4 DIRECTIVES DEFINING THE WAVEFUNCTION 6 e the significance of the sections nominated under control of the VECTORS and ENTER directives is a function of SCFTYPE e when restarting a task involving GVB wavefunctions the RESTORE parameter must be specified on the SCFTYPE directive Thus the data line SCFTYPE GVB 1 RESTORE signifies a GVB 1 PP calculation with pair coefficients restored from the Dumpfile e the format of the LEVEL directive is a function of SCFTYPE 4 Directives defining the wavefunction 4 1 SCF Wavefunctions The OPEN Directive The default electronic configuration in open shell RHF calculations corresponds to the high spin configuration in such cases the OPEN directive is not required If this default does not apply then the OPEN directive must be used to define the electronic configuration and hence the energy expression in both open shell RHF and open shell GVB calculations In performing such calculations the User must define the shell structure where orbitals which can have the same Fock operator are said to belong to the same shell 2 The OPEN directive is use
105. le state of the water molecule The first file generates the closed shell MOs the second performs the hole state calculation with the SWAP directive placing the oxygen 1s MO as the singly occupied orbital The Closed shell SCF TITLE H20 3 21G ZMAT ANGSTROM 0 H 1 ROH H 1 ROH 2 THETA VARIABLES ROH 0 956 HESSIAN 0 7 THETA 104 5 HESSIAN 0 2 END ENTER The Core Hole state open shell SCF RESTORE NEW TITLE H20 1S CORE HOLE STATE CHARGE 1 MULT 2 ZMAT ANGSTROM 0 H 1 ROH H 1 ROH 2 THETA VARIABLES ROH 0 956 HESSIAN 0 7 THETA 104 5 HESSIAN 0 2 END SWAP 15 END 6 SCF CONVERGENCE DEFAULT 21 RUNTYPE OPTIMIZE LEVEL 0 0 1 0 XTOL 0 003 ENTER 6 3 DIIS The DIIS directive consists of a single data line containing the character string DIIS in the first data field Subsequent data fields may be used e to suppress DIIS by presenting a data line of the form DIIS OFF when in default only level shifting will be in effect to request printing of the DIIS equations by specifying the character string PRINT to modify the onset of DIIS by specifying the value of TESTER this is achieved by typing the character string ONSET immediately followed by a floating point variable defining the required value of TESTER Thus the data line DIIS ONSET 0 2 would override the default onset of 0 1 e to route information necessary for SCF cycling to proceed in uninterrupted fashion across restart jobs Such a pr
106. mmended Vosko Wilk Nusair local density correlation functional 37 VWNRPA VWN5RPA or VWNRPA_C The keywords VWNRPA VWN5RPA or VWN RPA_C select the Vosko Wilk Nusair local density correlation functional with the RPA parametrisation 37 NULL The keyword NULL selects the null exchange correlation energy Obviously this is should be used only in very special cases B3LYP The keyword B3LYP selects the infamous hybrid exchange correlation functional proposed by Stephens et al 12 As Stephens et al did not use the recommended VWN functional as one of the components this functional has attracted much controversy The current understanding is that the functional employs VWN3 13 B1B95 The keyword B1B95 selects a meta hybrid exchange correlation functional build from Hartree Fock exchange 28 the Becke 88 exchange functional 72 and the Becke 95 meta correlation functional 15 B97 The keyword B97 selects the Becke 97 hybrid exchange correlation functional 23 B97 1 The keyword B97 1 selects the hybrid exchange correlation functional of the same form as B97 but reoptimised by Hamprecht et al 17 23 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 55 B97 2 The keyword B97 2 selects the hybrid exchange correlation functional of the same form as B97 but reoptimised by Wilson et al 24 23 BB1K The keyword BB1K selects a meta hybrid exchange correlation functional build from Hartree Fock exchange 42 the Becke 88
107. mple This example sets the parameters as recommended by Antony et al 49 for a B3LYP calculation on formaldehyde VDWAALS C6MODEL GEOMETRIC SCALE 1 05 ALPHA 20 0 RADIUS H 1 89 RADIUS C 2 74 RADIUS O 2 54 c6 H 2 43 c6 C 30 35 c6 0 12 14 END 9 Directives Controlling MCSCF Calculations Data input characterising the MCSCF calculation commences with the MCSCF data line and is typically followed by a sequence of directives terminated by presenting a valid Class 2 directive such as VECTORS or ENTER 9 DIRECTIVES CONTROLLING MCSCF CALCULATIONS 40 9 1 MCSCF The MCSCF data initiator consists of a single data line with the character string MCSCF in the first data field It acts to transfer control to those routines responsible for inputing all data relevant to the MCSCF calculation Termination of this data is achieved by presenting a valid Class 2 directive that is not recognised by the MCSCF input routines for example ENTER 9 2 ORBITAL The ORBITAL directive must be presented in a MCSCF calculation and acts to 1 define the active space in the calculation by partitioning the orbitals into a primary and secondary set 3 2 specify an initial reference configuration that will be employed for example in generating the complete Cl space in a CASSCF calculation The directive comprises a number of data lines with the first line containing the character string ORBITAL in the first data field Subsequent lines comprise
108. mple of Part 3 section 8 4 on the optimisation of HCN The following data file requests termination after two line searches through the MINMAX specification during which conservative settings of the optimisation parameters will apply TITLE HCN DUNNING DZ BOND S P ZMAT ANGSTROM C BQ 1 RCN2 X 2 1 0 1 90 0 N 2 RCN2 3 90 0 1 180 0 X 11 0 2 90 0 3 0 0 H 1 RCH 5 90 0 4 180 0 VARIABLES RCN2 0 580 RCH 1 056 END BASIS DZ H S BQ 1 0 1 0 P BQ 1 0 0 7 DZ C DZ N END RUNTYPE OPTIMIZE MINMAX 60 2 XTOL 0 005 STEPMAX 0 1 VALUE 0 3 ENTER 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 86 In the restart job shown below the modified parameter settings will apply from the third line search onwards RESTART OPTIMIZE TITLE HCN DUNNING DZ BOND S P ZMAT ANGSTROM C BQ 1 RCN2 X 21 01 90 0 N 2 RCN2 3 90 0 1 180 0 X 11 0 2 90 0 3 0 0 H 1 RCH 5 90 0 4 180 0 VARIABLES RCN2 0 580 RCH 1 056 END BASIS DZ H S BQ 1 0 1 0 P BQ 1 0 0 7 DZ C DZ N END RUNTYPE OPTIMIZE XTOL 0 0005 STEPMAX 0 2 VALUE 0 6 ENTER A somewhat more complex situation may arise when the user wishes to modify optimisation processing already performed in the startup job either because e problems have been encountered that can only be remedied by modifying the optimisation control parameters or e the user wishes to terminate the optimisation in a controlled fashion since the optimisation is deemed t
109. n also contains the current Cl coefficients Presenting the single data line ENTER in a startup job would act to request an atomic GUESS for generating a set of eigen vectors that would be be used to initiate the CASSCF process with the non canonicalised CASSCF MOs subsequently written to section 6 of the Dumpfile and the final canonicalised orbital set written to section 7 Presenting the same data line in a subsequent RESTART job would result in the eigenvectors of section 6 and Cl coefficients of section 7 being used to initiate the CASSCF process each being subsequently updated and overwritten In practice these default sections would be examined for content at job outset and the contents used for the CASSCF process assuming the sections had been written to by a previous job If the sections are not present on the Dumpfile then either i the closed shell MOS if present in section 1 will be used as the trial orbitals ii with no closed shell section a trial set will be generated using the VECTORS ATOMS mechanism 5 Wavefunction Analysis The variety of wavefunction analysis and property mod ules of GAMESS UK see Part9 also rely on the VECTORS directive to define the section number of the eigenvectors to be analysed Note that in contrast to SCF processing no default specification is available under RUNTYPE ANALYSE Ex plicit specification is required even if this section had been written to using one of the default op
110. n if started in the wrong region of the energy surface and by invoking Hessian mode following can locate transition states for alternative rearrangement and or dissociation reactions from the same starting point The algorithm may also be used to locate minima on a surface A description of the formalism and the ideas behind it together with a description of the algorithm and some practical examples are given in reference 7 14 1 Invocation of The Algorithm and Associated Parameters The Jorgensen and Simons optimisation algorithm is invoked by appending the keyword JOR GENSEN on the appropriate RUNTYPE directive i e RUNTYPE SADDLE JORGENSEN Search for saddle point RUNTYPE OPTIMIZE JORGENSEN Search for minimum point 14 JORGENSEN AND SIMONS OPTIMISATION ALGORITHM 98 Omission of the keyword will cause the program to default to the optimisation algorithms described above The following discussion makes the assumption that a search is being made for such a stationary point If no other relevant directives are specified the default is to evaluate the Hessian according to the TYPE specifications in the VARIABLES definition lines of the ZMATRIX directive A Hessian may still however be restored from a foreign dumpfile by specifying the LFN starting block and section number of the foreign dumpfile in the 4th and 5th fields on the RUNTYPE directive line e g RUNTYPE SADDLE JORGENSEN ED4 1 In addition to the keyword
111. nate two sets of level shifters to apply during an SCF calculation the first set to be used up to and including some user nominated iteration the second to apply after this point Note that the number and role of the level shifters within each set is a function of SCFTYPE Note also that the primary role of level shifting is to ensure the calculation arrives in the quadratic region of convergence from which point DIIS will effectively control the SCF iterations This on occasions requires setting higher values than those used say in a level shifting only environment where larger values would act to slow down convergence in the latter stages of the computation We describe below the format of the directive for each SCFTYPE 6 1 1 Closed shell RHF Calculations In the case of a closed shell RHF calculation the LEVEL directive consists of a single data line read to variables TEXT El IBRK E2 using format A F I F e TEXT should be set to the character string LEVEL e El is the level shifter up to iterative cycle specified by IBRK e IBRK is an integer used to a specify the cycle number 6 SCF CONVERGENCE DEFAULT 18 e E2 is the level shifter after the iterative cycle given by IBRK An alternative form of LEVEL is permitted consisting of only two parameters read to variables TEXT E1 using format A F If used this sets the IBRK parameter to the default 999 E2 will be given the value of 0 0 while E1 has its usual meaning The
112. new calculations with the history printed on each restart This printing may be suppressed through use of the NOPRINT directive with specification of the HISTORY keyword 13 8 1 SADDLE Data MINMAX This directive may be used to control the number of energy evaluations and line searches per mitted in the location of the transition state and consists of a single data line read to the variables TEXT IVAL LINE using format A 21 e TEXT is set to the character string MINMAX e IVAL is an integer specifying the maximum number of energy evaluations allowed in the optimisation e LINE is an integer defining the maximum number of line searches permitted in the opti misation 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 92 The MINMAX directive may be omitted when both IVAL and LINE will be set to the maximum allowed value of 60 The following specification is thus equivalent to the default MINMAX 60 60 Example In some cases the user may wish to perform just the initial point on the optimisation pathway to gauge the quality of the starting geometry though the magnitude of the gradient at that point This may be achieved though use of MINMAX as shown below Start up Job TITLE HCCH CCH2 RHF3 21G START UP JOB ZMAT ANGS C C 1 LI H 2 L2 1 A1 X 21 0 1 90 0 3 180 0 H 2 L3 4 A2 1 180 0 VARIABLES L1 1 24054 TYPE 3 L2 1 65694 TYPE 3 L3 1 06318 TYPE 3 A1 60 3568 TYPE 3 A2 60 3568 TYPE 3 END RUNTYPE SA
113. o be complete The first case would not be cured merely by presenting revised parameters in a restart job since the program will initially run through the pathway prior to applying the new parameters by which time the position may not be recoverable In such cases the user must identify from the output of the startup job a line search in the optimisation pathway prior to the problem and present this information to the program via a revised form of the MINMAX directive in a restart job The revised format consists of a single data line read to the variables TEXT TEXT1 LINES using format 2A l e TEXT is set to the character string MINMAX 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 87 e TEXTI is set to the character string REVISE e LINES is an integer defining the line search after which any optimisation parameters presented in the input stream are to apply The following specification would cause the original optimisation pathway to be followed for the first three line searches only beyond that point the optimisation would be restarted based on any revised control parameters MINMAX REVISE 4 In the example below we consider the SCF geometry optimisation of C4F4 In fact this optimi sation proceeds smoothly converging to the default accuracy XTOL 0 003 on the seventh line search using the data shown below TITLE kAK C4F4 3 21G x ZMAT ANGS X Ci Ri C1 R2 2 90 C1 Ri 3 90 2 180 C1 R2 4 90 3 180
114. ocess is important for example in large direct SCF calculations when perhaps only a single SCF cycle may be possible in a given step The successful functioning of DIIS relies on the process controlling the SCF over multiple iterations hence the need arises to save DIIS information This is achieved by presenting the LFNAME of a direct access file and starting block number to which DIIS information will be written Thus presenting the data line DIIS ED4 1 will result in the DIIS information being written to ED4 commencing at block 1 Example The following two data files illustrate this saving of DIIS information between separate jobs Assuming the file allocated to ED4 is saved in the Startup job below which terminated during SCF processing and is subsequently allocated to the Restart job the SCF cycling will be iden tical to that observed if the first job had been run to completion Startup Job 6 SCF CONVERGENCE DEFAULT TITLE C6H5 NO2 TZVP DIIS INFORMATION TO ED4 NOPRINT ZMAT ANGSTROM C N 1 RCN X 21 01 90 0 C 1 RCC1 2 T1 3 P1 C 1 RCC1 2 T1 3 P1 C 4 RCC2 1 T2 2 P2 C 5 RCC2 1 T2 2 P2 C 7 RCC3 5 T3 1 P3 O 2 RNO1 1 T5 3 90 0 O 2 RNO1 1 T5 3 90 0 H 4 RCH1 1 T6 2 P5 H 5 RCH1 1 T6 2 P5 H 6 RCH2 4 T7 11 P6 H 7 RCH2 5 T7 12 P6 H 8 RCH3 7 T8 14 P7 VARIABLES RCN 1 49 RCC1 1 37 RCC2 1 43 RCC3 1 37 RNO1 1 21 RCH1 1 084 RCH2 1 084 RCH3 1 084 T1 120 0 T2 120 0 T3 120 0 T5 120 0 T6 120 0 T7 120 0 T8 120 0 P
115. onjugate directions to be recalculated A step TANSTEP previous step length is taken along the current tangent to the polynomial and the function and gradients are calculated at this point The default is TANSTEP 0 1 13 9 5 Synchronous Transit Data MINMAX This directive may be used to control the number of energy evaluations and line searches per mitted in optimising a given structure The default is MINMAX 60 60 The first integer refers to the maximum number of energy evaluations allowed and the second to the maximum number of line searches 13 9 6 Synchronous Transit Data XTOL Defines the four acceptance criteria for the convergence of the synchronous transit algorithm The criteria are maximum change in variables lt _ xtol average change in variables lt xtol 2 3 maximum gradient lt xtolx 1 4 average gradient lt xtolx 1 6 The default corresponds to presenting the data line XTOL 0 001 13 9 7 Synchronous Transit Data STEPMAX Defines the maximum allowed movement in any of the variables in a single step The internal units of the variables are bohr for bond lengths and radians for angles The default is equivalent to STEPMAX 0 2 13 10 Restoring the Force Constant Matrix FCM An FCM directive may be given to specify the Force Constant Matrix Hessian to be restored in an OPTIMISE or SADDLE calculation Specifying FCM or a dumpfile name on a RUNTYPE OPTIMISE or RUNTYPE SADDLE directive is equival
116. oosing a functional without Hartree Fock exchange and evaluating the Coulomb energy with an auxiliary basis set The basic idea behind this technology is described by Dunlap et al 40 and is referred to as Coulomb fitting Currently Coulomb fitting can be used in energy and gradient evaluations The four directives that control this functionality JFIT JFITG JBAS and SCHWARZ are described below 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 66 11 9 1 JFIT and JFITG The JFIT directive is used to switch on Coulomb fitting it is read to the variables TEXT TEXTA and IMEM using format A A e TEXT should be set to the character string JFIT e TEXTA may be set to the character string MEMORY In this case the program will try to store as many of the required 3 center 2 electron integrals as possible in memory These integrals will only be calculated once during a KS calculation while those 3 center integrals that do not fit into memory will be recomputed whenever needed The pro gram will estimate how much memory is needed for the normal KS operation and set all other memory aside for the 3 center integral storage Although the implementation aims to avoid user intervention it may happen that the memory needed for the normal KS activities is underestimated This results in the calculation aborting with an out of memory error In such cases the User may either i increase the memory available to the calculation through use of the COR
117. orre sponds to presenting the data line XTOL 0 001 13 8 3 SADDLE Data STEPMAX This directive may be used to define the the maximum allowed movement in any of the variables in a single step of the transition state location Note that the internal units of the variables are bohr for bond lengths and radians for angles The directive consists of a single data line read to the variables TEXT STEP using format A F e TEXT should be set to the character string STEPMAX e STEP should be set to the maximum permitted movement in any variable The STEPMAX directive may be omitted when STEP will be set to 0 2 The default thus corresponds to presenting the data line STEPMAX 0 2 There is certainly at least one circumstance where changes to the default setting may prove crucial in achieving controlled convergence If the starting geometry is known to be poor or if ZMATRIX specification is such that a specific bond is not explicitly defined as can happen for example with aromatic compounds then the first step taken on the optimisation may prove both excessive and counter productive at best several extra points will be required to recover from this effect at worst a change of state may be induced in the SCF wavefunction This effect is fairly common if in addition the starting hessian is also poorly defined When this happens the user should consider starting the optimisation again presenting a STEPMAX directive of the form STEPMAX 0 1
118. proaches to correct for the lack of dispersion have been suggested GAMESS UK supports two versions of one of these approaches 47 48 49 Both these approaches were originally designed to be used in the context of DFT calculations but they may be useful in a wider context Both of the supported approaches are based on a simple model for the dispersion energy of two interacting atoms ij faam Rij Diy Raj Ce Fg 1 10 The function faamp is simply chosen such that it goes to zero when R goes to zero to prevent that atoms collapse onto eachother This damping function is of the form 1 Faamp Fiz gt 1 e AURij Ro 1 11 where a is a universal exponent and Ro is the sum of Van der Waals radii of atoms 7 and j The total dispersion energy may now be expressed as Natom 1 Natom Edisp 86 X SO Diy 12 i 1 j i 1 8 SPECIFICATION OF DISPERSION CORRECTIONS 37 where sg is a scale factor that depends on ab initio energy expression that is used in conjunction to the dispersion correction The dispersion energy expression 10 requires a Ce coefficient for every pair of chemical elements To reduce the number of these required parameters the pair Ce coefficients are approximated and expressed in terms of Ce coefficients of the elements The current implementation supports two models for this The Average C pair model In this model the pair Ce coefficient is approximated simply as the average of the elemental Ce coe
119. r of points e M is a floating point number defined below The grid points will be located at ri alog 1 2 a 2il Ti 2xNPT where 1 lt 2 lt NPT and a is an element dependent scale factor The recommended value for M is 3 0 25 Note that all points with gt NPT 1 exp 1 M 1 2 will have r gt a This means that with M 3 0 about 85 of all grid point have r lt a In practice this means that this radial grid has a tendency to focus on the area close to the atom Examples LOG 45 3 0 LOG LABEL H1 H1 45 1 0 LOG ELEMENT C H 45 3 0 LABEL 01 20 3 0 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 62 11 7 6 Scaling Radial Grids SCALE The SCALE directive provides the ability to scale the radial grids of all atoms by a uniform factor FACTOR This may prove helpful in moving points into a sensible range especially with the Euler MacLaurin radial integration grid 31 The directive consists of two data field read to the variables TEXT FACTOR using format A F e TEXT should be set to the character string SCALE e FACTOR specifies the required scaling factor Examples SCALE 3 0 SCALE LABEL Ci Hi 3 0 LABEL C2 01 4 0 SCALE 4 0 LABEL Ci Hi 3 0 SCALE 4 0 ELEMENT Ci H1 3 0 11 7 7 Weighting scheme WEIGHT The WEIGHT directive allows the user to select a weighting scheme to combine the atomic integration grids to a molecular integration grid The directive consists of two data field read to
120. rameters the pair Ce coefficients are approximated and expressed in terms of Ce coefficients of the elements The current implementation supports two models for this The Average Cg pair model In this model the pair Cg coefficient is approximated simply as the average of the elemental Ce coefficients 47 ao CH o 8 6 Ci C4 16 This is presently the default The Geometric Mean Cg pair model In this model the pair Cg coefficient is approxi mated as the geometric mean of the elemental Ce coefficients 48 49 Ce y Ci Ci 17 This is currently considered as the most accurate model It also supports the most chemical elements through published atomic Cg coefficients 48 11 5 1 The DISPERSION directive In the DFT input section the basic properties of the dispersion correction may be controlled throught the DISPERSION directive for a much more detailed control over these correction see section 8 This directive may consist of one or two data fields read to the variables TEXT and TEXTOPT using the format A A e TEXT should be set to the character string DISPERSION e TEXTOPT is an optional field which may be set to either of 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 57 ON to switch the dispersion corrections on although this is currently implied in specifying the DISPERSION correction OFF to explicitly swith the dispersion correction off AVERAGE to select the average Cg coefficient pair model presently the
121. request a DFT rather than HF calculation thus input for a closed shell DFT calculation would appear as follows TITLE H2C0 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE SUPER OFF NOSYM ZMATRIX ANGSTROM C D 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 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 DFT ENTER The directive DFT thus switches on the DFT specific modifications to the Hartree Fock scheme Leaving the directive out 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 32 e the Lee Yang and Parr LYP correlation functional 34 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 52 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 25 31 and Lebedev angular grid 43 using the MHL8SSF weighting scheme with screening and MHL angular grid pruning 31 Note that this choice corresponds to the QUADRATURE MEDIUM setting described below e
122. riables in a single step of the geometry optimisation Note that the internal units of the variables are bohr for bond lengths and radians for angles The directive consists of a single data line read to the variables TEXT STEP using format A F e TEXT should be set to the character string STEPMAX e STEP should be set to the maximum permitted movement in any variable The STEPMAX directive may be omitted when STEP will be set to 0 2 The default thus corresponds to presenting the data line STEPMAX 0 2 There is certainly at least one circumstance where changes to the default setting will prove crucial in achieving controlled convergence If the starting geometry is known to be poor or if ZMATRIX specification is such that a specific bond is not explicitly defined as can happen for example with aromatic compounds then the first step taken on the optimisation can cause the energy to go up and at best several extra points will be required to recover from this effect This effect is fairly common if in addition the starting hessian is also poorly defined When this happens the user should consider starting the optimisation again presenting a STEPMAX directive of the form STEPMAX 0 1 An additional side effect of excessive steps in the optimisation is a possible change of state in the SCF calculation particularly in closed shell wavefunctions If this happens the subsequent optimisation will almost certainly prove meaningless Pres
123. rmation e the Direct Cl calculation The TYPE CI specification implies the execution of all three steps Performing the calculation under such control would involve the straightforward specification RESTART CI RUNTYPE CI in any restart jobs Consider now performing the same calculation in a sequence of steps The SCF computation might say be completed as the first step under control of RUNTYPE SCF specification The second step the integral transformation might involve the directive sequence RESTART NEW BYPASS SCF RUNTYPE TRANSFORM assuming of course that the two electron integral file in the SCF step had been generated in the appropriate format Note that since the TRANSFORM specification implies both SCF and integral transformation we need BYPASS the SCF step Finally having generated the transformed integrals the third step would involve the data specification RESTART NEW BYPASS TRANSFORM RUNTYPE CI This type of breakdown is typical of that employed when e performing many different Cl calculations based on the same set of transformed integrals e having to analyse the SCF calculation to provide the necessary data specification for the subsequent Cl Strictly speaking the TYPE SCF specification itself implies of course the execution of two separate steps but it is unusual to invoke this functionality The SCF job above could be split into two jobs the first involving just integral evaluation through the specifica
124. rovided by an extension to the directive whereby different angular grid may be specified for different radii In this case the LEBEDEV directive comprises the following data fields e TEXT should be set to the character string LEBEDEV e pairs of data fields are then presented each pair characterising a specific radial zone and read to the variables NPT RZ using format I F where NPT specifies the grid size in the th radial zone The floating point values of RZ subdivide the radial coordinate into different zones The values RZ are fractions of the Bragg Slater radius 46 of the atom Each zone runs from RZ _1 to RZ The first zone starts at 0 while the last zone runs up to infinity e NPT is again an integer specifying the required number of points in the outer most zone running up to infinity Lebedev published the grids with 38 50 86 110 146 194 266 302 434 590 770 974 and 1202 points to be exact for polynomials up to orders 9 11 15 17 19 23 27 29 35 41 47 53 and 59 respectively Examples LEBEDEV 302 LEBEDEV 194 0 1 302 0 5 434 LEBEDEV LABEL C1 C2 194 0 1 302 0 5 434 ELEMENT CL 590 11 7 3 Angular integration Grid GAUSS LEGENDRE The GAUSS LEGENDRE directive requests a Gauss Legendre grid for the angular integration This grid is based on separating functions on a sphere into 2 functions of angles 0 0 lt 9 lt 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 60 Tr and 0
125. s above that function and gradient evaluations are used during a line search For an OPTXYZ run which usually tries to do a line search until the energy goes down the LSEARCH 1 specification indicates that a gradient evaluation is requested and each point is used even if the energy is higher For OPTXYZ specifying the first parameter as 0 function evaluations and specifying the second variable allows one to override the standard maximum number of steps along a line normally 3 before the hessian is reset and the program tries again To try for 7 points in OPTXYZ one specifies LSEARCH O 7 13 9 2 Synchronous Transit Data TOLMAX The TOLMAX directive may be used to control how far a search for a minimum in the n 1 subspace 4 may proceed before another search for a maximum is performed Smaller values will cause the program to search for a maximum more often The default is TOLMAX 0 1 13 9 3 Synchronous Transit Data TOLSTEP The TOLSTEP directive is used to maintain good conjugate directions to the principal direction of negative curvature If the step along this direction was too large in the previous iteration then the program takes a small step in order to estimate a better set of conjugate directions The default is equivalent to TOLSTEP 0 1 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 96 13 9 4 Synchronous Transit Data TANSTEP The TANSTEP directive may be used when the TOLSTEP test requires the c
126. set to the character string LEVEL e EA1 EB1 are the a spin orbital and P spin orbital level shifters up to the iterative cycle specified by IBRK e IBRK is an integer used to specify the cycle number e EA2 EB2 are the a spin and spin level shifters after the iterative cycle specified by IBRK An alternative form of LEVEL is permitted consisting of only three parameters read to variables TEXT EA1 EB1 using format A 2F In this form TEXT EA1 and EB1 have their usual meanings whilst the program will set IBRK 999 and EA2 EB2 to zero The LEVEL directive may be omitted when the program will assign the following default settings EA1 1 0 EBi 1 0 IBRK 5 EA2 0 3 EB2 0 3 These defaults are doubled in value for systems containing first row transition metals atoms thus EA1 2 0 EB1 2 0 IBRK 999 EA2 2 0 EB2 2 0 6 SCF CONVERGENCE DEFAULT 20 6 2 Core Hole States The present implementation of LEVEL within the open shell RHF program is such that core hole states may be converged with an appropriate setting of the parameters of the LEVEL directive Specifically such states may be studied by presenting the data line LEVEL 0 0 1 0 where the doubly occupied partially occupied level shifter is set to zero It is assumed in such studies that the open shell orbital comprises the core orbital involved in the ionization process Example The following two data files may be used to optimise the geometry of the 1s core ho
127. sfully for a large number of cycles without compromising on the quality of the wavefunction for less problematic steps An example of its usage is below next 0 tester below 1 E 06 info Converged normally as tester lt 1 E 06 next 0 totcyc above 50 tester below 1 E 05 info converged with slacker tester of 1 E 05 as totcyc gt 50 7 4 7 Information on a phase change INFO This directive consists of the keyword INFO format A followed by a string of text that may extend up to the end of the logical line 80 characters by default This directive can be used to print a string to the output file indicating why a particular phase change has been carried out e g info Jumping to phase 3 as tester lt 0 001 7 5 Example newscf input file The example below demonstrates a newscf convergence scheme that uses the following phases and criteria for shifting between them Phase 1 e Level shifters of 2 0 and 2 0 alpha and beta e Switch to phase 2 when tester lt 0 01 7 SCF CONVERGENCE ALTERNATE DRIVER Phase 2 e Level shifters of 0 5 and 0 5 DIIS and configurational locking e Switch to phase 3 when tester lt 0 002 Phase 3 e DIIS and configurational locking e convergence when tester lt 5 0d 6 The input is as follows time 1000 core 3000000 restart new punch coor conn punch basi vect 1 occu scfe eige mult 2 symt 6 title Cu NO DZ Cation new geom new code geometry 1 931427 0 080801 0
128. sis functions associated with it e The default grid parameters are chosen to equate those of Carbon atoms according to the current quadrature accuracy setting low medium high veryhigh or sg1 e The grid parameters for BQ centers can be changed using the same directives as for atoms In this context the name BQ can be thought of as a chemical element like C or H Although the ELEMENT and LABEL constructs work for BQ centers similar as they do for all normal atoms some care is required In particular it is not allowed to try and change the grid of a BQ center that does not have one Therefore the ELEMENT construct will not work if there is at least one BQ center without any basis functions 11 8 Energy Gradient Evaluation GRADQUAD The GRADQUAD directive controls the form of the energy gradient expression in a DFT calcu lation This directive consists of 2 data fields read to variables TEXT TEXTOPT using format A A e TEXT should be set to the character string GRADQUAD e TEXTOPT should be set to ON or YES to include the gradients of the quadrature weights and grid points in the energy gradient evaluation OFF or NO to ignore the contributions from the gradient of the quadrature For details see for example Johnson et al 30 11 9 Coulomb fitting The cost of DFT calculations of medium sized molecules can be reduced significantly by avoiding the calculation of 4 center 2 electron integrals This can be achieved by ch
129. sive SCF steps satisfy the colinearity criteria d1 d2 gt TEST 4 jd x d2 4 7 SCF CONVERGENCE ALTERNATE DRIVER 30 where dl fi f 2 5 and d f fa 6 and f f_1 and f_ are the current previous and next previous fock matrices the extrapolation f COEF x d2 7 will be applied Typically TEST should be around 0 95 and COEF around 1 In addition there is also a test on d1 d2 so that if successive steps are in the same direction but of very different lengths extrapolation is suppressed The line below demonstrates the use of the directive with the recomended values EXTRAP 0 95 1 7 3 6 NEWEXT This directive consists of the single keyword NEWEXT in format A and resets the extrapo lation counter to zero so that extrapolation will be inactive for the first cycle 7 3 7 RESTORE This directive consists of the single keyword RESTORE in format A The restore directive recovers the best set of vectors attained during the calculation thus far at the start of the phase 7 3 8 LOCK This directive consists of the single keyword LOCK in format A and applies configurational locking to the phase Normally the electrons populate the orbitals according to Hund s rules so that they are filled up sequentially starting from the lowest energy orbital and leaving no gaps until all the electrons are placed in an orbital When configurational locking is applied the overlap between the o
130. tal set the user is strongly recommended to use the first order super Cl option and to continue with this until the degree of convergence monitored by the maximum Brillouin element suggests switching to the pseudo second order NR technique Instigating NR too rapidly however will lead to divergence with the maximum first derivative increasing leading finally to the error message Hessian diagonalisation has failed to converge Experience suggests that a maximum Brillouin element of 0 05 0 01 represents the optimum point at which to instigate NR control with between 5 10 cycles of super Cl normally required to reach this point 2 The sequence of directives specified is dynamic and is not remembered between separate runs of the program Thus while the data sequence SUPERCI 1 TO 7 NEWTON 8 TO 20 HESSIAN 8 to 20 may be presented in a startup job the user should modify this sequence in any restart job to reflect the current degree of convergence Thus if the startup job dumped say on cycle 11 with the maximum first derivative suggesting satisfactory convergence of the NR process the data sequence NEWTON 1 TO 20 HESSIAN 1 TO 20 should be presented in the restart job 7 SCF CONVERGENCE ALTERNATE DRIVER 26 7 3 Within a given run of the program the sequence is remembered and will be applied for example in each separate CASSCF calculation of a geometry optimisation Some caution should be exercised at the outset
131. ter string PRINT when the trial vectors will be printed If BTEXT is omitted no vectors will be sent to the printer Valid ATEXT strings include the following e VECTORS ATOMS Construct an initial starting guess based on concatenating the 1 particle density matrices for each of the component atoms of the molecular system The present implementation of ATOMS represents a significant improvement over that available in previous releases of the code and should normally be the option of choice It is now the default option in the absence of the VECTORS directive The following extra optims are recognised in addition to a print directive ALWAYS The atomic startup is used again in every point in a geometry optimisation to determine the start orbitals instead of the orbitals of the previous point GROUND The atomscf routines try to use the groundstate of the atoms normally an average of their lowest states is used which is usually quite adequate UHF The atomic startup produces alpha and beta density matrices which are used straightaway in the UHF scf Therefore This option only makes sense if the two density matrices differ which can be effected using the CONFIGURATION or SPECIFY subdirective x As the density matrices are not idempotent the integrated density will not be correct Therefore an ACCURACY IGNORE should be given in DFT calculations CONFIGURATION or SPECIFY Allows the user to specify explicitly th
132. the functional and proceed in the direction of minimum change The use of the LOCK directive is automatic in open shell GVB and CASSCF MCSCF calculations 12 6 SWAP The first data line should contain the character string SWAP in the first data field Subsequent data lines are read to variables I J using format 21 The effect is that the l th and J th molecular orbitals as generated by the VECTORS directive are interchanged When all the interchanging lines have been presented the directive should be terminated by a data line containing the character string END in the first data field The following notes may prove helpful e The SWAP directive is normally used to switch from a configuration known not to be the ground state into the ground state e upon completion of the SWAP directive revised molecular orbital lists are held in memory but not in the Dumpfile Example SWAP 10 12 11 13 END 13 CONTROLLING GEOMETRY AND TRANSITION STATE OPTIMIZATION 81 Molecular orbitals 10 and 11 are interchanged with molecular orbitals 12 and 13 respectively In the case of UHF calculations the syntax of this directive is modified to reflect the presence of both a and 8 orbitals Now the directive initiator is read to variables TEXT SPIN using format 2A e TEXT should be set to character string SWAP e SPIN should be set to one of the character strings ALPHA or BETA and will cause swap ping of either a or 8 spin vectors respectiv
133. the gradient of the energy will be evaluated without considering the gradient of the quadrature weights and grid points this corresponds to GRADQUAD OFF 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 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 H2C0 3 21G CLOSED SHELL DFT B LYP DEFAULT QUADRATURE 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 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 C D 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 11 DIRECTIVES CONTRO
134. the variables TEXT SCHEME using format 2A e TEXT should be set to the character string WEIGHT e SCHEME specifies the required weighting scheme and should be set to one the following character strings BECKE The original Becke weighting scheme 33 BECKESCR The Becke weighting scheme 33 with additional screening HML The Murray Handy and Laming weighting scheme 31 This scheme differs from the Becke scheme in that it used a different cell function It leads to more accurate integrals than the Becke scheme SSF The Stratmann Scuseria and Frisch weighting scheme 26 For sufficiently large quadrature grids this scheme seems to be the most accurate SSFSCR The Stratmann Scuseria and Frisch weighting scheme 26 with screening MHL4SSF The Stratmann Scuseria and Frisch weighting scheme 26 with screen ing but employing the cell function by Murray Handy and Laming weighting scheme 31 with m equals 4 MHL8SSF The Stratmann Scuseria and Frisch weighting scheme 26 with screen ing but employing the cell function by Murray Handy and Laming weighting scheme 31 with m equals 8 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 63 The screening referred to reduces the cost of the normalisation of the molecular grid weights This reduction becomes larger with increasing molecule size The weighting scheme is a global option and can not be set on a per atom basis i e the ELEMENT and LABEL keywords can not
135. ting ia use level shifting and damping AAA use damping extrapolation and restrict orbital mixing in GVB or open shell calculations dla dot use damping and restrict orbital mixing 14 use damping extrapolation level shifting and restrict orbital mixing iii use level shifting damping and restrict orbital mixing 6 5 AVERAGE AVERAGE ON OFF lt tolerance gt In SCF calculations convergence problems may arise if the molecule has a partly occupied set of degenerate orbitals A way of dealing with this situation is to occupy all degenerate orbitals equally using fractional occupations if neseccary This equals building the density from an average of a number of states The AVERAGE directive controls this procedure which is on by default The options on and off do the obvious alternatively the tolerance for detecting degenerate orbitals can be specified All orbitals in the energy range of the HOMO energy plus minus the tolerance will be included in the degenerate set By default the tolerance is 10 6 SCF CONVERGENCE DEFAULT 24 6 6 SMEAR The SMEAR directive implements Fermi smearing 11 for filling up the molecular orbitals Normally orbitals are either fully occupied or empty Fermi smearing allows orbitals to be fractionally filled according to a step function that depends on the Fermi temperature employed Fermi smearing can be useful in certain problematic convergence cases where degenereci
136. tion 2 RUNTYPE 4 RUNTYPE INTEGRAL and the second by the directive sequence RESTART NEW BYPASS RUNTYPE SCF where the BYPASS directive avoids regeneration of the integral list A similar sequence to the Cl example above is often required when carrying out both OVGF and TDA Green s function calculations of ionization energies This would normally involve performing an initial SCF calculation under control of RUNTYPE SCF followed by the Green s function calculation thus RESTART NEW BYPASS SCF RUNTYPE GF where the integral transformation and OVGF computation of the ionization energies are per formed in the same job Finally consider RUNTYPE specification when performing geometry or transition state calcula tions It is of course possible in the startup job to present a data sequence of the form RUNTYPE OPTIMIZE ENTER If however the SCF converges to say an excited state on the first point any subsequent computation will be wasted It is normally better practice to perform the initial SCF under RUNTYPE SCF control then initiate the optimization with a sequence such as RESTART NEW BYPASS SCF RUNTYPE OPTIMIZE ENTER Subsequent restarts would be carried out with the sequence 3 SCFTYPE 5 RESTART OPTIMIZE RUNTYPE OPTIMIZE ENTER Although perhaps an obvious point note the removal of the BYPASS directive failure to re move this will almost certainly lead to an erroneous energy and or gradients in the opt
137. tion assuming again that this section has been written to previously If the closed shell vectors section does not exist then the eigenvectors will be generated from an atomic guess The choice of section number s for the output of eigenvectors i e those sections typically nominated on the ENTER directive is taken directly from Table 2 clearly this can lead to the final vectors over writing the input eigenvectors We illustrate these choices by considering a number of cases below as a function of SCFTYPE 1 Closed Shell SCF Here we are only involved in considering a single Section on the Dumpfile that contains the closed shell SCF eigenvectors Thus presenting the single data line ENTER in a startup job would act to request an atomic GUESS for generating the initial SCF eigen vectors that would be stored and subsequently updated and written to section 1 of the Dumpfile see Table 2 during the SCF process Presenting the same data line in a RESTART job would result in the eigenvectors of section 1 being used as the trial vector set and subsequently updated and overwritten during the SCF process In practice this default section would be examined for content at job outset and the contents used for the SCF process assuming the section had been written to by a previous job If the section is not present on the Dumpfile then a trial set will be generated using the VECTORS ATOMS mechanism If the User wished to keep copies of both initi
138. tion would be VECTORS ATOMS ENTER 10 or just ENTER 10 where the vectors generated by concatenating the atomic SCF densities are written to Section 10 of the Dumpfile Any subsequent SCF undertaken during the job will refresh this set of vectors e VECTORS NOGEN section The NOGEN option is specific to generating a trial set of GVB orbitals with section an integer referencing a section on the Dumpfile where a suitable starting set of either SCF or localised MOs may be found For each GVB pair two trial orbitals are required the strongly occupied MO corresponding to an SCF occupied MO and a weakly occupied orbital The NOGEN facility will generate such weakly occupied orbitals from the strongly occupied counterparts The user must ensure that given an n pair GVB treatment the top n orbitals from section correspond to the strongly occupied MOs of each pair This might typically be achieved under control of the SWAP directive 12 2 Section specification from the Parent Dumpfile The above discussion leads in obvious fashion to the second method of specifying the trial orbitals namely by nominating a Section on the Dumpfile wherein such orbitals may be found the orbitals having been written to that Section by some preceding run of the program under control of the ENTER directive In contrast to previous versions of GAMESS UK which required explicit specification of these section numbers the current release provides a set of de
139. tions during for example previous SCF processing 12 4 Specification from a Foreign Dumpfile GETQ The GETQ option causes restoration of eigenvectors from a foreign Dumpfile Characterisation of such a Dumpfile is achieved by specification through data input of 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 78 e the LEN of the data set on which this Dumpfile resides The foreign Dumpfile may reside on a direct data set assigned using a DDNAME in the range EDO to ED19 or on a sequential data set assigned using a DDNAME in the range MTO to MT19 e the starting block of the Dumpfile e the Section number wherein the required vectors are to be found this integer having been that associated with the ENTER directive whether by default or by explicit specification of the run which created the trial vectors A given set of eigenvectors is deemed to represent valid input to GETQ if it has the following attributes 1 It is derived from a previous calculation performed at either the same or at a different geometry 2 It is derived from a previous calculation where the symmetry adapted option is different 3 It is derived from a previous calculation conducted in a smaller basis set The program maps the old basis onto the new using standard projection techniques and it is now routine practice to use for example the vectors generated in a SV 3 21G basis to initiate an SCF calculation in a triple zeta
140. tive The syntax and usage of the directive is very much a function of the status of the computation in hand We may identify two differing situations where the User must either e define a mechanism for generating the orbitals or rely on the default mechanism ATOMS see below e nominate a Section on either the parent Dumpfile or some foreign Dumpfile wherein a suitable set of orbitals may be found 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 user may avoid the task of nominating sections These defaults which are a function of SCFTYPE are summarised in Table 2 12 1 Mechanism Specification At the outset of a calculation with no associated SCF computation available the User must either define a mechanism for generating the trial MOs though keyword specification on the VECTORS line or rely on the default mechanism note that the mechanism chosen is often a function of basis set If presented for such usage the VECTORS directive comprises a single data line read to the variables TEXT ATEXT BTEXT using format 3A e TEXT should be set to the character string VECTORS e ATEXT should be set to the appropriate string see below defining the generate mecha nism to be employed 12 CONTROLLING THE INPUT ORBITALS THE VECTORS DIRECTIVE 70 e BTEXT is an optional string that may be set to the charac
141. tive may be used to change the expo nent a for the damping function of equation 11 The directive consists of two data fields read to the variables TEXT and EXPONENT using the format A F e TEXT should be set to the character string ALPHA e EXPONENT should be set to the exponent of the damping function for the current Cg coefficient pair model It has to be a non negative floating point value 9 DIRECTIVES CONTROLLING MCSCF CALCULATIONS 39 8 0 1 6 The RADIUS directive The RADIUS directive may be used to change the Van der Waals radius of a chemical element The directive consists of three data fields read to the variables TEXT ELEMENT and RADO using the format A A F e TEXT should be set to the character string RADIUS e ELEMENT should be set to the chemical symbol of the element e RADO should be set to the Van der Waals radius of the element for the current Ce coefficient pair model The value should be specified in Bohr atomic units 8 0 1 7 The C6 directive The C6 directive may be used to change the Ce coefficient of a chemical element The directive consists of three data fields read to the variables TEXT ELEMENT and COEFF using the format A A F e TEXT should be set to the character string C6 e ELEMENT should be set to the chemical symbol of the element e COEFF should be set to the C coefficient of the element for the current Cg coefficient pair model The value should be specified in Hartree Bohr atomic units Exa
142. tive specification permits this recalculation to be suppressed through a data line of the form RECALCULATE OFF 14 6 CUTOFFS This directive may be used to request relaxation of certain constraints in optimisation and should be used with caution 14 7 EIGMIN The EIGMIN directive consists of a single data line read to variables TEXT VMIN using format A F e TEXT should be set to the character string EIGMIN e VMIN should be set to the minimum allowed value for eigenvalues of the Hessian matrix 148 EIGMAX The EIGMAX directive consists of a single data line read to variables TEXT VMAX using format A F e TEXT should be set to the character string EIGMAX e VMAX should be set to the maximum allowed value for eigenvalues of the Hessian matrix 149 MAXJORGEN The MAXJORGEN directive consists of a single data line read to variables TEXT MAXJOR using format A I e TEXT should be set to the character string MAXJORGEN e MAXJOR should be set to the maximum number of allowed cycles in the optimisation In the absence of this directive MAXJOR will be set to 40 14 10 RFO The RFO directive consists of a single data line read to variables TEXT TXTRFO using format 2A 14 JORGENSEN AND SIMONS OPTIMISATION ALGORITHM 100 e TEXT should be set to the character string RFO e TXTRFO should be used to control the nature of the steps taken in the search procedure and may be set to the character string ON or OFF The def
143. ults for the next four inputs but in their absense the ORMAS code will perform a full Cl calculation as described above That is the defaults are NSPACE 1 NORB NACT MINE NELS MAXE NELS meaning all active orbitals are in one partition e NSPACE Number of orbital groups you wish to define e NORB A list of NSPACE integers These specify the number of orbitals in each active space or group e MINE A list of NSPACE integers These specify the minimum numbers of electrons that must always occupy the orbital groups In other words MINE I is the minimum number of electrons that can occupy space in any of the determinants 10 DIRECTIVES CONTROLLING MASSCF CALCULATIONS AT e MAXE A list of NSPACE integers These specify the maximum numbers of electrons that must always occupy the orbital groups In other words MAXE I is the maximum number of electrons that can occupy space in any of the determinants e ROOT Selects the root of the Cl problem to solve for This enables the selection of ground and singly excited states the default is ROOT 0 for the ground state ROOT 1 will select the first excited state and so on Default is 0 e NSTATE Number of states to average over Default is 1 e WSTATE A list of NSTATE integers specifying the weights of the states to average over default entry is 1 0 for the first state e SYMSTATE Symmetry of the target state Default is the input symmetry Additional input
144. ural orbitals to the Dumpfile and to specify the canonicalisations in effect for the three categories of orbital core active and secondary The directive consists of a single data line read to the variables TEXT ISECNO TEXTC TEXTA TEXTS using format A I 3A 9 DIRECTIVES CONTROLLING MCSCF CALCULATIONS 44 e TEXT should be set to the character string CANONICAL e ISECNO should be set to a section number on the Dumpfile for output of the MCSCF natural orbitals e TEXTC is a character string for controlling the canonicalisation of the core orbitals In generating the optimum MOs for subsequent use in Cl calculations TEXTC should be set to the string FOCK e TEXTA is a character string for controlling the canonicalisation of the active orbitals In generating the MCSCF natural orbitals TEXTA should be set to the string DENSITY e TEXTS is a character string for controlling the canonicalisation of the secondary orbitals In generating the optimum MOs for subsequent use in Cl calculations TEXTS should be set to the string FOCK Example CANONICAL 10 FOCK DENSITY FOCK would be used to route the natural orbitals to section 10 on the Dumpfile Note that the above settings are now applied in default Version 6 3 onwards so the user need only present the CANONICAL directive to override these defaults e g a different section for the MCSCF natural orbitals 9 4 PRINT The PRINT directive may be used to increase the default MCSCF
145. ut Control oo da co ek aa a a a a a 72 Overall Control Flags eg we i ee a Sew 7 2 1 Controlling Printed Output PRINT 722 SCF exit stats SOPTEAIL 2 2c sc eee ee Ow ae ee 7 3 Controlling the convergence of a calculation a CONVERGENCE CONTROLS A oe s scs Ye de et ee ee a oe eo 7 3 2 Level Shifters LEVEL 0 0 0 000 0000 00050 a Diesel Bes Se a a te ed Sk a ow oh et tom INEWONS oa ade Y a Pm bk we Oe a awe E 135 EXTRAPOLATION 25 5 4 24 eso 8642S Sb ed bee es T30 NEWEST 20 0036 Boa ee Oe eh eR ae ee ee ee Y Far RESTORE roninai oree 4 66 4 15 rad de k on A 2 KOCK a a oe a A ew re See ke hs Poo SMEAR fh bt eck Aa Sos a a Go ee ee a TA Changing Phase sica aa Fe a eS TAL TESTER o e A Bi a ee a ae ee Eg 7 4 2 Change in TESTER DTESTER 2 0 0 0 eee 16 16 16 17 17 17 18 19 20 21 23 23 24 25 CONTENTS T43 Change inenergy DE oc ea Glew ewe ee a ee p e E 7 4 4 Absolute change in energy DEABS 7 4 5 Number of cycles in this phase NCYC o 7 4 6 Total number of SCF cycles TOTCYC 7 4 7 Information on a phase change INFO 15 Example rewset input tile coo sos we rs e dos Specification of Dispersion Corrections 8 0 1 VDWAALS Directives controlling the dispersion corrections Directives Controlling MCSCF Calculations We Ss ee A eee oR ee A ee aed 92 ORBITAL scora
146. well as more novel situations involving more than two orbital spaces Secondly the use of multiple small active spaces has been shown to accurately recover the quality of much larger full Cl calculations at a fraction of the cost 53 In this way ORMAS may be viewed as a powerful tool for generating N particle wave functions A MASSCF calculation is invoked by the directive SCFTYPE MASSCF The above keywords by themselves are insufficient to specify a MASSCF calculation MASSCF requires minimal information regarding the numbers of electrons and orbitals involved In most cases a keyword is to be followed by one or more integers or a floating point number in any standard representation 10 1 Basic MASSCF input keywords and their parameters The minimum requirements for defining a MASSCF calculation are as follows e MASSCF Keyword identifying the MASSCF input clause this is a flag no numerical parameter needed e NCORE Total number of orbitals doubly occupied in all determinants e NACT Total number of active orbitals e NELS Total number of active electrons Additional input parameters controlling convergence of the full Newton Raphson solver are as follows e TOLENG Convergence tolerance on the total energy Default value is 1 0d 10 e ACURCY Newton Raphson and Davidson convergence Default value is 1 0d 5 10 DIRECTIVES CONTROLLING MASSCF CALCULATIONS 46 e DAMP Newton Raphson damping factor
147. wton update method search for a saddle point on the potential energy surface using in default the trust region method 5 numerical force constant calculation at an equilibrium geometry analytical force constant calculation at an equilibrium geometry Polarisability calculation Hyperpolarisability calculation Magnetisability calculation Calculation of Raman Intensities Calculation of IR intensities single point Integrals SCF and 4 index transformation single point Integrals SCF transformation and Cl calculation single point Integrals SCF transformation and Green s function OVGF calculation single point Integrals SCF transformation and Green s function 2ph TDA calculation single point Integrals SCF transformation and Response function RPA TDA or MCLR calculation analyse a nominated set of eigenvectors either by computing 1 electron properties localised orbitals or by performing DMA Mulliken or graphical analysis 2 1 Notes on RUNTYPE Specification The simplest RUNTYPE is either that requesting just an SCF calculation TYPE SCF or some analysis of a pre computed wavefunction TYPE ANALYSE All other TYPEs comprise multiple tasks each of which could itself be controlled by its own TYPE specification Consider for example Direct Cl calculations performed under TYPE CI specification this of course involves three separate tasks namely 2 RUNTYPE 3 e the SCF computation e the integral transfo
148. xample 2 ooo da La Boe ee bb EGS REA Bee dE i 16 The ENTER Directive 17 STOP vi 100 101 101 101 102 102 102 102 103 103 103 104 104 104 104 105 106 107 1 INTRODUCTION 1 1 Introduction The Class 2 directives define the nature of the computation in hand and are used to input the details necessary to enable this computation to proceed In this chapter we concentrate on those directives required to characterise 1 SCF M ller Plesset MCSCF MASSCF and CASSCF calculations 2 Density Functional Theory DFT calculations 3 Geometry optimisation transition state calculations and force constant calculations Data input required in performing Direct Cl and Table Cl calculations and in using the various wavefunction analysis tools are considered below in Parts 5 6 and 7 respectively 2 RUNTYPE The RUNTYPE directive is used to define the type of computation to be performed in the present run of the program and consists of a single a line with the first two data fields read to variables TEXT TYPE using format 2A e TEXT should be set to the character string RUNTYPE e TYPE should be set to a character string defining the type of computation Valid strings are shown in the table below Subsequent data fields are a function of the TYPE setting and may be used to further charac terise the nature of the computation We consider the format for each TYPE specification in the notes below e In the absen
149. y Chem Phys Lett 73 1980 393 doi 10 1016 0009 2614 80 80396 4 P Pulay J Comp Chem 3 1982 556 560 doi 10 1002 jcc 540030413 F W Bobrowicz and W A Goddard in Modern Theoretical Chemistry Vol 3 ed H F Schaefer Plenum New York 1977 79 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 S Bell and J S Crighton J Chem Phys 80 1984 2464 doi 10 1063 1 446996 C J Cerjan and W H Miller J Chem Phys 75 1981 2800 doi 10 1063 1 442352 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 J Baker J Comp Chem 7 1986 385 395 doi 10 1002 jcc 540070402 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 M Dupuis and H F King Int J Quantum Chem
150. y precise than there is no reason to integrate the exchange correlation energy very accurately Through choosing a smaller quadrature computation can be saved in the early iterations Along with the calculation converging the quadrature is improved Near the convergence criterion the full quadrature grid as input will be applied Note that DENTOL and RHOTOL are global parameters for which LABEL and ELEMENT can not be used However PSITOL can be set on a per atom basis Examples SCREEN SCREEN OFF SCREEN P 1 0D 7 PSI 1 0D 5 SCREEN P 1 0D 7 PSI 1 0D 5 ELEMENT C 1 0D 6 LABEL H1 1 0D 5 The use of screening may significantly improve efficiency 11 DIRECTIVES CONTROLLING DFT CALCULATIONS 64 11 7 9 Angular Grid Pruning ANGPRUNE This directive activates angular grid pruning as function of radius uses the scheme proposed by Murray Handy and Laming 31 This scheme chooses the number of angular grid points according to the equation Ntheta Min Ktheta Niheta r Bragg Ntheta where e Niheta IS the current number of grid points in the theta coordinate e Niheta is the maximum number of grid points in the theta coordinate e Kineta IS some scaling factor which is set to 5 in as suggested by Murray et al e Bragg is the Bragg Slater radius of the atom 46 e ris the radius of the current angular shell From the above equation it is clear that this pruning scheme is designed to be used with the Gauss Legendre angular grid When it is applied

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