GAMESS-UK USER'S GUIDE and REFERENCE MANUAL Version
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1. 2 8 1 BEGIN Example In an all electron calculation on MgNag there are 70 electrons in doubly occupied core orbitals The first valence MO thus carries the number 36 and the data line BEGIN 36 starts the orbital counting with this MO 2 9 RPA Data QZ Usually the RPA calculation is carried out for the ground state of a molecule In this case the symmetric RPA matrix is positive definite and the projected generalized eigenvalue problems can be reduced to ordinary eigenvalue problems This is the default strategy of the iterative algorithm If however the user wishes to perform a calculation on a state different from the ground state or if the RPA matrix is extremely ill conditioned she he can resort to the QZ algorithm of Moler and Stewart which treats generalized indefinite eigenvalue problems This path detects and discards complex eigenvalues lt is initiated by presentation of the single data line QZ Note that the QZ algorithm is considerably slower than the standard method for positive definite matrices The occurrence of complex eigenvalues during the standard reduction is usually indicated by the message PROBLEM IN ITERATION STEP 1 ERED2 IS NOT POSITIVE DEFINITE which terminates the RPA procedure for that particular symmetry In this case the user should first check if she he is really calculating on the Hartree Fock ground state Note that the QZ algorithm is the default in Direct RPA calculations 2 RPA AND TDA CAL2. SYMM 3 5 SPLIT O END VECTORS 2 3 ENTER 2 3 REFERENCES 13 References 1 C Fuchs V Bona i Kouteckv and J Koutecky J Chem Phys 98 1993 3121 doi 10 1063 1 464086 2 P J rgensen H J Aa Jensen and J Olsen J Chem Phys 89 1988 3654 doi 10 1063 1 454885
3. Usually there is no loss of speed of convergence when split trial vectors are used from the very beginning Setting ITER to zero is therefore recommended with this directive 4 7 MCLR Data Further directives The directives MAXRED MAXIT BEGIN POLA and THRESH are also available in MCLR calculations They are identical to the corresponding directives in the RPA module with one exception the THRESH directive must not be terminated by the keyword END since this is reserved for signaling the end of the MCLR directives The reader is referred to the corresponding sections for a detailed description of the directives We list below the complete input for an MCLR calculation on the water molecule using a TZVP basis and performing a full valence space calculation We start with the MCSCF job omitting the SCF job s 4 7 1 MCSCF calculation RESTART TITLE H2C0 TZVP MCSCF BYPASS ZMAT 0 4 MULTICONFIGURATIONAL LINEAR RESPONSE CALCULATIONS 12 H 1 1 809 H 1 1 809 2 104 52 END BASIS TZVP RUNTYPE SCF SCFTYPE MCSCF MCSCF ORBITAL DOCi DOCi DOC3 DOC1 DOC2 UOC1 UOC3 END ENTER 4 7 2 MCLR calculation RESTART TITLE H2C0 TZVP MCSCF BYPASS MCSCF ZMAT 0 H 1 1 809 H 1 1 809 2 104 52 END BASIS TZVP SCFTYPE MCSCF MCSCF ORBITAL DOCi DOC1 DOCS DOC1 DOC2 UOC1 UOC3 END RUNTYPE RESPONSE MCLR ORBITAL DOCi DOCi DOC3 DOC1 DOC2 UOC1 UOC3 END SECTIONS SCF 1 MCSCF 8 CANONICAL 10 CIVEC 9 SYMM 1 5 SYMM 2 5
4. line should be set to the character string END The numbers following the keywords EIGEN EQSYS define the thresholds to which the residual in the eigenvalue algorithm and equation system solver respectively is converged The default value is 0 001 for both algorithms The data line TABLE 0 1 causes printing of all eigenvector components with modulus larger than or equal to 0 1 in the result tables for TDA and RPA The default value is 0 2 Finally the data line ANALYSIS 0 01 causes printing of all eigenvector components c with c gt 0 01 provided a detailed analysis of the eigenvectors is requested by means of the ANALYSE directive 2 RPA AND TDA CALCULATIONS 6 2 8 RPA Data BEGIN In the result table of an RPA calculation the leading components of the eigenvectors are listed attached with symmetry labels of the orbitals involved in the corresponding one electron excitation e g 0 85 2 a 1 ba Usually the labeling starts with the first MO i e the one with the lowest energy Now if there is a core of orbitals from which virtually no excitations are expected in the lowest excited states the user may wish to start labeling the orbitals at the first valence MO This is accomplished with the BEGIN directive which consists of a single data line read to variables TEXT NBEGIN using format A e TEXT should be set to the character string BEGIN e NBEGIN is an integer specifying the number of the first MO to be labeled
5. of the iterative process either by runtime problems or by a user s operation this file contains the approximate eigenvectors of the last iteration step that was completed These vectors may be used in a later job to resume the calculation at that iteration step This is accomplished by the data line RESTORE RPA file where file is the above mentioned file containing the saved vectors Note that the keyword RPA has to be replaced by TDA if the job was interrupted during a TDA calculation Note also that the restart run must begin with the particular irrep in which the termination occurred and that the same number of roots must be specified 4 Multiconfigurational linear response calculations A multiconfigurational linear response MCLR calculation 1 also known under the term time dependent multiconfigurational SCF is performed by presenting the data line 4 MULTICONFIGURATIONAL LINEAR RESPONSE CALCULATIONS 10 RUNTYPE RESPONSE MCLR in the input file A necessary condition for performing an MCLR calculation is the successful completion of a corresponding multiconfigurational SCF calculation with the GAMESS UK MCSCF module The Dumpfile ED3 and the transformed integral file ED6 must be saved The MCLR calculation is then performed as a restart job In the following we list the directives which are available in the MCLR module Note that the first four are obligatory 4 1 MCLR Data ORBITAL The set of active orbitals must be sp
6. ASIS SCF PRIOR TO RPA CALCULATION SUPER OFF NOSYM ENTER e An integral transformation using the MOs from the SCF job as input vectors The Dumpfile ED3 and the transformed integral file ED6 must be kept RESTART TITLE H2CO TZVP R SP BASIS INTEGRAL TRANSFORMATION SUPER OFF NOSYM BYPASS SCF RUNTYPE TRANSFORM ENTER Note that the SCF computation is BYPASS ed with the SCF vectors from the first run now restored from the default closed shell SCF eigenvector section section 1 and used in the transformation e The final RPA job must be declared as a restart job and BYPASS s the integral transfor mation RESTART TITLE H2CO TZVP R SP BASIS CONVENTIONAL RPA CALCULATION SUPER OFF NOSYM BYPASS TRANSFORM RUNTYPE RESPONSE RPA RPA Data ENTER The RPA input data is terminated by the ENTER directive where the default SCF eigen vectors section is again in the absence of section specification In the following sections the directives controlling the RPA calculation are described 2 RPA AND TDA CALCULATIONS 3 2 1 RPA Data SYMM The computation of excitation energies and corresponding oscillator strengths is initiated by the SYMM directive comprising the variables TEXT1 ISYM ILOW TEXT2 IHIGH using format A 21 A 1 e TEXTI should be set to the character string SYMM e TEXT2 should be set to the character string TO The excited states no ILOW to IHIGH of the irreducible representation ISYM ar
7. CONTENTS Computing for Science CFS Ltd CCLRC Daresbury Laboratory Generalised Atomic and Molecular Electronic Structure System a _ 3 _ _ ___ __ __ _ l GAMESS UK USER S GUIDE and REFERENCE MANUAL Version 8 0 June 2008 PART 7 RPA and MCLR CALCULATIONS M F Guest J Kendrick J H van Lenthe and P Sherwood Copyright c 1993 2008 Computing for Science Ltd This document may be freely reproduced provided that it is reproduced unaltered and in its entirety Contents 1 Introduction 2 RPA and TDA calculations 241 RPA Datas SYMM ooo g e sd a 211 SYMM Exempla cocos bl Awe B Anke RS moe eS A 2 2 RPA Data TDA sn ne aed a x o a CORR oe We A lo 23 RPA Data POLA 22x19 en Be Re RG E e Cody 24 RPA Data MAXBED iua ade wa ara a RR ee we 25 RPA Datas MAXIT ooo a ok ene ds al e de Be a ox YU s 26 RPA Data ANALYSE g eed ee be oss 24 RPA Dates THRESH o 6444 5 a Os cee wehbe e eme Ss ao CO A 4 wo m CONTENTS ji 20 RPA Data BEGIN sv cios pes Ear Exe aq REO SEE do eos 6 28 BEGIN Example 2 24 oz Eoo a a a 6 29 RPA Data QZ oodo nae Bob oe AM a Se Sa ce ts Ad 6 2 10 Auxiliary Wes uu ue ko xx A ee EROR ee ee eee eR A 7 2410 1 SCF caleulati h ocna chou dd e RR ee Ro Rd 7 210 2 Integral transformati n us uc rs ee E e Z RS S T 2 10 3 RPA calculation o sa ssim oo Room hod boa e T 8 3 Direct RPA calculations 8 3d PREF IIA 9 3 2 WAAVEG cou uw e ee bos bue qe UD deae tal l TRE oe a Ds 9 3 3 Dumping a
8. CULATIONS f 2 10 Auxiliary files The RPA program automatically generates a file named rpa spectrum and or tda spectrum if a TDA calculation is performed which contains a table of the excitation energies in a u and corresponding oscillator strengths This file may serve as input for a suitable plotting program If the user wishes to keep this file for plotting she he should place a corresponding command line at the end of the shell script file which moves rpa spectrum to the user s permanent directory The files tda table tex and rpa table tex contain the TEX input for a list of the excited states computed with TDA and RPA respectively with excitation energies oscillator strengths and most important single excitations If a calculation is performed on the states of symmetry i 1 lt i lt 8 a file tm4i is generated which contains the input for a plot of the RPA analogue of the transition density matrix Finally we list the complete input data for an RPA plus polarisability calculation on the water molecule using a 4 31G basis 2 10 1 SCF calculation TITLE H20 4 31G BASIS SUPER OFF NOSYM ZMAT 0 H 1 1 809 H 1 1 809 2 104 52 END BASIS 4 31G ENTER 2 10 2 Integral transformation RESTART TITLE H20 4 31G BASIS INTEGRAL TRANSFORMATION BYPASS SCF SUPER OFF NOSYM ZMAT 0 H 1 1 809 H 1 1 809 2 104 52 END BASIS 4 31G RUNTYPE TRANSFORM ENTER 3 DIRECT RPA CALCULATIONS 8 2 10 3 RPA calculation RE
9. START TITLE H20 4 31G BASIS RPA CALCULATION BYPASS TRANSFORM SUPER OFF NOSYM ZMAT 0 H 1 1 809 H 1 1 809 2 104 52 END BASIS SV 4 31G RUNTYPE RESPONSE RPA TDA SYMM 1 1 TO 5 SYMM 2 1 TO 5 SYMM 3 1 TO 2 MAXRED 25 MAXIT 20 ANALYSE THRESH EIGEN 0 001 EQSYS 0 0001 TABLE 0 25 ANALYSIS 0 05 END POLA 0 0 0 1 0 2 ENTER 3 Direct RPA calculations For large atomic orbital basis sets the integral transformation step in conventional RPA cal culations can become prohibitive In this case it is possible to resort to a Direct SCF like implementation of the RPA procedure which breaks up the four index transformation into two two index transformation whenever the RPA matrix acts on a trial vector The Direct RPA module is started by the input lines RUNTYPE RESPONSE RPA DIRECT in the input file In this case the only preparatory run is a closed shell SCF calculation which may be conventional or direct and in which the integrals may be generated in supermatrix or 2E format Only the Dumpfile of the SCF calculation must be kept All directives that are available for conventional RPA calculations can also be used for the Direct RPA case with two exceptions The polarisability module has not yet been implemented and the QZ directive is redundant vide supra The following additional directives are available 4 MULTICONFIGURATIONAL LINEAR RESPONSE CALCULATIONS 9 3 1 PREF This directive controls the prefactor tolerance for t
10. alue of MAXR is 50 e MAXRR is an integer specifying the maximal size of the reduced matrices during solu tion of the linear response equations for polarisability calculations The default value of MAXRR is 50 Within the MAXRED directive the specification of MAXRR is optional Note that there is no danger in specifying a value of MAXR or MAXRR which is too large with respect to the memory available The program automatically adjusts the value of MAXR if the iterative procedure consumes too much memory If the user however absolutely insists on the desired value for MAXR she he should increase the available memory using the MEMORY predirective The value of MAXR should at least be three times as large as the largest number of eigenvalues wanted for one specific symmetry except for very large calculations The following table gives recommended values for MAXR Number of eigenvalues desired Recommended value of MAXR 10 50 80 20 80 100 30 90 120 50 150 200 100 200 300 200 400 If the iterative algorithm reaches the maximum dimension before convergence it restarts the procedure using the current approximate eigenvectors as starting vectors 2 5 RPA Data MAXIT This directive sets the maximal number of iterations for the iterative algorithms in the RPA module The data line MAXIT 50 10 sets the maximum number of cycles to 50 for the eigenvalue problem and to 10 for the linear equation solver The defaul
11. ding 4 3 MCLR Data SYMM This directive controls the calculation of excited states lt consists of the variables TEXT ISYM IHIGH using format A 2l TEXT should be set to the character string SYMM The integer ISYM indicates the irreducible representation and IHIGH is the number of roots to 4 MULTICONFIGURATIONAL LINEAR RESPONSE CALCULATIONS 11 be calculated in the irrep ISYM Note that the syntax of this directive is different from the corresponding directive in the RPA module In particular it is not possible to calculate an interval ILOW IHIGH of roots with ILOW different from 1 4 4 MCLR Data END This directive which consists of the single keyword END terminates the input which controls the MCLR calculation It must always be present 4 5 MCLR Data REDUCE The default algorithm for solving the small generalized eigenvalue problems during the iterative MCLR calculation is the QZ algorithm see the description of the QZ directive in the RPA module The REDUCE directive which consists of a single data line with the keyword RE DUCE forces the program to reduce the generalized eigenvalue problems to standard eigenvalue problems 4 6 MCLR Data SPLIT This directive initiates the use of split trial vectors as described in 2 It consists of variables TEXT ITER using format A l where TEXT is set to the character string SPLIT and ITER is an integer indicating after which iteration step split trial vectors are to be used
12. e then com puted 2 1 1 SYMM Example Calculation of the excitation energies for the lowest five states of each of the optically allowed symmetries Biu Boxy Ba of a molecule with Dat symmetry requires the data lines SYMM 2 1 TO 5 SYMM 3 1 TO 5 SYMM 5 1 TO 5 in the input 2 2 RPA Data TDA By presenting the data line TDA an additional Tamm Dancoff TDA calculation is performed for the specified irreps and roots corresponding to a Cl in the space of single excitations The line TDA ONLY can be used to suppress the RDA calculation performing a TDA calculation only 2 3 RPA Data POLA This directive initiates the computation of dynamic polarisabilities within the time dependent Hartree Fock model Each data line should begin with the character string POLA followed by one or several up to 10 floating point numbers representing the frequencies in atomic units for which the polarisabilities are requested If more than 10 frequencies are required a new data line must be presented 2 RPA AND TDA CALCULATIONS 4 2 4 RPA Data MAXRED The maximal size of the reduced matrices in the iterative RPA algorithm can be adjusted with the MAXRED directive consisting of a single dataline read to the variables TEXT MAXR MAXRR using format A 21 e EXT should be set to the character string MAXRED e MAXR is an integer specifying the maximal size of the reduced matrices in the iterative eigenvalue search The default v
13. ecified by means of the ORBITAL directive The individual lines of this directive must be identical to those presented in the preceding MCSCF calculation Since this directive is described in detail in the MCSCF part and is usually copied into the MCLR job from the MCSCF job we refer the reader to the corresponding section 4 2 MCLR Data SECTIONS In order to perform an MCLR calculation several vectors have to be retrieved from the Dumpfile The SECTIONS directive specifies in which sections of the Dumpfile the corresponding vectors are stored Note that these sections must still be specified even if the default sections have been used at vector generation time in the absence of explicit section specification on the corresponding ENTER directive The data lines SECTIONS SCF 1 MCSCF 8 CANONICAL 10 CIVEC 9 instruct the program to read the SCF eigenvectors from section 1 the MCSCF MOs from section 8 the pseudocanonical MCSCF orbitals from section 10 and the MCSCF CI vector from section 9 of the Dumpfile Note that with the possible exception of CANONICAL as specified by the CANONICAL MCSCF directive these section numbers correspond to the defaults in place at vector generation time in the closed shell SCF and MCSCF module Note that the default section for the MCSCF NOs is now section 10 and it is this section number that should be specified in the data above The indentation is of course not necessary but convenient for better rea
14. he integral generator It consists of a single data line with variables TEXT EXP using format A l where TEXT is set to the character string PREF and EXP is a positive integer setting the prefactor tolerance to 10 FXP The default value for EXP is 7 3 2 MAXVEC The direct RPA procedure is organized in such a way that a maximal number of trial vectors with respect to the main memory available is contracted with the integrals generated in one batch lt may however sometimes be necessary to reduce this number since valuable memory is needed for other purposes e g to increase the maximal size of the reduced matrices during the iterations The MAXVEC directive allows to limit the number of trial vectors which are treated in one batch to a specific value M It consists of a single data line with the variables TEXT M using format A l where TEXT is set to the character string MAXVEC and M is the above mentioned integer 3 3 Dumping and restoring trial vectors Since Direct RPA calculations on larger systems are rather time consuming it is desirable to have the possibility to interrupt a calculation and restart it at a later time Dumping and restoring intermediate results is possible with the DUMP and RESTORE directives The user may dump vectors by specifying the data line DUMP file where file is the complete path of a file in some permanent directory that may be chosen freely In case the RPA or TDA calculation aborts in the middle
15. nd restoring trial vectors 0000 9 4 Multiconfigurational linear response calculations 9 41 MCLR Data ORBITAL LL 10 T2 MOLE Data SECTIONS oo ec te dee R N s 10 45 MELK Data SYMM ox eu denas bed ee SE deum Se poen 10 44 MCLR Data END L 11 45 MCLR Data REDUCE 060 mo RR EUR S Ru 11 45 MGER Dsta SPLIT po i i eases ee Reg a m Romo Red 11 4 7 MCLR Data Further directives 2l 11 ATA MCSGF caleulatigft ius 264 0 65 4 meom geom Rome ne 11 472 MCER calculation lt 26644 405 66 Rea Bae a eae i 12 1 INTRODUCTION 1 1 Introduction Under the common runtype RESPONSE the user may perform calculations of electronic transi tion energies and corresponding oscillator strengths using either the Random Phase Approxima tion RPA method or the Multiconfigurational Linear Response MCLR procedure The RPA calculations may be performed either within the conventional approach where the two electron integrals are transformed or with a direct implementation The next sections describe in detail how to perform calculations with the linear response module 2 RPA and TDA calculations Calculations of excitation energies and oscillator strengths based on the Random Phase Approx imation RPA are initiated by specifying the data line RUNTYPE RESPONSE RPA in the input file Data input characterising the details of the calculation is presented immediately after the RUNTYPE data line Termination of this data is accom
16. plished by presenting a valid Class 2 directive such as VECTORS RUNTYPE RESPONSE is in fact a combination of tasks requesting integral generation SCF integral transformation in conventional RPA calculations and finally the response calculation itself While in simple cases it may be feasible to perform all steps in a single calculation it will often be necessary to break up the calculation into multiple jobs driving through each of the tasks under control of the appropriate RUNTYPE directive with use made of the BYPASS directive in the latter stages of the computation The data input required when performing an RPA calculation in a single job is shown schemat ically below TITLE H2C0 TZVP R SP BASIS RPA CALCULATION SUPER OFF NOSYM RUNTYPE RESPONSE RPA RPA Data ENTER When splitting the RPA calculation into multiple steps we will be involved in performing the following tasks e A closed shell SCF calculation requesting through use of the SUPER directive full integral list generation required in the subsequent transformation Note that in most cases this 2 RPA AND TDA CALCULATIONS 2 part of the calculation may also be conveniently broken up into two parts the first being a normal SCF where the integrals are generated in supermatrix form and the second being a restart job with the SUPER OFF NOSYM data line Dumpfile ED3 and Mainfile ED2 from the SCF calculation must be kept TITLE H2C0 TZVP R SP B
17. t value is 30 for both algorithms As for MAXRED specification of the second integer is optional within the MAXIT directive 2 RPA AND TDA CALCULATIONS 5 2 6 RPA Data ANALYSE The result table printed after successful completion of the iterative TDA RPA procedure con tains the most important one electron excitations of the corresponding states If y z denotes an RPA eigenvector then all components of the vector y z with modulus larger than a certain threshold which may be specified in the THRESH directive see below are listed in this table With the help of the ANALYSE directive which consists of the single data line ANALYSE the user may in addition examine smaller components without having them listed in the result table The corresponding threshold is again specified by means of the THRESH directive see below The additional output generated by the ANALYSE directive also contains the dipole integrals useful for an investigation which mono excitations contribute to a large oscillator strength and the weights of the vectors y and z in the RPA eigenvectors y z 2 7 RPA Data THRESH It is possible to define various thresholds to control the convergence and output The first data line of the THRESH directive should be set to the character string THRESH Each following line should begin with one of the character strings EIGEN EQSYS TABLE ANALYSIS followed by a floating point number using format A F The last data
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