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Manual for the MRCC Program System

1. Options on or off If maxact on the maximum number of virtual and occupied inactive labels must be specified in the subsequent line as an integer vector The integers must be separated by spaces The vector should contain as many elements as the excitation rank of the highest excitation in the cluster operator The integers are maximum number of virtual occupied inactive labels allowed on amplitudes of single double excitations respectively Default maxact off Example Suppose that we have up to quadruple excitations and the single double triple and quadruple excitations are allowed to have maximum of 1 2 2 and 1 inactive virtual and occupied la bels respectively Then the input file should include the following lines maxact on 1221 maxex Level of highest excitation included in the cluster operator in the case of MRCI CC calculations In an MR calculation all single double or higher excitations out of the reference determinants are included in the cluster operator see the description of keyword nacto however the very high excitations are frequently irrelevant Using this option the latter can be dropped If maxex is set to a positive integer n only up to n fold excitations will be included in the cluster operator The excitation manifold can be further selected by imposing constrains on the number of active inactive labels of the excitations see keyword maxact See Refs 2 and 3 for more details Options 6
2. 43 1 The algorithms based on the Laplace transformed technique use minimax quadratures obtained from Ref 68 2 The default quadratures are taken from the Quad file which is located in the BASIS directory created at the installation In addition to the default quadratures any further quadrature can be used by adding it to the BASIS Quad file or alterna tively to the GENBAS file to be placed in the directory where MRCC is executed The format is as follows On the first line give the label of the quadrature as KNNRXXX where NN is the number of the quadrature points and XXX is the upper limit of the interval in which the Laplace transform is approx imated variable R in Ref 68 The subsequent NN lines must contain respectively the weights and quadrature points Example to use Laplace transform give dendec Laplace dens Construction of density derivative density and transition density ma trices for property calculations If mod dens 2 1 only one particle if mod dens 2 0 both one and two particle density matrices will be calculated and contracted with the available property integrals See Refs 3 5 9 11 12 for more details Options 1 2 Density matrix calculation for geometry optimizations first order properties etc 3 4 Density matrix first derivatives for second order property calculations available only with CFOUR 5 6 Transition density matrices for transition moment calcula tions 7 8 Second and t
3. PBEO hybrid functional of Perdew Burke and Ernzerhof 0 75 PBEx 0 25 HF exchange PBEc 73 83 PW91 Perdew and Wang 1991 exchange correlation functional PW91x PW91c 74 HCTH120 HCTH120 exchange correlation functional of Boese and co workers 84 HCTH147 HCTH147 exchange correlation functional of Boese and co workers 84 HCTH407 HCTH407 exchange correlation functional of Boese and Handy 85 48 B2PLYP Grimme s two parameter double hybrid functional includ ing MP2 correction 0 47 B88 0 53 HF exchange 0 73 LYP 0 27 MP2 correlation 86 B2GPPLYP two parameter double hybrid functional including MP2 correction of Martin and co workers 0 35 B88 0 65 HF ex change 0 64 LYP 0 36 MP2 correlation 87 DSDPBEP86 dispersion corrected spin component scaled double hybrid functional of Kozuch and Martin 0 30 PBEx 0 70 HF exchange 0 43 P86 0 53 MP2 antiparallel spin cor relation 0 25 MP2 parallel spin correlation 88 89 Note that the dispersion correction is only included if the D3 post fix is added see the note below dRPA75 the dual hybrid random phase approximation dRPA75 method of Mezei et al 90 The KS orbitals are obtained with the 0 25 PBEx 0 75 HF exchange PBEc functional while the energy is calculated using the 0 25 PBEx 0 75 HF exchange dRPA correlation expression user User defined functional Any combination of the LDA B88 PBEx PW91x LYP VWN5 PW
4. VWN5 correlation functional V of Vosko Wilk and Nusair 76 PW Perdew Wang 1992 correlation functional 77 P86 Perdew s 1986 correlation functional 78 PBEc correlation functional of Perdew Burke and Ernzerhof 73 PW91c Perdew and Wang 1991 correlation functional 74 BLYP Becke s 1988 exchange functional 72 and the correlation functional of Lee Yang and Parr B88 LYP 75 BHLYP Becke s half and half exchange in combination with the LYP correlation functional 0 5 B88 0 5 HF exchange LYP 72 75 79 B3LYP Becke s three parameter hybrid functional including the correlation functional of Lee Yang and Parr 0 08 LDA 0 72 B88 0 2 HF exchange 0 19 VWN5 0 81 LYP 69 70 72 75 76 80 B3LYP3 Becke s three parameter hybrid functional including the correlation functional of Lee Yang and Parr 0 8 LDA 0 72 B88 0 2 HF exchange 0 19 VWN3 0 81 LYP 69 70 72 75 76 80 81 Note that this is equivalent to the B3LYP functional of the GAUSSIAN package B3PW91 Becke s three parameter hybrid functional including the 1991 correlation functional of Perdew and Wang 0 08 LDA 0 72 B88 0 2 HF exchange 0 19 VWN5 0 81 PW91c 169 70 72 74 76 80 B97 Becke s 1997 exchange correlation functional including 0 1943 HF exchange 82 BP86 BP86 exchange correlation functional B88 P86 72 78 PBE exchange correlation functional of Perdew Burke and Ernz erhof PBEx PBEc 73
5. M Francl W J Petro W J Hehre J S Binkley M S Gordon D J DeFrees and J A Pople Self consistent molecular orbital meth ods XXIII A polarization type basis set for second row elements J Chem Phys 77 3654 1982 J S Binkley J A Pople and W J Hehre Self consistent molecular orbital methods 21 Small split valence basis sets for first row elements J Am Chem Soc 102 939 1980 M S Gordon J S Binkley J A Pople W J Pietro and W J Hehre Self consistent molecular orbital methods 22 Small split valence basis sets for second row elements J Am Chem Soc 104 2797 1983 A D McLean and G S Chandler Contracted Gaussian basis sets for molecular calculations I Second row atoms Z 11 18 J Chem Phys 72 5639 1980 T Clark J Chandrasekhar G W Spitznagel and P v R Schleyer Efficient diffuse function augmented basis sets for anion calculations III The 3 21 G basis set for first row elements Li F J Comp Chem 4 294 1983 Florian Weigend and Reinhart Ahlrichs Balanced basis sets of split valence triple zeta valence and quadruple zeta valence quality for H to Rn Design and assessment of accuracy integrals over Gaussian func tions Phys Chem Chem Phys 7 3297 2005 96 50 52 53 54 55 56 fiat 57 58 59 Kirk A Peterson Thomas B Adler and Hans Joachim Werner Sys tematically convergent basis sets for explicitl
6. located to your PATH environmental variable The test jobs will be automat ically executed and you will receive feedback about the results of the tests The corresponding output files will be left in the MTEST directory and you can also check them If all the tests complete successfully your installation is correct with high probability The execution of the test jobs will take for a couple of hours If you want to run the test on another machine e g on a node of a cluster you should copy the entire MTEST directory to that machine and start the mtest script there Please note that there are some test jobs that allocate a small amount of memory to test the out of core algorithms of the program MINP_ smallmem If you run these test jobs with OpenMP parallelized executables i e the build mrcc script was run with the pOMP switch on more than two cores some of them will fail since the memory requirement for OpenMP parallel runs grows with the number of cores In this case the failure of these tests does not indicate a problem with your installation Please also note that you can also create your test jobs e g if you modify the code compile the program with new compiler versions or use unusual combination of keywords To that end you should calculate a reliable energy for your test job e g using a stable compiler version include the test keyword and the calculated energy to the MINP file see the description of the keyword for more
7. ly K llay and Jurgen Gauss Calculation of frequency dependent hyperpolarizabilities using general coupled cluster models J Chem Phys 127 134109 2007 Darragh P O Neill Mih ly K llay and J rgen Gauss Analytic evalu ation of Raman intensities in coupled cluster theory Mol Phys 105 2447 2007 Mihaly K llay and J rgen Gauss Approximate treatment of higher excitations in coupled cluster theory II Extension to general single determinant reference functions and improved approaches for the canonical Hartree Fock case J Chem Phys 129 144101 2008 J rgen Gauss Mih ly K llay and Frank Neese Calculation of elec tronic g tensors using coupled cluster theory J Phys Chem A 113 11541 2009 Sanghamitra Das Debashis Mukherjee and Mihaly K llay Full imple mentation and benchmark studies of Mukherjee s state specific multi reference coupled cluster ansatz J Chem Phys 132 074103 2010 Huliyar S Nataraj Mih ly K llay and Lucas Visscher General imple mentation of the relativistic coupled cluster method J Chem Phys 133 234109 2010 93 17 Sanghamitra Das Mih ly K llay and Debashis Mukherjee Inclusion 22 23 24 25 26 27 28 of selected higher excitations involving active orbitals in the state specific multi reference coupled cluster theory J Chem Phys 133 234110 2010 Mihaly K llay Huliyar S Nataraj Bijaya K Sahoo Bhanu
8. that is the number of atoms a blank line then for each atom the atomic symbol or atomic number and the x y and z components of Cartesian coordinates Cartesian coordinates in xyz format can also be generated by MOLDEN see also Sect 14 1 tmol Cartesian coordinates in a format similar to that used by the TURBOMOLE package that is the number of atoms a blank line then for each atom the x y and z components of Cartesian coordinates and the atomic symbol or atomic number Note For the use of ghost atoms see the description of keyword ghost Default geom zmat which is equivalent to geom i e if it is not spec ified whether the geometry is supplied in Z matrix format or in Cartesian coordinates Z matrix format is supposed Nevertheless the coordinates must be given in the subsequent lines in any case Examples the following four geometry inputs for H2O2 are equivalent 1 Z matrix format bond lengths in A 2 xyz format coordinates in bohr atoms are specified by atomic symbols unit bohr geom xyz 4 H 0 00000000 0 00000000 0 00000000 61 0 1 82736517 0 00000000 0 00000000 0 2 41444411 2 68807873 0 00000000 H 3 25922198 2 90267673 1 60610134 3 xyz format coordinates in bohr atoms are specified by atomic numbers unit bohr geom xyZ 4 1 0 00000000 0 00000000 0 00000000 8 1 82736517 0 00000000 0 00000000 8 2 41444411 2 68807873 0 00000000 1 3 25922198 2 90267673 1 60610134 4 TURBOMOLE format coordina
9. 0 H1R H1R2A R 0 9575 A 104 51 34 basis special cc pVQZ cc pVTZ cc pVDZ 5 Consider the water molecule and use the cc pVTZ basis set for the hydrogens and aug cc pV TZ for the oxygen The following two inputs are identical basis atomtype O aug cc pVTZ H cc pVTZ or basis aug cc pVTZ 6 Consider the water molecule If you specify basis cc pVTZ min minimal basis sets generated from cc pVTZ will be used for the atoms that is only one s function two s and one p shells will be retained from the s p kernel of the H O cc pVTZ basis set 7 Consider the PbO molecule If you want to use the cc pVDZ basis set for O and the cc pVDZ PP basis with the corre sponding ECP for Pb you only need to set basis cc pVDZ PP in the MINP file basopt Use this keyword to turn on off basis set optimization Besides set ting this keyword a user supplied GENBAS file is also required for basis set optimization jobs It is also possible to set the value of basopt to be equal to an appropriate energy In this case the basis set parameters are optimized so that the absolute value of the difference between this value and the actual energy is minimized This option comes handy when optimizing a density fitting basis set In this case the differ ence between the actual and non density fitted energy obtained from a previous calculation will be minimized See also Sect 6 9 Options on off or lt any real number gt Default basopt off Ex
10. 0 1 0 1 2 0 0 0 0 0 0 0 optalg Specifies the optimization algorithm For basis set optimization at the moment the downhill simplex method of Nelder and Mead 112 is the only available option Options simplex the simplex method of Nelder and Mead Default optalg simplex optmaxit Maximum number of iteration steps allowed in an optimization The maximum number of function evaluations is also controlled by the parameter optmaxit it is set to 15xoptmaxit If the optimiza tion is terminated with a message the maximum number of function evaluation is exceeded than you can increase the value of optmaxit appropriately Options lt any positive integer gt Default optmaxit 50 Example to allow 60 iteration steps set optmaxit 60 opttol Convergence threshold for optimization The optimization is termi nated when the energy difference becomes less then this value and the steptol criterion is also fulfilled Options lt any positive real number gt Default opttol 1e 6 Example for a convergence threshold of 5 107 set opttol 5e 7 orblocc Specifies what type of orbital localization is performed for the core molecular orbitals 73 Options All the options introduced for keyword orbloco also work for orblocc see the description of keyword orbloco for details Default orblocc orbloco Example to avoid the localization of core orbitals specify orblocc off orbloco Specifies what type of orbital localization is performed for occ
11. 10 5 Density fitted calculations are only possible with MRCC 6 2 Geometry optimizations and first order properties Geometry optimizations and first order property calculations can be per formed using analytic gradients with the following methods orbitals and interfaces Available methods 1 arbitrary single reference coupled cluster methods Refs 1 and 3 CCSD CCSDT CCSDTQ CCSDTQP CC n arbitrary single reference configuration interaction methods Refs 1 and 3 CIS CISD CISDT CISDTQ CISDTQP Cl n full CI multi reference CI approaches Refs 2 and 3 multi reference CC approaches using a state selective ansatz Refs 2 and 3 arbitrary single reference linear response equation of motion EOM CC methods Refs 3 and 5 LR CCSD EOM CCSD LR CCSDT EOM CCSDT LR CCSDTQ EOM CCSDTQ LR CCSDTQP EOM CCSDTQP LR CC n EOM CC n linear response equation of motion MRCC schemes Refs 3 and 5 Available reference states and programs RHF CFOUR and COLUMBUS ROHF standard orbitals CFOUR and COLUMBUS UHF CFOUR MCSCF COLUMBUS Notes 1 In addition to geometries most of the first order properties dipole mo ments quadrupole moments electric field gradients relativistic contri butions etc implemented in CFOUR and COLUMBUS can be calcu lated with MRCC 11 2 Geometry optimizations and first order property calculations can also be pe
12. 10 mrcc In the above script it is supposed that the user has a file named myhosts with the names of the compute nodes and that the user has a temporary directory scr USER on each node The script will execute mrcc on 10 nodes specified in myhosts no program is executed on the submit node 10 The programs of the suite In this section we discuss the major characteristics of the programs of the MRCC package and also provide some information about their use and the corresponding outputs dmrcc Driver for the program system It calls the programs of the suite except build mrcc It is recommended to run always dmrcc but advanced users may run the programs one by one e g for the purpose of debugging See also Sect 9 for further details minp Input reader and analyzer This program reads the input file MINP checks keywords options and dependencies sets default values for keywords integ An open ended atomic orbitals integral code This code reads and an alyzes the molecular geometry reads the basis sets and calculates one and two electron integrals as well as property integrals over Gaussian type atomic orbitals Both the Obara Saika and the Rys quadrature schemes are implemented for the evaluation of two electron integrals In principle integrals over basis functions of arbitrary high angular mo mentum can be evaluated using the Obara Saika algorithm scf Hartree Fock and Kohn Sham SCF code It solves the RHF UHF ROHF
13. KS calculation using local correlation schemes e g local ARPA See the examples below For a correlated calculation with KS orbitals excluding calcu 50 lations with double hybrid functionals the HF energy com puted with KS orbitals is used as reference energy 6 For the B2ZPLYP B2GPPLYP DSDPBEP86 and dRPA75 functionals as well as for user defined double hybrid func tionals including MP2 SCS MP2 dRPA etc correlation calc is automatically set to MP2 dRPA etc Note that you can accelerate the MP2 dRPA part of a double hybrid DFT calculation for large molecules using local correlation approaches For the built in double hybrid functionals just add the L prefix while for the user defined functionals set localcc on See the examples below 7 The DSDPBEP86 functional uses special parameters for the calculation of the D3 correction which are read by the DFT D3 program from the dftd3par HOST file located in your home directory This file will be created by the program but you must be sure that the program is able to access your home directory Also note that if you already have this file in your home it will be overwritten so please do not forget to save it before executing MRCC Examples 1 To perform a DFT calculation with the B3LYP functional give dft B3LYP or calc B3LYP 2 The B3LYP functional can also be defined using the user op tion as calc scf dft user 5 0 08 LDA 0 72 B88 0 20 HFx 0 19
14. Lett 77 3865 1996 J P Perdew J A Chevary S H Vosko K A Jackson M R Ped erson D J Singha and C Fiolhais Atoms molecules solids and surfaces Applications of the generalized gradient approximation for exchange and correlation Phys Rev B 46 6671 1992 C Lee W Yang and R G Parr Development of the Colle Salvetti correlation energy formula into a functional of the electron density Phys Rev B 37 785 1988 S H Vosko L Wilk and M Nusair Accurate spin dependent electron liquid correlation energies for local spin density calculations A critical analysis Can J Phys 58 1200 1980 J P Perdew and Y Wang Accurate and simple analytic represen tation of the electron gas correlation energy Phys Rev B 45 13244 1992 John P Perdew Density functional approximation for the correlation energy of the inhomogeneous electron gas Phys Rev B 33 8822 1986 Axel D Becke A new mixing of Hartree Fock and local density functional theories J Chem Phys 98 1372 1993 Axel D Becke Density functional thermochemistry II The role of exact exchange J Chem Phys 98 5648 1993 P J Stephens F J Devlin and M J Frisch C F Chabalowski Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields J Phys Chem 98 11623 1994 Axel D Becke Density functional thermochemistry V Systematic op timization of exch
15. P Das and Lucas Visscher Relativistic general order coupled cluster method for high precision calculations Application to the Al atomic clock Phys Rev A 83 030503 R 2011 Zoltan Rolik and Mihaly Kallay Cost reduction of high order coupled cluster methods via active space and orbital transformation techniques J Chem Phys 134 124111 2011 Zoltan Rolik and Mihaly K llay A general order local coupled cluster method based on the cluster in molecule approach J Chem Phys 135 104111 2011 Sanghamitra Das Mih ly K llay and Debashis Mukherjee Supe rior performance of Mukherjee s state specific multi reference coupled cluster theory at the singles and doubles truncation scheme with local ized active orbitals Chem Phys 392 83 2012 Zolt n Rolik L r nt Szegedy Istv n Ladj nszki Bence Lad czki and Mih ly K llay An efficient linear scaling CCSD T method based on local natural orbitals J Chem Phys 139 094105 2013 Zolt n Rolik and Mih ly K llay A quasiparticle based multireference coupled cluster method J Chem Phys 141 134112 2014 Mih ly K llay A systematic way for the cost reduction of density fitting methods J Chem Phys 141 244113 2014 D vid Mester J zsef Csontos and Mih ly K llay Unconventional bond functions for quantum chemical calculations Theor Chem Acc 134 74 2015 Mih ly K llay Linear scaling implementation of the direct random phase a
16. P86 PBEc PW91c B3LYP3 B97 HCTH120 HCTH147 and HCTH407 functionals the HF exchange denoted by HFx as well as the MP2 dRPA and SOSEX correlation denoted respectively by MP2 dRPA and SOSEX can be defined In the case of the latter correlation corrections the antiparallel and parallel spin components of the correlation energy can be separately scaled Then the s and t postfix should be added to the above labels respec tively E g instead of the MP2 label the MP2s and MP2t labels should be used Note that for B97 the HF exchange will be neglected The combination should be specified in the subse quent lines as follows see also the examples below lt number of entries gt lt coefficient 1 gt lt functional name 1 gt lt coefficient 2 gt lt functional name 2 gt lt coefficient 3 gt lt functional name 3 gt userd User defined functional but different functionals are used for the calculation of the density and the energy It is useful for defining special double hybrid functionals The combina tion should be specified in the subsequent lines as follows see also the examples below 49 Default Notes 1 lt number of entries for density gt lt coefficient 1 gt lt functional name 1 gt lt coefficient 2 gt lt functional name 2 gt lt coefficient 3 gt lt functional name 3 gt lt number of entries for energy gt lt coefficient 1 gt lt functional name 1 gt lt coefficient 2 gt lt
17. RKS or UKS equations using either conventional or direct SCF techniques It also performs the semi canonicalization of orbitals if requested for ROHF wave functions 26 orbloc Orbital localization program It performs the localization of MOs using the Cholesky Boys or generalized Boys procedures It also con structs the domains for local correlation calculations drpa An efficient three index integral transformation density fitted MP2 RPA dRPA SOSEX and RPAX2 code The dRPA method is imple mented using the modified algorithm of Ref 31 which scales as the fourth power of the system size see Ref 24 mulli Domain construction for local correlation calculations It assigns the localized MOs LMOs to atoms using the Boughton Pulay method and for each occupied LMO it constructs a domain of occupied and virtual LMOs on the basis of their spatial distance Projected atomic orbitals PAOs are also constructed if requested ovirt Integral transformation and orbital optimization code This program performs the four index integral transformations of AO integral for cor relation calculations It also carries out the construction of optimized virtual orbitals OVOs MP2 natural orbitals and local natural or bitals in the case local CC calculations ccsd A very fast hand coded MO integral based CCSD and CCSD T code The code has been optimized for local CC calculations but can also be used for conventional CC calculations Curr
18. canonical HF orbitals is saved under the name MOLDEN CAN and the canonical MOs are 90 replaced by the localized ones in the MOLDEN file You can use both files to visualize the MOs that you are interested in Please note that MOLDEN can also be used for the generation of input molecular structures in Z matrix or xyz format see the description of the geom keyword on page 60 14 2 xyz file Cartesian coordinates are also written to file COORD xyz in xyz XMol format which can be processed by many molecular visualization programs This interface can also be controlled by the molden keyword see page 69 for the description of the keyword 15 Acknowledgments The authors of the MRCC program are very grateful to e Professor Jiirgen Gauss Universitat Mainz for continuous support and discussions development and maintenance of the CFOUR interface and for the permission to use the basis set format of CFOUR e Dr Michael Harding TU Karlsruhe for continuous support and for his help in the parallelization of the code e Professor Hans Joachim Werner Universitat Stuttgart Professor Pe ter J Knowles Cardiff University and Dr Andy May Cardiff Uni versity for the development and maintenance of the MOLPRO interface and many useful suggestions e Professor P ter G Szalay E tv s University Budapest for his con tinuous support and for the development of the COLUMBUS interface e Professor Lucas Visscher VU Universi
19. details and copy the MINP file to the MTEST directory renaming it as MINP_ lt job_name gt Then the new job will be automatically executed when the mtest script is invoked next time 9 Running MRCC Please be sure that the directory where the MRCC executables are located are included in your PATH environmental variable Note that the package in cludes several executables and all of them must be copied to the aforemen tioned directory not only the driver program dmrcc Please also check your LD_LIBRARY_PATH environmental variable which must include the directories 24 containing the libraries linked with the program This variable is usually set before the installation but you should not change by removing the names of the corresponding directories Please do not forget to copy the input file MINP see Sect 11 to the directory where the program is invoked 9 1 Running MRCC in serial mode To run MRCC in serial the user must invoke the driver of the package by simply typing dmrcc on a Unix console To redirect the input one should execute dmrcc as dmrcc gt out where out is the output file 9 2 Running MRCC in parallel using OpenMP Several executables of the package can be run in OpenMP parallel mode hence it is recommended to use this option on multiprocessor machines The pre built binaries available at the MRCC homepage support OpenMP parallel execution If you prefer source code installation to compile the pro gram fo
20. functional name 2 gt lt coefficient 3 gt lt functional name 8 gt See option user for the possible values of lt functional name n gt and lt functional name n gt Note that currently the weight of the HF exchange HFx if any must be identical for the density and the energy and consequently does not need to be specified again in the second block dft off The functionals implemented in MRCC were obtained from the Density Functional Repository 91 92 Empirical dispersion corrections can be calculated for partic ular functionals and also for the HF energy using the DFT D3 approach of Grimme and co workers 93 94 by attach ing the D3 postfix to the corresponding options BLYP D3 BHLYP D3 B3LYP D3 B3PW91 D3 BP86 D3 PBE D3 PBEO D3 HCTH120 D3 B2PLYP D3 B2GPPLYP D3 DSDPBEP86 D3 HF D3 See also the description of keyword edisp For a simple DFT calculation i e without subsequent corre lation calculations the value of keyword calc can be SCF HF RHF or UHF Note that you do not need to set its value since it is set to SCF by default Alternatively you can select the DFT functional using keyword calc and in this case you do not have to set keyword dft see the description of calc For a correlated calculation with KS orbitals you should select the functional with this keyword and the value of keyword calc must be set to the desired correlation method Note that you can also accelerate the post
21. in accurate eval uation of roots and weights of Rys polynomials J Chem Phys 131 064107 2009 112 J A Nelder and R Mead A simplex method for function minimiza tion Comput J 7 308 1965 113 J M Foster and S F Boys Canonical configurational interaction procedure Rev Mod Phys 32 300 1960 102 114 J Pipek and P Mezey A fast intrinsic localization procedure applica ble for ab initio and semiempirical linear combination of atomic orbital wave functions J Chem Phys 90 4916 1989 115 i Gerald Knizia Intrinsic atomic orbitals An unbiased bridge between quantum theory and chemical concepts J Chem Theor Comp 9 4834 2013 116 Ss Francesco Aquilante Thomas Bondo Pedersen Alfredo M Sanchez de Meras and Henrik Koch Fast noniterative orbital localization for large molecules J Chem Phys 125 174101 2006 117 ss Pavel Neogrady Michal Pito k and Miroslav Urban Optimized vir tual orbitals for correlated calculations an alternative approach Mol Phys 103 2141 2005 118 R S Mulliken Electronic population analysis on LCAO MO molecular wave functions I J Chem Phys 23 1833 1955 119 I Mayer Charge bond order and valence in the ab initio SCF theory Chem Phys Lett 97 270 1983 120 Georg Hetzer Peter Pulay and Hans Joachim Werner Multipole ap proximation of distant pair energies in local MP2 calculations Chem Phys Lett
22. integrals 2 For DF methods option herm is not available 2 For DF methods if intalg os or intalg auto the Coulomb integrals are evaluated by the algorithm of Ahlrichs 105 which only enables the use of spherical harmonic Gaussians Consequently Cartesian Gaussians are only available with intalg rys in DF calculations see the description of key word gauss 4 The derivative integrals are evaluated by the solid harmonic Hermite scheme even if another option is used for the undif ferentiated integrals Consequently differentiated integrals and thus energy derivatives cannot be evaluated with Carte sian Gaussian basis sets Default intalg auto 65 Example to use the Obara Saika scheme for all angular momenta add intalg os itol Threshold for integral calculation Integrals less than 107 E will be neglected Options lt any integer gt Default itol max 10 scftol 4 scfdtol Example for an accuracy of 10715 E one must give itol 15 lcorthr Controls the accuracy of local correlation calculations by setting the relevant thresholds bpcompo bpcompv lnoepso lnoepsv naf_cor osveps spairtol see also Ref 26 for details Options Loose Relatively loose thresholds will be used Maximum aver age errors of 2 kcal mol 2 kJ mol for energy differences are expected Tight Tight thresholds will be used Maximum average errors of 1 kcal mol 1 kJ mol for energy differences are expected O The truncation th
23. keyword mem see page 69 mrcc Automated string based many body code It performs the single point energy as well as derivative calculations for general CC LR CC and CI methods Abelian spatial symmetry is utilized and a partial spin adaptation is also available for closed shell systems build mrcc Installation script of the suite See Sect 7 for a detailed de scription 11 Input files The input file of the MRCC package is the MINP file This file must be placed in the directory where the program is invoked In addition if you use your own basis sets see keyword basis angular integration grids for DFT calculations see keyword agrid or Laplace quadrature for Laplace transform calculations see keyword dendec you may also need the GENBAS file and then it must be also copied to the above directory In general the execution of MRCC is controlled by keywords The list of the keywords is presented in Sect 12 The keywords and the corresponding options must be given in the MINP file as lt keyword gt lt option gt You can add only one keyword per line but there are keywords which require multiple line input and the corresponding variables must be specified in the subsequent lines as lt keyword gt lt option gt lt input record 1 gt lt input record 2 gt lt input record n gt 28 The input is not case sensitive Any number of lines can be left blank be tween two items however if a keyword requires mu
24. numbering if irreps Default by default the the state symmetry is determined on the basis of the occupation of the HF determinant Examples 1 for the second irrep of the point group type symm 2 2 for the By irrep of the D2 point group type symm Blu talg Specifies the algorithm for the calculation of the T correction in the case of the CCSD T method Options occ The outmost loops run over the occupied indices of the triples amplitudes virt The outmost loops run over the virtual indices of the triples amplitudes Default talg occ for conventional CCSD T calculations talg virt for local CCSD T Notes 1 For algorithmic reasons in the case of local CCSD T calcula tions talg virt is the only option and it is not possible to use talg occ 2 For conventional CCSD T calculations talg occ is recom mended since the algorithm is somewhat faster than the other one In turn its memory requirement is higher The program checks automatically if the available memory is sufficient for the first algorithm i e talg occ If this is not the case talg will be automatically set to virt 86 Example to change the default for a conventional CCSD T calcula tion set talg virt test A keyword for testing MRCC If an energy value is specified using this keyword it will be compared to the energy calculated last time e g the CCSD T energy and not the CCSD or HF energy if calc CCSD T in the Mrcc run An error massage wi
25. of the program Note that you will find several program versions on the homepage Unless there are overriding reasons not to do so please always download the last version To unpack the file type tar xvzf mrcc tar gz To install MRCC run the build mrcc script as build mrcc lt compiler gt i lt option1 gt p lt option2 gt g d lt folder gt lt compiler gt specifies the compiler to be used Currently the supported com piler systems are 21 Intel Intel compiler GNU GNU compiler g77 or gfortran PGF Portland Group Fortran compiler G95 G95 Fortran 95 compiler PATH Pathscale compiler HP HP Fortran Compiler DEC Compaq Fortran Compiler DEC machines XLF XL Fortran Compiler IBM machines Solaris10 Sun Solaris10 and Studiol0 Fortran Compiler AMD64 If the build mrcc script is invoked without specifying the lt compiler gt vari able a help message is displayed Optional arguments i specifies if 32 or 64 bit integer variables are used Accordingly lt option1 gt can take the value of 32 or 64 Default 64 for 64 bit machines 32 otherwise p generates parallel code using massage passing interface MPI or OpenMP technologies Accordingly lt option2 gt can take the MPI or OMP values MPI parallelization is available with the PGF Intel GNU and So laris10 compilers while OpenMP parallelization has been tested with PGF Intel GNU and HP compilers Please note that currently the two parall
26. open shell orbitals with al pha electron 1 for open shell orbitals with beta electron 0 otherwise In the case of relativistic calculations type 1 for each occupied spinor 0 otherwise 1 Frozen orbitals must not be considered here in any case 2 If the MO integrals are taken over from another program the numbering of orbitals may be different from that of the parent program Here the order of MOs doubly occupied open shell virtual and in each of this blocks the MOs are reordered according to the orbital energies natural orbital occupations in the case of MCSCF orbitals 76 3 If the MO integrals are taken over from another program and this line is omitted the program will fill the orbitals with electrons from the bottom automatically In this manner we do not need this line for closed shells or a doublet ref det but e g for high spin states the Fermi vacuum must be defined here 4 For relativistic calculations DIRAC interface this line is al ways required The spinors are symmetry blocked accord ing to the Fermion irreps of the corresponding double group Complex conjugate irreps follow each other Within each ir rep the spinors are numbered according to orbital energies Please note that this line is automatically printed by the dirac mointegral_ export program and you do not have to do it by hand However for technical reasons always a closed shell occupation is generated and you may need to remove or add
27. orbital integral code integ Gyula Samu density fitting integrals integ In addition Mat Farkas Klara Petrov David Mester P ter Nagy Bence Kornis Levente Dojcs k Huliyar S Nataraj and Sanghamitra Das have also contributed to the development of the MRCC code 4 Citation If results obtained with the MRCC code are published an appropriate citation would be MRCC a quantum chemical program suite written by M K llay Z Ro lik J Csontos I Ladj nszki L Szegedy B Lad czki and G Samu See also Z Rolik L Szegedy I Ladj nszki B Lad czki and M K llay J Chem Phys 139 094105 2013 as well as www mrcc hu In addition credit must be given to the corresponding papers which describe the underlying methodological developments The corresponding references are given in Sect 6 of the manual If MRCC is used combined with other program systems the users are also requested to include appropriate citations to those packages as required by their authors 5 Interfaces MRCC can be used as a standalone code but interfaces have been devel oped to the CFOUR COLUMBUS DIRAC MOLPRO ORCA and PsI quantum chemistry packages MRCC in standalone mode can currently be used for single point energy calculations with the standard nonrelativistic Hamilto nian while the interfaces enable the calculation of molecular properties as 5 well as several other features such as the use of relativistic Hamilto
28. scfdamp 0 8 scfdiis Specifies if DIIS convergence acceleration is used in the SCF calcu lations Options on or off Default scfdiis on 81 Example to turn off DIIS convergence accelerator add scfdiis off scfdiis_end Specifies the last iteration step in which the DIIS convergence acceleration is applied Options lt any positive integer gt Default scfdiis_end scfmaxit that is the DIIS procedure is not turned off Example to turn off the DIIS convergence accelerator after iteration step 20 give scfdiis_end 20 scfdiis_start Specifies the first iteration step in which the DIIS conver gence acceleration is applied Options lt any positive integer gt Default scfdiis_start 1 that is the DIIS procedure is active from the first iteration Example to turn on the DIIS convergence accelerator in iteration step 5 give scfdiis_start 5 scfdiis_step Specifies the frequency of DIIS extrapolations The extrapo lation will be carried out in every scfdiis_step th iteration cycle Options lt any positive integer gt Default scfdiis_step 1 that is the DIIS extrapolation is performed in each iteration step Example to carry out DIIS extrapolation only in every second itera tion step give scfdiis_step 2 scfdtol Convergence threshold for the density matrix in SCF calculations The square of the Frobenius norm of the difference density will be smaller than 107 lt 74t Options lt any integer gt Default
29. some electrons Default refdet none that is the reference determinant is identical to the HF determinant Examples 1 We have 20 correlated orbitals 10 electrons and we are inter ested in a high spin triplet state Suppose that orbitals 1 to 4 are doubly occupied while orbitals 5 and 6 are singly occu pied by alpha electrons Using the serialno option the input should include the following four lines note the blank line at the end refdet serialno 1 4 5 6 2 The same using the vector option refdet vector 22221100000000000000 3 We perform a relativistic calculation for the Be atom with 20 correlated spinors We have 6 6 4 and 4 spinors in the four Fermion irreps Ey 2g E_1 2g E1 2u and E_j 2 of the C3 double group respectively and two occupied spinors in both of the gerade irreps Thus using the vector option the occupation vector should be given as refdet vector 11000011000000000000 TT 4 The same using the serialno option note the blank lines refdet serialno 1 2 7 8 rest Use this keyword to restart canonical i e not local CI and CC cal culations from previously calculated wave function parameters cluster amplitudes CI coefficients A amplitudes etc if ccprog mrcc Options 1 The program restarts from the previously calculated parame ters 2 The program executes automatically the lower level calculations of the same type consecutively e g CCSD CCSDT and CCSDTQ if CCSDTQ is request
30. states the multiplicity will be arbitrary only Ms is conserved For closed shell reference determinants the multiplicity strictly speaking the parity of S can be controlled by keywords nsing and ntrip see below 69 Options lt any positive integer gt Default for atoms the corresponding experimental multiplicity is set for molecules mult 1 singlet for an even number of electrons mult 2 doublet otherwise Example for a triplet state one should give mult 3 nacto Number of active occupied spinorbitals By default nacto pieces of spinorbitals under the Fermi level are supposed to be active This can be overwritten using keyword active which enables the user to select the active orbitals manually see the description of keyword active In a MRCI CC calculation a complete active space CAS is supposed defined by keywords nacto and nactv or alternatively by active and up to n fold excitations from the reference determinants of this space are included in the excitation manifold where n is determined by keyword calc 2 for CCSD 3 for CCSDT See Ref 2 for more details See also keywords nactv maxex and maxact Options lt any positive integer gt or 0 Default nacto 0 Example for two active occupied spin orbitals give nacto 2 nactv Number of active virtual spinorbitals By default nactv pieces of spinorbitals above the Fermi level are supposed to be active which can be overwritten using keyword active For a detaile
31. that atom in the order the atoms appear at the specification of the geometry Notes 1 By default the following ECP are available for elements Na to Rn in MRCC the LANL2DZ ECP s of Hay and Wadt 55 57 LANL2DZ ECP 10 LANL2DZ ECP 18 LANL2DZ ECP 28 LANL2DZ ECP 36 LANL2DZ ECP 46 LANL2DZ ECP 60 LANL2DZ ECP 68 LANL2DZ ECP 78 the Stuttgart K6oln ECPs for the def2 basis sets 97 99 def2 ECP 28 def2 ECP 46 def2 ECP 60 the Stuttgart Koln multiconfiguration Dirac Hartree Fock adjusted ECPs 59 61 62 100 103 MCDHF ECP 10 MCDHEF ECP 28 MCDHF ECP 60 59 Please note that some of the above ECPs are not available for all elements 2 If you need ECPs other than the default ones you can e g download them from the EMSL Basis Set Exchange 28 30 Please choose format AcesII when downloading the ECPs 3 If you use your own ECPs these must be copied to the end of the corresponding file in the BASIS directory Alternatively you can also create a file called GENBAS in the directory where MRCC is executed and then you should copy your ECPs to that file 4 The labels of the ECPs must be identical to those used in the BASIS files or the GENBAS file For the default ECPs just type the name of the ECPs as given above e g LANL2DZ ECP 10 def2 ECP 28 etc If you employ non default ECPs you can use any label Default ecp auto Examples 1 To use the MCDHF ECP 10 pseudopotential for all atom
32. this keyword By default the reference determi nant is identical to the HF determinant but sometimes it is necessary to change this Options none The reference determinant is identical to the HF determi nant serialno Using this option one can define the occupation of the correlated orbitals in the reference determinant specifying their serial numbers This option requires three more lines In the first line the serial numbers of the doubly occupied orbitals must be given while in the second and third lines those or bitals should be specified which are singly occupied by an al pha or a beta electron respectively For the format of these lines see the description of the serialno option of the active keyword For relativistic calculations the occupation of the spinors i e not that of the Kramers pairs should be given For technical reasons all electrons are treated as alpha elec trons and the serial numbers of the occupied spinors must be given in the second line the first and third lines must be left blank vector Using this option one can set the occupation numbers for Notes each correlated orbital In the subsequent line an integer vec tor should be supplied with as many elements as the number of correlated orbitals correlated spinors for relativistic calcu lations not Kramers pairs The integers must be separated by spaces In the case of non relativistic calculations type 2 for doubly occupied orbitals 1 for
33. to the program by setting the mem keyword 12 Keywords In this section the keywords of the MRCC input file are listed in alpha betical order active The active orbitals for multi reference active space CI CC calcu lations can be specified using this keyword Note that this keyword overwrites the effect of keywords nacto and nactv Options none All orbitals are inactive i e single reference calculation serialno Using this option one can select the active orbitals spec ifying their serial numbers The latter should be given in the subsequent line as lt ny gt lt ng gt lt Nk gt lt N gt a where n s are the serial numbers of the correlated orbitals 29 Serial numbers separated by dash mean that lt nz gt through lt n gt are active Note that the numbering of the orbitals is relative to the first correlated orbital that is frozen orbitals are excluded vector Using this option one can set the active inactive feature for each correlated orbital In the subsequent line an integer vector should be supplied with as many elements as the num ber of correlated orbitals The integers must be separated by spaces Type 1 for active orbitals and 0 for inactive ones Default active none Examples 1 We have 20 correlated orbitals Orbitals 1 4 5 6 9 10 11 12 and 14 are active Using the serialno option the input should include the following two lines active serialno 1 4 6 9 12 14 2 Th
34. 000000 0000000 0000000 O OO OR OM OO On One N 8682724 0689991 3164240 7443083 0000000 O OoOo actual lines 457 36952 0000000 0000000 0000000 0000000 0000000 0000000 1193324 1608542 1434564 0000000 O H OO GOG OOO O O 1 8812885 0000000 0000000 0000000 0000000 h O O O o0Oo00000O0O0OO 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 description Carbon atom basis name lt comment line gt blank line lt number of angular momentum types 0s lp lt number of contracted functions lt number of primitives blank line gt exponents for s functions gt blank line lt contraction coefficients for s functions gt blank line exponents for p functions gt blank line contraction coefficients for p functions In a basis set optimization process you need two files in the working directory the appropriate MINP file with the basopt keyword set and a user supplied GENBAS file that contains the basis set information in the above format You do not need to write the GENBAS file from scratch you can use the files in the BASIS directory of MRCC to generate one or you can use the Environmental Molecular Sciences Laboratory EMSL Basis Set Library 28 30 to download a basis in the appropriate form AcesII format Note that you can optimize several basis sets at a time all
35. 1 x y Ry Ry Yz z Character table for the C2 point group E Co Oh Ov Ay 1 1 1 1 z 2 y 2 B 1 1 1 1 y Re yz Bo 1 1 1 1 x Ry z A 1 1 1 1 Rz y 89 Character table for the Co point group E Caz i oh Ag 1 1 1 1 Rega 2 y Bg 1 1 1 1 Re Ry zz yz A 1 St tlle Bu D a 28 1 jay Character table for the D point group E C z Coty Ca z A 1 1 1 1 ete B 1 1 1 1 z Rz y B 1 1 1 1 y Ry zz Bs 1 1 1 Le lg Ra TZ Character table for the D point group E C2 z C2 y C2 x a Try Oxz Oyz A 1 1 1 1 1 1 1 Ll ay 2 Big 1 C 2h f 1 t Sh 3R ay Bag 1 1 1 1 1 1 1 1 R zz Bag 1 1 1 1 t oN al 1 Re yz Ay 1 1 1 1 1 1 1 1 Biu 1 1 1 1 1 1 1 ez Bo 1 1 1 1 1 1 1 lly Bau 1 1 1 1 1 1 1 zxz 14 Interface to molecular visualization soft ware 14 1 MOLDEN For the visualization of molecular structures molecular orbitals and elec tron densities an interface has been developed to the MOLDEN program 122 Cartesian coordinates basis function information and MO coefficients are saved to file MOLDEN using MOLDEN format After the termination of MRCC MOLDEN should be started by typing molden MOLDEN The MOLDEN inter face can be controlled by the molden keyword see page 69 for the description of the keyword If the MOs are localized the MOLDEN file containing the
36. 290 143 1998 121 4 Christoph Riplinger and Frank Neese An efficient and near linear scaling pair natural orbital based local coupled cluster method J Chem Phys 138 034106 2013 122 pasate Gijs Schaftenaar and Jan H Noordik Molden a pre and post processing program for molecular and electronic structures J Comput Aided Mol Design 14 123 2000 103
37. 8 0 The excitation manifold is not truncated lt any positive integer gt The excitation manifold is truncated at n fold excitations see above Default maxex 0 Example to truncate the excitation manifold at triple excitations set maxex 3 mem Specifies the core memory used Options lt any positive integer gt MB The amount of memory to allocate is specified in megabytes lt any positive integer gt GB The amount of memory to allocate is specified in gigabytes Default mem 256MB Example to allocate 8 GB core memory the user should set mem 8GB molden Specifies whether input file for the MOLDEN program and an xyz file containing the Cartesian coordinates are written see also Sect 14 Options on Cartesian coordinates basis set information and MO coeff cients are saved to file MOLDEN This file can be opened by MOLDEN and used to visualize the structure of the molecule and the MOs In addition Cartesian coordinates are also written to file COORD xyz in xyz XMol format which can be processed by many molecular visualization programs off The construction of the MOLDEN input and the COORD xyz file is turned off Default molden on Example if you do not need MOLDEN input and the COORD xyz file add molden of f mult Spin multiplicity 2S 1 of the Hartree Fock or Kohn Sham wave function If a CI or CC calculation is also performed the same mul tiplicity is supposed for the ground state wave function For excited
38. CC n na a sS 9 CCSDT 1a CCSDTQ 1a CCSDTQP la CC n 1a e CCSDT 1b CCSDTQ 1b CCSDTQP 1b CC n 1b e CC2 CC3 CC4 CCS CCn e CCSDT 3 CCSDTQ 3 CCSDTQP 3 CC n 3 8 multi reference CI approaches Ref 2 9 multi reference CC approaches using a state selective ansatz Ref 2 10 arbitrary single reference linear response equation of motion EOM CC methods Ref 5 LR CCSD EOM CCSD LR CCSDT EOM CCSDT LR CCSDTQ EOM CCSDTQ LR CCSDTQP EOM CC SDTQP LR CC n EOM CC n 11 linear response equation of motion MRCC schemes Ref 5 Available reference states and programs RKS UKS MRCC RHF MRCC CFOUR COLUMBUS and MOLPRO ROHF standard orbitals MRCC CFOUR COLUMBUS and MOLPRO ROHF semi canonical orbitals MRCC and CFOUR UHF MRCC CFOUR and MOLPRO MCSCF COLUMBUS and MOLPRO Notes 1 Single point calculations are also possible with several types of rela tivistic Hamiltonians and reference functions see Sect 6 7 for more details 2 Reduced scaling approaches for the above CC and CI methods are avail able Ref 19 See Sect 6 8 for details 3 Local CC approaches for arbitrary single reference and perturbative coupled cluster models local MP2 approaches and local dRPA are available Refs 20 22 26 and 27 See Sect 6 8 for details 4 CCn calculations with ROHF orbitals are not possible for theoretical reasons see Ref 13 for explanation
39. J Chem Phys 96 6796 1992 David E Woon and Thom H Dunning Jr Gaussian basis sets for use in correlated molecular calculations III The atoms aluminum through argon J Chem Phys 98 1358 1993 David E Woon and Thom H Dunning Jr Gaussian basis sets for use in correlated molecular calculations V Core valence basis sets for boron through neon J Chem Phys 103 4572 1995 Kirk A Peterson and Thom H Dunning Jr Accurate correlation con sistent basis sets for molecular corevalence correlation effects The sec ond row atoms Al Ar and the first row atoms B Ne revisited J Chem Phys 117 10548 2002 95 40 41 42 43 44 45 46 47 48 49 P C Hariharan and J A Pople The influence of polarization functions on molecular orbital hydrogenation energies Theor Chim Acta 28 213 1973 R Krishnan J S Binkley R Seeger and J A Pople Self consistent molecular orbital methods XX A basis set for correlated wave func tions J Chem Phys 72 650 1980 W J Hehre R Ditchfield and J A Pople Self consistent molecular orbital methods XII Further extensions of Gaussian type basis sets for use in molecular orbital studies of organic molecules J Chem Phys 56 2257 1972 J D Dill and J A Pople Self consistent molecular orbital methods XV Extended Gaussian type basis sets for lithium beryllium and boron J Chem Phys 62 2921 1975 M
40. KS UKS local density approximation LDA general ized gradient approximation GGA hybrid and double hybrid func tionals for the available functionals see the description of keyword dft dispersion corrections density fitted resolution of identity MP2 spin component scaled MP2 SCS MP2 and scaled opposite spin MP2 SOS MP2 currently only for RHF and UHF references Ref 24 density fitted resolution of identity random phase approximation RPA also known as ring CCD rCCD direct RPA dRPA also known as direct ring CCD drCCD second order screened exchange SOSEX and approximate RPA with exchange RPAX2 currently the dRPA and SOSEX methods are available for RHF RKS and UHF UKS ref erences while the RPA method is only implemented for RHF RKS Refs 24 and 26 arbitrary single reference coupled cluster methods Ref 1 CCSD CCSDT CCSDTQ CCSDTQP CC n arbitrary single reference configuration interaction methods Ref 1 CIS CISD CISDT CISDTQ CISDTQP Cl n full CI arbitrary perturbative coupled cluster models Refs 7 6 and 13 e CCSD T CCSDT Q CCSDTQIP CC n 1 fn e CCSDT Q A CCSDTQIP A CC n 1 n A e CCSDT Q B CCSDTQ P B CC n 1 n B e CCSD T CCSDT Q CCSDTQ P CC n 1 n e CCSDT Q A CCSDTQ P A CC n 1 n A e CCSDT Q B CCSDTQ P B CC n 1 n B e CCSD T CCSDT Q CCSDTQ P
41. Manual for the MRCC Program System Release date September 7 2015 Wee ec ae 1782 Department of Physical Chemistry and Materials Science Budapest University of Technology and Economics http www mrcc hu Contents 1 Introduction 4 2 How to read this manual 4 3 Authors 4 4 Citation 5 5 Interfaces 5 DE CCFOUR Taan et Be Nd eh ee Oe oe Ae aly 6 5 2 COLUMBUS a Me oats ga taunt Bene de sah peace hace ite he ag 6 9 9 DIRAG e at fom ae Big edt he my Bee od eRe a 7 Dae MOLPRO arne ark Soe Kee a a e ina ar GF Bh aa 8 6 Features 8 6 1 Single point energy calculations o 0a ooa a 9 6 2 Geometry optimizations and first order properties 11 6 3 Harmonic frequencies and second order properties 12 6 4 Higher order properties oao a a 13 6 5 Diagonal Born Oppenheimer corrections 14 6 6 Electronically excited states 1 0 020 000 0000 2s 14 6 7 Relativistic calculations 5 2 Gt Gogo e Bes te e amp P Goi 16 6 8 Reduced scaling and local correlation calculations 16 6 9 Optimization of basis sets 2 2 7 6 8 e once Gia ha Dy aed 17 7 Installation 20 7 1 Installation of pre compiled binaries 20 7 2 Installation from source code ooa a a a GS Se 21 7 3 Installation under Windows oaoa a 23 8 Testing MRCC 24 9 Running MRCC 24 9 1 Running MRCC in serial mode 0 25 9 2 Running MRCC in parallel using OpenMP 25 9 3
42. Q 3 CCSDTQP 3 CC lt n gt 3 The corresponding iterative approximate single reference CC calculation see Ref 7 CCSDT Q A CCSDTQ P A CC lt n 1 gt lt n gt A The corresponding single reference CC calculation with per turbative corrections using ansatz A see Ref 13 CCSDT Q B CCSDTQ P B CC lt n 1 gt lt n gt B The corresponding single reference CC calculation with per turbative corrections using ansatz B see Ref 13 CCSDT Q A CCSDTQ P A CC lt n 1 gt lt n gt A The corresponding single reference CC calculation with per turbative corrections using ansatz A see Ref 13 CCSDT Q B CCSDTQ P B CC lt n 1 gt lt n gt B The corresponding single reference CC calculation with per turbative corrections using ansatz B see Ref 13 CIS CISD CISDT CISDTQ CISDTQP CI lt n gt FCI The corresponding single reference CI calculation if the num ber of active orbitals is zero see Ref 1 the corresponding MRCISD MRCISDT etc calculation otherwise see Ref 2 Notes 1 In the above options n is a positive integer which is the ex citation level of the highest excitation n is supposed to be equal to or greater than 6 since for smaller n s the CC lt n gt and similar options are equivalent to one of the other options e g CC 5 is equivalent to CCSDTQP or CC 3 4 is identi cal with CCSDT Q 2 If more than one root is requested for CC calculations the cor responding line
43. Running MRCC in parallel using MPI 25 10 The programs of the suite 26 11 Input files 28 12 Keywords 13 Symmetry 14 Interface to molecular visualization software TAT INFOLDEN 260 2 e fa aS at AOS te Bk ee ae Ya 14 2 Sey ee 2 dhs a aes ok Bets ok Bo he eth Soak Gt tht 15 Acknowledgments References 29 89 90 90 91 91 92 1 Introduction MRCC is a suite of ab initio and density functional quantum chemistry programs for high accuracy electronic structure calculations developed and maintained by the quantum chemistry research group at the Department of Physical Chemistry and Materials Science TU Budapest Its special feature the use of automated programming tools enabled the development of tensor manipulation routines which are independent of the number of indices of the corresponding tensors thus significantly simplifying the general implementa tion of quantum chemical methods Applying the automated tools of the pro gram several quantum chemistry models and techniques of high complexity have been implemented so far including arbitrary single reference coupled cluster CC and configuration interaction CI methods multi reference CC approaches CC and CI energy derivatives and response functions arbitrary perturbative CC approaches Many features of the package are also available with relativistic Hamiltonians allowing for accurate calculations on heavy element systems The developed cost reduction tech
44. Scaled opposite spin second order Mgller Plesset SOS MP2 calculation 65 using an N scaling algorithm based on the Cholesky decomposition Laplace transform of energy denom inators in practice one dRPA iteration is performed see be low Note that it is only possible with the density fitting resolution of identity approximation and by default a DF SOS MP2 RI SOS MP2 calculation is performed that is options SOS MP2 DF SOS MP2 and RI SOS MP2 are syn onyms dRPA Direct random phase approximation dRPA calculation see Eqs 7 and 8 in Ref 66 Note that dRPA calculations are only possible with the density fitting resolution of identity approximation and by default a DF dRPA RI dRPA calculation is performed that is options dRPA DF dRPA and RI dRPA are synonyms RPA Random phase approximation RPA calculation see Eqs 10 and 13 in Ref 66 where it is referred to as RPAx SO2 Note that RPA calculations are only possible with the density fitting resolution of identity approximation and by default 37 a DF RPA RI RPA calculation is performed that is op tions RPA DF RPA and RI RPA are synonyms SOSEX Second order screened exchange SOSEX 67 calculation see Eqs 7 and 9 in Ref 66 the dRPA energy is also computed Note that SOSEX calculations are only possible with the density fitting resolution of identity approximation and by default a DF SOSEX RI SOSEX calculation is perform
45. VWN5 0 81 LYP 3 The B2PLYP double hybrid functional can also be defined us ing the user option as calc scf dft user 4 0 47 B88 0 73 LYP 0 53 HFx 51 0 27 MP2 4 The DSDPBEP86 double hybrid functional can also be defined using the user option as calc SCF dft user 5 0 30 PBEx 0 43 P86 0 70 HFx 0 53 MP2s 25 MP2t 5 SOSEX calculation with Kohn Sham orbitals calculated with the LDA exchange functional calc SOSEX dft LDA 6 To perform a DFT calculation with the B2PLYP double hybrid functional and add the D3 dispersion correction set dft B2PLYP D3 or calc B2PLYP D3 7 B2PLYP calculation the MP2 contribution is evaluated using local MP2 approximation calc LB2PLYP 8 User defined functional different functionals are used for the calculation of the density 0 25 PBEx 0 75 HF exchange PBEc and the energy 0 25 PBEx 0 75 HF exchange MP2 correlation dft userd jo 3 0 75 HFx 0 25 PBEx 1 00 PBEc 2 0 25 PBEx 1 00 MP2 9 The dRPA75 dual hybrid functional can also be defined using the userd option as dft userd 3 0 75 HFx 0 25 PBEx 1 00 PBEc 52 2 0 25 PBEx 1 00 dRPA 10 Local dRPA calculation with Kohn Sham orbitals calculated with the PBE functional calc LdRPA dft PBE diag Type of diagonalization algorithm used for the CI and LR CC calcu lations Options david Standard Davidson diagonalization olsen Another algorithm proposed by Olsen using only two ex pansion
46. a calcula tion performed with the same basis set type scfiguess restart Note that you need the SCFDENSITIES file from the previous run 3 You would like to generate a good initial guess for an aug ce pVTZ SCF calculation First run a calculation with the cc pVTZ basis set cc pVTZ min is also a good option that is your input file should contain the basis cc pVTZ line Then restart your aug cc pVTZ calculation from the cc pVTZ density matrix To that end the MINP file should include the following lines basis aug cc pVTZ 83 scfiguess restart Note that the SCFDENSITIES and the VARS files from the cc pVTZ run must be copied to the directory where the aug cc pVTZ calculation is executed scfmaxit Maximum number of iteration steps in SCF calculations Options lt any positive integer gt Default scfmaxit 50 Example to increase the maximum number of SCF iterations to 200 give scfmaxit 200 scflshift Level shift parameter for the SCF calculation Options off No level shifting lt any real positive number gt The value of the level shift parame ter in a u on Equivalent to scflshift 0 2 Default scflshift off Example To use a level shift value of 0 5 a u give scflshift 0 5 scftol Convergence threshold for the energy in SCF calculations The en ergy will be accurate to 10 8t Ep Options lt any integer gt Default scftol max 8 cctol for property calculations scftol max 6 cctol otherwise Example fo
47. ael Dolg and Hermann Stoll Energy consistent pseudopotentials for group 11 and 12 atoms adjust ment to multi configuration Dirac Hartree Fock data Chem Phys 311 227 2005 104 ae Robert Polly Hans Joachim Werner Frederick R Manby and Peter J Knowles Fast Hartree Fock theory using local fitting approximations Mol Phys 102 2311 2004 Reinhart Ahlrichs Efficient evaluation of three center two electron in tegrals over Gaussian functions Phys Chem Chem Phys 6 5119 2004 105 Maii 106 S Reine E Tellgren and T Helgaker A unified scheme for the cal culation of differentiated and undifferentiated molecular integrals over solid harmonic Gaussians Phys Chem Chem Phys 9 4771 2007 107 Jetze Sikkema Lucas Visscher Trond Saue and Miroslav Iia The molecular mean field approach for correlated relativistic calculations J Chem Phys 131 124116 2009 108 S Obara and A Saika Efficient recursive computation of molecular integrals over Cartesian Gaussian functions J Chem Phys 84 3963 1986 109 R Lindh U Ryu and B Liu The reduced multiplication scheme of the Rys quadrature and new recurrence relations for auxiliary function based two electron integral evaluation J Chem Phys 95 5889 1991 110 Harry F King and Michel Dupuis Numerical integration using Rys polynomials J Comput Phys 21 144 1976 111 N Flocke On the use of shifted Jacobi polynomials
48. ally If the perturbation lowers the symmetry of the system you must change the computational point group keyword cmpgrp or turn off symmetry symm off Default epert none Example to add the y and 2 dipole length operators to the Hamilto nian with coefficients 0 01 and 0 001 a u respectively the input should include the following lines epert 2 y 0 01 z 0 001 eps Threshold for the cumulative populations of MP2 natural orbitals NOs or optimized virtual orbitals OVOs to be used together with keyword ovirt The cumulative population for an MO is calculated by summing up the occupation number of that particular MO and all the MOs with 58 larger occupation numbers and then this number is divided by the number of electrons See Ref 19 for more details Options lt any real number in the 0 1 interval gt Virtual orbitals with cu mulative populations of higher than this number will be dropped Default eps 0 975 Example to set a threshold of 0 95 type eps 0 95 excrad Radius of local fitting domains for the exchange contribution in di rect density fitted HF calculations 104 In direct DF HF calculations in each iteration step the MOs are localized For each localized MO Lowdin atomic charges are computed and all atoms are selected which have a charge greater than 0 05 All further atoms will be included in the fitting domain of the MO whose distance from the aforementioned atoms is smaller than a threshold For fir
49. amples 1 To optimize a basis set variationally set basopt on 2 To optimize a basis set minimizing the difference of the calcu lated energy and 76 287041 E set basopt 76 287041 35 bpcompo Boughton Pulay completeness criterion 63 for occupied orbitals In various local correlation approaches the Boughton Pulay procedure is used to identify the atoms on which an LMO is localized The least squares residual of the parent LMO and the LMO truncated to the selected atoms is required to be less than one minus this criterion Options lt any real number in the 0 1 interval gt This number will be used as the completeness criterion Default bpcompo 0 985 Example to set a threshold of 0 99 type bpcompo 0 99 bpcompv Boughton Pulay completeness criterion 63 for virtual orbitals pro jected atomic orbitals See also keyword bpcompo Options lt any real number in the 0 1 interval gt This number will be used as the completeness criterion Default bpcompv 0 98 Example to set a threshold of 0 95 type bpcompv 0 95 calc Specifies the type of the calculation Options SCF or HF Hartree Fock SCF calculation the type of the Hartree Fock wave function can be controlled by keyword scftype see also keyword scftype RHF UHF ROHF Restricted unrestricted or restricted open shell Hartree Fock SCF calculation respectively The type of the Hartree Fock wave function is also defined at the same time if these opti
50. an Anthony D Dutoi and Martin Head Gordon Scaled opposite spin second order Meller Plesset correlation energy An economical electronic structure method J Chem Phys 121 9793 2004 Julien Toulouse Wuming Zhu Andreas Savin Georg Jansen and J nos G ngy n Closed shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions J Chem Phys 135 084119 2011 Andreas Gr neis Martijn Marsman Judith Harl Laurids Schimka and Georg Kresse Making the random phase approximation to elec tronic correlation accurate J Chem Phys 131 154115 2009 Akio Takatsuka Seiichiro Ten no and Wolfgang Hackbusch Mini max approximation for the decomposition of energy denominators in Laplace transformed M ller Plesset perturbation theories J Chem Phys 129 044112 2008 P A M Dirac Quantum mechanics of many electron systems Proc Roy Soc London A 123 714 1929 J C Slater A simplification of the Hartree Fock method Phys Rev 81 385 1951 98 val 72 73 74 79 80 81 W Kohn and L J Sham Self consistent equations including exchange and correlation effects Phys Rev 140 A1133 1965 Axel D Becke Density functional exchange energy approximation with correct asymptotic behavior Phys Rev A 38 3098 1988 John P Perdew Kieron Burke and Matthias Ernzerhof Generalized gradient approximation made simple Phys Rev
51. ange correlation functionals J Chem Phys 107 8554 1997 99 83 84 85 88 89 piema 90 91 John P Perdew Matthias Ernzerhof and Kieron Burke Rationale for mixing exact exchange with density functional approximations J Chem Phys 105 9982 1996 A Daniel Boese Nikos L Doltsinis Nicholas C Handy and Michiel Sprik New generalized gradient approximation functionals J Chem Phys 112 1670 2000 A Daniel Boese and Nicholas C Handy A new parametriztion of exchange correlation generalized gradient approximation functionals J Chem Phys 114 5497 2001 Stefan Grimme Semiempirical hybrid density functional with pertur bative second order correlation J Chem Phys 124 034108 2006 Amir Karton Alex Tarnopolsky Jean Francois Lamere George C Schatz and Jan M L Martin Highly accurate first principles bench mark data sets for the parametrization and validation of density func tional and other approximate methods Derivation of a robust gen erally applicable double hybrid functional for thermochemistry and thermochemical kinetics J Phys Chem A 112 12868 2008 Sebastian Kozuch and Jan M L Martin DSD PBEP86 in search of the best double hybrid DFT with spin component scaled MP2 and dispersion corrections Phys Chem Chem Phys 13 20104 2011 Sebastian Kozuch and Jan M L Martin Spin component scaled dou ble hybrids An extensive search for the bes
52. any options of the DFTD3 code The options will be passed over to DFTD3 without any consistency check the user should take care of the compatibility of these options with the calculation performed by MRCC Note that the coordinate file name must not be specified here the coordinates will be taken from the COORD xyz file generated by MRCC Note If edisp auto or the D3 postfix is added to the corresponding options the empirical dispersion correction is by default evaluated with the Becke and Johnson BJ damping function 94 57 Default edisp off Example 1 to calculate the D3 dispersion correction including BJ damping to the B3LYP energy give calc B3LYP D3 2 to calculate the D3 dispersion correction to the B3LYP energy without the BJ damping the input should include calc B3LYP edisp func b3 lyp zero epert Use this option to add an external perturbation to the Hamiltonian e g an external electric dipole field Options none No perturbations are added lt any integer in the 0 9 interval gt the number of the operators added to the Hamiltonian The operators and the correspond ing coefficients in a u should be specified in the subsequent lines as follows lt operator 1 gt lt coefficient 1 gt lt operator 2 gt lt coefficient 2 gt lt operator 8 gt lt coefficient 3 gt where the operator can be x y Z XX yy ZZ Xy XZ yZ Note The symmetry of the perturbation is not taken care of automat ic
53. ar response LR CC for excitation energies it is equivalent to equation of motion CC EOM CC calcula tion is performed automatically for the excited states 3 The active orbitals can be selected and the MRCI CC calcu lations can be controlled by keywords nacto nactv active maxex and maxact 4 In principle all methods can be used with the density fit ting resolution of identity approximation It is possible in two ways You can attach the prefix DF or RI to the cor responding option from the above list Then for a HF cal culation keyword dfbasis_scf will be set to auto while for 39 a correlated calculation both dfbasis_scf and dfbasis_cor will be given the value auto Alternatively you can also set the values for keywords dfbasis_scf and dfbasis_cor see their description 5 Local correlation methods can be run if the prefix L is added to the corresponding option of the keyword e g as LCCSD LCCSD T etc This is equivalent to setting localcc on Default calc SCF Examples 1 Torun a CCSD T calculation the user should set calc CCSD T 2 For DF HF RI HF calculations type calc DF HF which is equivalent to the following input calc SCF dfbasis_scf auto 3 For a local CCSD T calculation set calc LCCSD T 4 For a RI MP2 calculation set calc MP2 5 Fora DFT calculation with the B3LYP functional set calc B3LYP 6 Direct RPA calculation with Kohn Sham orbitals calculated with the PBE functional
54. ary basis sets for den sity fitting resolution of the identity SCF calculations 54 cc pV X Z RI JK aug cc pV X Z RI JK X D T Q 5 def2 QZVPP RI JK From Na to La and from Hf to Rn the following basis sets are available which must be used together with the corresponding ECP see also the description of keyword ECP the LANL2DZ basis sets of Hay and Wadt 55 57 the def2 Gaussian basis sets of Weigend and Ahlrichs 49 def2 SV P def2 SVP def2 TZVP def2 TZVPP def2 QZVP def2 QZVPP the correlation consistent PP basis sets of Peterson and co workers 58 62 cc pVXZ PP and aug cc pV X Z PP ASD T Q 5 the auxiliary basis sets of H ttig for correlation calcula tions with the PP basis sets cc pVXZ PP RI and aug cc pVXZ PP RI X D T Q 5 32 Please note that some of the above basis sets are not available for all elements If you need basis sets other than the default ones you can e g download them from the EMSL Basis Set Exchange 28 30 Please choose format AcesII when downloading the basis sets If you use your own basis sets these must be copied to the end of the corresponding file in the BASIS directory Alternatively you can also create a file called GENBAS in the directory where MRCC is executed and then you should copy your basis sets to that file The labels of the basis sets must be identical to those used in the BASIS files or the GENBAS file For the default ba
55. c pVTZ F12 basis set and the aug cc pVTZ RI auxiliary basis the input should only include the following lines basis cc pVTZ F12 calc DF HF dfbasis_scf Specifies whether the density fitting approximation will be used in the HF or KS SCF calculation and also specifies the fitting basis set For the syntax see the description of keyword dfbasis_cor The important difference is that if dfbasis_scf auto the aug cc pVX Z RI JK basis sets will be used as auxiliary basis sets for Dunning s Peterson s and Pople s basis sets while for the def2 basis sets the def2 QZVPP RI JK auxiliary basis is taken Default dfbasis_scf auto if dfbasis_corfnone and for DFT calcu lations dfbasis_scf none otherwise dfintran Specifies the integral transformation program to be used for the transformation of three center Coulomb integrals Options drpa the drpa program will be called ovirt the ovirt program will be called Default dfintran ovirt if ovirtAoff dfintran drpa otherwise Example to use the ovirt code set dfintran ovirt dft Use this keyword to perform DFT calculations and to specify the func tional Options off No DFT calculation is carried out LDA Slater Dirac exchange local density approximation 69 71 B88 Becke s 1988 exchange functional 72 PBEx exchange functional of Perdew Burke and Ernzerhof 73 PW91x Perdew and Wang 1991 exchange functional 74 LYP correlation functional of Lee Yang and Parr 75 47
56. calc dRPA dft PBE ccprog Specifies the CC program to be used Options mrcc The automated string based CC program mrcc will be called ccsd The very fast hand coded CCSD T code ccsd will be ex ecuted currently the spatial symmetry cannot be utilized Note Please note that the mrcc code was optimized for high order CC calculations such as CCSDT Q and CCSDTQ which require different algorithms than CCSD T Thus it is slow for CCSD T but optimal for high order CC models Default ccprog ccsd for CCSD and CCSD T calculations ccprog mrcc otherwise Example to use the mrcc code for CCSD or CCSD T calculations give ccprog mrcc 40 cctol Convergence threshold for the energy in correlated calculations The energy will be accurate to 10 t Ep Options Default lt any integer gt cctol 8 for property calculations cctol 6 otherwise Example for an accuracy of 1078 E one must give cctol 8 charge Charge of the system Options Default lt any integer gt charge 0 Example for the Cl ion one should give charge 1 ciguess The initial guess vectors for CI and LR CC calculations can be specified Options using this keyword on The initial trial vectors are supplied by the user and should off Default be given in the subsequent lines as follows For each state the corresponding initial guess vector must given by the number of non zero elements of the vector on the first line followe
57. coupled cluster wave functions with arbitrary excitations J Chem Phys 113 1359 2000 D Andrae U HauSermann M Dolg H Stoll and H Preu Energy adjusted ab initio pseudopotentials for the second and third row tran sition elements Theor Chem Acc 77 123 1990 M Kaupp P v R Schleyer H Stoll and H Preuss Pseudopotential approaches to Ca Sr and Ba hydrides Why are some alkaline earth MX2 compounds bent J Chem Phys 94 1360 1991 Thierry Leininger Andreas Nicklass Wolfgang K chle Hermann Stoll Michael Dolg and Andreas Bergner The accuracy of the pseudopoten tial approximation non frozen core effects for spectroscopic constants of alkali fluorides XF X K Rb Cs Chem Phys Lett 255 274 1996 Bernhard Metz Marcus Schweizer Hermann Stoll Michael Dolg and Wenjian Liu A small core multiconfiguration Dirac Hartree Fock adjusted pseudopotential for Tl application to TIX X F Cl Br I Theor Chem Acc 104 22 2000 Bernhard Metz Hermann Stoll and Michael Dolg Small core multiconfiguration Dirac Hartree Fock adjusted pseudopotentials for post d main group elements Application to PbH and PbO J Chem Phys 113 2563 2000 101 102 K A Peterson B C Shepler D Figgen and H Stoll On the spec troscopic and thermochemical properties of ClO BrO IO and their anions J Phys Chem A 110 13877 2006 103 foci Detlev Figgen Guntram Rauhut Mich
58. d by as many lines as the number of non zero elements In each line the corresponding excitation operator and the value for this element of the vector must be provided in the following format lt n gt lt sp gt lt Sp2 gt lt SPn gt lt a1 gt lt az gt lt an gt lt i1 gt lt i2 gt lt in gt lt coeff gt where lt n gt is the level of excitation and the electrons are promoted from occupied orbitals lt i gt lt ig gt lt in gt to virtual orbitals lt a gt lt ag gt lt an gt with spins lt spy gt lt spo gt lt SPn gt lt spk gt is 1 for alpha and 0 for beta respectively lt coeff gt is the corresponding coefficient Initial trial vectors are not specified the program applies sim ple unit vectors as initial guess The unit vectors are deter mined on the basis of the diagonal elements of the Hamilto nian if n roots are requested n unit vectors corresponding to the n lowest diagonals will be used ciguess off 41 Example Suppose that we have two excited states in a LR CC calcu lation Then the initial guess can be given as follows ciguess on 1 11641 0 3 11730 1 2107755 1 0 21176340 1 For the first state there is only one entry a single excitation of the alpha electron from orbital 4 to orbital 6 with a coefficient of 1 0 For the second root the initial guess vector contains three entries A single excitation from orbital 3 to orbital 7 w
59. d description see keyword nacto Options lt any positive integer gt or 0 Default nactv 0 Example for two active virtual spin orbitals give nactv 2 nafalg Specifies how natural auxiliary functions NAFs will be constructed in the case spin unrestricted MOs NAFs can be calculated by diago nalizing W W 2 or W see Ref 24 for the definitions The latter option is somewhat more efficient but can be dangerous for pro cesses involving atoms Options albe NAFs are constructed from W W 2 alpha NAFs are constructed from W Default nafalg albe 70 Example to use W set nafalg alpha naf_cor Specifies whether natural auxiliary functions NAFs will be used for density fitted correlated calculations and also specifies the threshold for the occupation numbers of NAFs see Ref 24 Options off NAFs will not be constructed lt any real number in the 0 1 interval gt A NAF basis will be con structed and NAFs with occupation numbers smaller than this number will be dropped on Equivalent to naf_cor 1e 2 for local correlation methods and to naf_cor 5e 3 otherwise Default naf_cor 1e 2 for local correlation methods naf_cor off oth erwise Example to use NAFs and set a threshold of 10 type naf_cor 1e 2 naf_scf Specifies whether NAFs will be used for density fitted SCF calcu lations and also specifies the threshold for the occupation numbers of NAFs see Ref 24 The syntax is analogous with that f
60. d for automatic point group recognition Two atoms will be considered symmetry equivalent if the difference in any component of their Cartesian coordinates after the symmetry operation is less than 1078 bohr Options lt any integer gt 63 Default gtol 7 Example for a tolerance of 1074 bohr give gtol 4 hamilton Specifies what type of Hamiltonian is used in relativistic calcula tions This keyword has only effect if iface Dirac Options X2Cmmf exact 2 component molecular mean field Hamiltonian 107 DC other types of relativistic Hamiltonians such as the full Dirac Coulomb Hamiltonian or the the exact 2 component Hamil tonian Default hamilton DC Example if you use the exact 2 component molecular mean field Hamil tonian set hamilton X2Cmmf iface Specifies whether MRCC is used together with another program sys tem In this case the transformed MO integrals are calculated by that program and not by MRCC See Sect 5 for the description of various interfaces Options none Transformed MO integrals are calculated by MRCC Cfour MRCC is interfaced to CFOUR Columbus MRCC is interfaced to COLUMBUS Dirac MRCC is interfaced to DIRAC Molpro MRCC is interfaced to MOLPRO Notes 1 If you use MRCC together with CFOUR or MOLPRO you do not need to use this keyword The MRcc input file is auto matically written and MRCC is automatically called by these program systems The user is not required to write the MRCC
61. d option give drpaalg nofit 54 ecp Specifies the effective core potential ECP used in all calculations By default the ECPs are taken from the files named by the chemical symbol of the elements which can be found in the BASIS directory created at the installation The ECPs are stored in the format used by the CFOUR package In addition to the ECPs provided by default any ECP can be used by adding it to the corresponding files in the BASIS directory Alternatively you can also specify your own ECP in the file GENBAS which must be copied to the directory where MRCC is executed Options none No ECPs will be used auto The ECPs will be automatically selected no ECP will be used for atoms with all electron basis sets while the ECP ad equate for the basis set of the atom will be selected otherwise lt ECP label gt If the same ECP is used for all atoms the label of the ECP can be given here atomtype If different ECPs are used or no ECP is used for par ticular atoms but the atoms of the same type are treated in the same way ecp atomtype should be given and the user must specify the ECP for each atomtype for which an ECP is used in the subsequent lines as lt atomic symbol gt lt ECP label gt special In the general case if different ECPs are used for each atom then one should give ecp special and specify the ECP for each atom in the subsequent lines by giving the label of the corresponding ECP or none if no ECP is used for
62. e same using the vector option active vector 100111001112101000000 agrid Specifies the angular integration grid for DFT calculations The grid construction follows the design principles of Becke 32 the smoothing function for the Voronoi polyhedra are adopted from Ref 33 with m 10 Angular grids are taken from the Grid file which is located in the BASIS directory created at the installation By default the 6 14 26 38 50 74 86 110 146 170 194 230 266 302 350 434 590 770 974 1202 1454 and 1730 point Lebedev quadratures 32 are included in the file which are labeled respectively by LD0006 LD0014 etc In addition to the above grids any angular integration grid can be used by adding it to the BASIS Grid file or alternatively to the GENBAS file to be placed in the directory where MRCC is executed The format is as follows On the first line give the label of the grid as XXNNNN where XX is any character and NNNN is the number of the grid points see the above examples The subsequent NNNN lines must contain the Cartesian coordinates and the weights for the grid points For the selection of the angular grids by default an adaptive scheme motivated by Ref 34 is used The important difference is that the grids are optimized for each atom separately to avoid discontinuous potential energy surfaces For the construction of the radial integration grid see the description of keyword rgrid 30 Optio
63. ed that is options SOSEX DF SOSEX and RI SOSEX are syn onyms RPAX2 RPAX2 calculation see Eqs 17 to 19 in Ref 31 Note that RPAX2 calculations are only possible with the density fitting resolution of identity approximation and by default a DF RPAX2 RI RPAX2 calculation is performed that is options RPAX2 DF RPAX2 and RI RPAX2 are synonyms CCS CCSD CCSDT CCSDIQ CCSDTQP CC lt n gt The corresponding single reference CC calculation if the num ber of active orbitals is zero see Ref 1 the corresponding SRMRCCSD SRMRCCSDT etc calculation otherwise see Ref 2 CCSD T CCSDT Q CCSDTQ P CC lt n 1 gt lt n gt The corresponding single reference CC calculation with per turbative corrections see Ref 7 CCSD T CCSDT Q CCSDTQ P CC lt n 1 gt lt n gt The corresponding single reference CC calculation with per turbative corrections see Ref 7 CCSD T L CCSDT Q L CCSDTQ P L COC nal gt lt n gt L The corresponding CCSD T CCSDT Q ete calculation see Ref 7 CCSDT 1a CCSDTQ 1a CCSDTQP 1a CC lt n gt ta The corresponding iterative approximate single reference CC calculation see Ref 7 CCSDT 1b CCSDTQ 1b CCSDTQP 1b CC lt n gt 1b The corresponding iterative approximate single reference CC calculation see Ref 7 CC2 CC3 CC4 CC5 CC lt n gt The corresponding iterative approximate single reference CC calculation see Ref 7 38 CCSDT 3 CCSDT
64. ed and restarts each calcu lation from the previous one this is only available for energy calculations 3 Same as rest 1 however only selected roots from the previous calculation will be used as initial guess The serial number of the roots must be specified in the subsequent line as lt n gt lt ng gt lt N3 gt where lt n gt is the serial number of the states The num ber of states given here must be equal to nstate or nsing ntrip Please note that the ground state solution is not auto matically selected it should also be given here if needed It is recommended to use root following diag follow together with this option 4 Same as rest 2 but the initial vectors are selected as in the case of rest 3 Notes use the restart option e g 1 after system crash 2 if the iteration procedure did not converge in the given number of steps 3 for geometry optimization 4 for potential curve calculations 5 if you are interested in high order CC CI energies Then it is worth restarting the calculations with higher excitations using the converged vectors of the same method including 78 lower excitations e g CCSDT using the converged CCSD amplitudes CCSDTQ using the CCSDT amplitudes and so on With this trick 1 3 iteration steps can be saved usually but more ones in the case of strong static correlation i e large cluster amplitudes Use exclusively rest 2 for this purpose that is not rest 1 6
65. elization schemes cannot be combined Default no parallelization g source codes are compiled with debugging option use this for develop ment purposes Default no debugging option d source codes are compiled for development no optimization is performed use this for development purposes Default codes are compiled with highest level optimization f specifies the installation folder Executables basis set libraries and test jobs will be copied to directory lt folder gt If this flag is not used you will find the executables etc in the directory where you perform the installation Notes 1 After the installation please do not forget to add the directory where the MRCC executables are located to your PATH environmental variable 22 This is the lt folder gt directory if you used the f flag at the installation otherwise the directory where you executed the build mrcc script The build mrcc script has been tested on several platforms with sev eral versions of the supported compilers and libraries Nevertheless you may need to customize the compiler flags names of libraries etc These data can be found in the build mrcc config file please edit this file if necessary Please do not change build mrcc To ensure the best performance of the software the use of Intel compiler is recommended If you use MRCC together with MOLPRO you can also use the MOLPRO installer to install MRCC please follow the inst
66. ently it only functions for closed shell systems and the spatial symmetry is not utilized prop This program solves the CPHF equations constructs relaxed density matrices calculates first order molecular properties and Cartesian gra dients goldstone This program generates the formulas for mrcc The program also estimates the memory requirement of the calculation This is a very crude the symmetry and spin is not treated exactly but quick estimate The real memory requirement which is usually much smaller is calculated by xmrcc after the termination of goldstone xmrcc It calculates the exact memory requirement for mrcc Note that it may take a couple of minutes for complicated wave functions e g MRCC derivatives It prints out five numbers at the end in MBytes Real 8 Minimal and optimal memory for double precision real 8 ar rays Integer Memory allocated by mrcc for integer arrays 2T Total Real 8 Integer The minimal and the optimal amount of total required memory It is not worth starting the calculation if the real physical memory of the machine is smaller than the Minimal value The performance of the program is optimal if it can use at least as much memory as the Optimal value If the memory is between the Minimal and Optimal values out of core algorithms will be executed for particular tasks and it may result in slow down of the code Please note that the memory available to the program can be specified by
67. etails Options lt any positive real number gt Orbital pairs with multipole based pair correlation energy estimates smaller than this number in Ep will be considered as distant pairs Default wpairtol min 1e 6 0 01 spairtol Example to set a threshold of 5 10 E type wpairtol 5e 6 88 13 Symmetry The MRCC program can handle Abelian point group symmetry The han dling of symmetry can be controlled by keywords cmpgrp see page 42 and symm see page 86 In the following we give the character tables used by the program The symmetry of electronic states can be specified by keyword symm using either the serial number of the irrep or its symbol The serial number of an irrep is given by its position in the below tables as appropri ate To specify the state symmetry by the symbol of the irrep replace the superscripts in the irrep symbol by lowercase letters e g give B2g for B g For the A and A irreps of C group use A and A respectively apostrophe and quotation mark Character table for the Ci point group E A 1 T Y Z Rz Ry Rz 2 2 2 L Y Z LY TZ YZ Character table for the C point group E i Aig 1 1 Re Ry Rz T y Be TY TZ YZ Aju 1 l T Y Z Character table for the C point group E Oh A 1 1 x y Rz 2 Y2 2 y A 1 1 z Re Ry yz z Character table for the Cy point group HO A 1 1 Z Ty ae yY z Ty B 1
68. frequencies and second order properties can be evaluated for CI methods using analytic second derivatives and the CFOUR interface 15 6 7 Relativistic calculations Treatment of special relativity in single point energy calculations is pos sible for all the methods listed in Sect 6 1 using various relativistic Hamil tonians with the following interfaces 1 With MOLPRO relativistic calculations can be performed with Douglas Kroll Hess Hamiltonians using RHF UHF ROHF and MCSCF or bitals The interface also enables the use of effective core potentials see MOLPRO s manual for the specification of the Hamiltonian and effective core potentials 2 With CFOUR exact two component X2C and spin free Dirac Coulomb SF DC calculations can be performed The evaluation of mass velocity and Darwin corrections is also possible using analytic gradients for all the methods and reference functions listed in Sect 6 2 See the de scription of the RELATIVISTIC keyword in the CFOUR manual for the specification of the Hamiltonian 3 With DIRAC relativistic calculations can be carried out with the full Dirac Coulomb Hamiltonian and several approximate variants thereof using Kramers paired Dirac Fock orbitals See Refs 16 and 18 as well as Sect 5 3 for more details Treatment of special relativity in analytic gradient calculations is possible for all the methods listed in Sect 6 2 using various relativistic Hamiltonians with the followi
69. fy the basis sets for each atomtype in the subsequent lines as lt atomic symbol gt lt basis set gt special In the general case if different basis set are used for each atom then one should give basis special and specify the basis sets for each atom in the subsequent lines by giving the label of the corresponding basis sets in the order the atoms appear at the specification of the geometry Notes 1 By default the following basis sets are available for elements H to Kr in MRCC 31 Dunning s correlation consistent basis sets 35 39 cc pVXZ cc pCVXZ aug cc pVXZ aug cc pCVXZ X D T Q 5 6 Gaussian basis sets of Pople and co workers 40 48 STO 3G 3 21G 6 31G 6 311G 6 31G 6 311G 6 31G 6 311G 6 31 G 6 31 G 6 31 G 6 311 G 6 311 G 6 311 G the def2 Gaussian basis sets of Weigend and Ahlrichs 49 def2 SV P def2 SVP def2 TZVP def2 TZVPP def2 QZVP def2 QZVPP F12 basis sets for explicitly correlated wave functions de veloped by Peterson et al 50 cc pVXZ F12 X D T Q the Gaussian basis sets of Dunning and Hay LANL2DZ 51 the auxiliary basis sets of Weigend et al for correla tion calculations using the density fitting resolution of the identity approximation 52 53 cc pVXZ RI aug cc pVXZ RI X D T Q 5 6 def2 SV P RI def2 SVP RI def2 TZVP RI def2 TZVPP RI def2 QZVP RI def2 QZVPP RI Weigend s Coulomb exchange auxili
70. g cc pV_X Z RI JK sets by adding diffuse functions as described above for the d aug cc 33 p C VXZ basis sets 9 For Dunnings s and Pople s basis sets add the min postfix to the basis set name to generate a minimal basis set dropping all the polarization correlation functions 10 If the aug cc pV XZ PP basis set does not exist for an ele ment with Z lt 28 the program will automatically attempt to use the corresponding aug cc pV X Z basis instead Default none that is the basis set must be specified excepting the case when MRCC is used together with another code that is iface none Examples 1 Consider any molecule and suppose that the cc pVDZ basis set is used for all atoms The input must include the following line basis cc pVDZ 2 To use Dunning s doubly augmented cc pVDZ basis set d aug cc pVDZ for all atoms the input must include the following line basis d aug cc pVDZ 3 Consider the water molecule and use the cc pVDZ basis set for the hydrogens and cc pVTZ for the oxygen The input must include the following lines basis atomtype O cc pVTZ H cc pVDZ 4 Consider water again and use the cc pVQZ cc pVTZ and cc pVDZ basis sets for the oxygen atom for the first hydrogen and for the second hydrogen respectively Note that the or der of the basis set labels after the basis special statement must be identical to the order of the corresponding atoms in the Z matrix Cartesian coordinates geom
71. g pair if the absolute value of the pair correlation energy estimate is greater than spairtol In the subsequent calculations strong pairs will be treated at a higher level while for the other pairs weak and distant the corresponding pair correlation energy estimates will be added to the correlation energy See also Ref 26 for more details Options lt any positive real number gt Orbital pairs with pair correlation en ergy estimates greater than this number in E will be con sidered as strong pairs Default spairtol 1le 4 Example to set a threshold of 10 E type spairtol 1e 5 steptol Convergence threshold for optimization The optimization is termi nated when the change in the parameters becomes less then this value and the opttol criterion is also fulfilled Options lt any positive real number gt Default steptol 1e 4 Example to set a threshold of 10 type steptol 1e 5 85 symm Spatial symmetry irreducible representation of the state See Sect 13 for the implemented point groups conventions for irreps etc Options 0 No symmetry adaptation that is all calculations will use the C point group off Equivalent to symm 0 1 2 8 Serial number of the irrep see Sect 13 lt irrep label gt Label for the irrep see Sect 13 Note Irreps can only be specified by their serial numbers if MRCC is used with another program In that case please check the manual or output of the other program system for the
72. he canonical expressions give Imp2dens off lnoepso Threshold for the occupation numbers for occupied local natural orbitals LNOs see also keyword lnoepsv See Ref 22 for more details Options lt any real number in the 0 1 interval gt Orbitals with occupation numbers greater than 1 lnoepso will be frozen Default Inoepso 3e 5 Example to set a threshold of 7 5 1077 type lnoepso 7 5e 7 lnoepsv Threshold for the occupation numbers for virtual local natural or bitals LNOs see also keyword lnoepso See Ref 22 for more details Options lt any real number in the 0 1 interval gt Orbitals with occupation numbers smaller than this number will be dropped Default lnoepsv 1le 6 Example to set a threshold of 3 1077 type lnoepsv 3e 7 localcc Specifies if local correlation calculation is performed See Refs 20 22 and 26 for more details Options 67 off No local correlation calculation is performed on Local correlation calculation is performed Note Local correlation methods can also be run if the prefix L is added to the corresponding option of keyword calc see the de scription of calc Default localcc off Example for local correlation calculations give localcc on maxact Maximum number of inactive labels One can impose restrictions on the cluster operator using this keyword The maximum number of virtual occupied inactive labels on the singly doubly excited clusters can be specified
73. hird derivatives of the density matrix for third order property calculations available only with CFouR Default dens 2 for QM MM calculations dens 0 otherwise Notes 1 Transition moment as well as excited state gradient calcula tions can be performed for only one excited state at a time that is nsing ntrip or nstate cannot exceed 2 To com pute the transition moment or gradient for a higher excited state you need to converge the equations to that root The best practice is to run a calculation with the desired number of excited states and then restart the calculation selecting a 44 higher solution see the description of keyword rest You can also try to start the calculation from a good initial guess see the description of keyword ciguess 2 If dens 0 a population analysis is also performed and Mul liken and Lowdin atomic charges as well as Mayer bond orders are computed Example for the calculation of both one and two particle density ma trices set dens 2 dfalg Specifies how the inverse of the two center Coulomb integral matrix is decomposed in density fitting direct SCF calculations There are two possibilities the matrix can be decomposed by calculating its square root or by Cholesky decomposition The latter option is more efficient but can be numerically unstable for large basis sets Options invsqrt Inverse square root of the two center integral matrix is used Cholesky Cholesky decomposition of
74. ht after it no blanks are allowed You might wonder why this is needed if the default behavior is optimization Well this makes life easier If you want to optimize just a few parameters it is easier to con strain all parameters first then mark those which are needed to be optimized see the example below 1 To reoptimize all parameters in the above basis set but the exponents and coefficients of s type functions you should copy the basis set to the GENBAS file and put mark after the angular momentum quantum number of 0 The first lines of the GENBAS file 19 C 6 31G Pople s Gaussian basis set 2 O 1 3 10 4 3047 5249 457 36952 2 Both s and p type functions are fixed but the first s exponent C 6 31G Pople s Gaussian basis set 2 0 1 3 2 10 4 3047 5249 457 36952 During the optimization the GENBAS file is continuously updated and if the optimization terminated successfully it will contain the optimized values in this case it is equivalent to the GENBAS opt file see below the only difference is that the file GENBAS opt may contain the special marks i e Further files generated in the optimization are e GENBAS init the initial GENBAS file saved e GENBAS tmp temporary file updated after each iteration can be used to restart conveniently a failed optimization process e GENBAS opt this file contains the optimized parameters after a suc cessf
75. ic units will be used Default unit angs Example to use bohrs rather than angstroms the user should set unit bohr verbosity Controls the verbosity of the output Options 0 1 2 3 The verbosity of the output increases gradually with increasing value of the option Error messages are not sup pressed at any level Default verbosity 2 Example to increase the amount of information printed out give verbosity 3 wpairtol Threshold for the selection of weak pairs in local MP2 and RPA methods For each orbital pair the estimate of the pair correlation energy is calculated with a multipole approximation 120 121 An orbital pair will be considered as distant pair if the absolute value of the multipole based pair correlation energy estimate is smaller than wpairtol For the distant pairs the corresponding multipole based pair correlation energy estimates will be added to the correlation energy and distant pairs will be neglected in the subsequent calculations For the remaining pairs a more accurate pair correlation energy estimate will be calculated using orbital specific virtuals OSVs controlled by keyword osveps and these pairs will be further classified as weak and strong pairs controlled by keyword spairtol see the description of keyword spairtol The extended domain of an occupied orbital will include those orbitals for which the latter accurate pair correlation energy estimate is greater than spairtol See also Ref 26 for more d
76. if you are interested in calculating the energies for all methods in a hierarchy e g executing all CC methods up to CCS DTQP Use exclusively rest 2 for this purpose that is not rest 1 7 to generate brute force initial guess for excited state calcula tions rest 3 or 4 That is if you do not want to bother with the initial guess for excited states but you know ap proximately the energy of the excited states then execute a low level method e g LR CCS CIS for many roots Se lect the desired roots on the basis of their energies and use them as initial guess in high level calculations For other options for the initial guess for excited state calculations see keyword ciguess 8 Please note that the program always needs the file fort 16 from the previous calculation for the restart and also fort 17 if more than one root is sought or for geometry optimization Default rest 0 Examples 1 to restart a CC calculation after power failure set rest 1 2 to restart a LR CCSD calculation using the first third and fifth roots of a previous LR CCS calculation the input should include the following two lines rest 3 135 rgrid Specifies the radial integration grid for DFT calculations For the details of the grid construction see the description of keyword agrid Options GS Gauss Chebyshev quadrature A modified version of the map ping function of Ref 34 is employed the function is scaled by the atomic scaling para
77. ill convert the COLUMBUS integral files to the MRCC format Prepare input file MINP for MRCC as described in Sect 11 Run dmrcc as described in Sect 9 It is recommended to execute first some inexpensive calculation e g CISD with MRCC and compare the HF and CISD energies in order to test your input files For property calculations create the COLUMBUS and the MRCC input files In the COLUMBUS input set the corresponding MRCI property calculation Copy the MRCC input file MINP to the WORK directory of COLUMBUS If the directory does not exist create it Then execute the runc_mrcc script 5 3 DIRAC The interface to the DIRAC code enables four component relativistic cal culations with the full Dirac Coulomb Hamiltonian and several approximate variants thereof Single point energy calculations are possible with all the methods implemented in MRCC using Kramers paired Dirac Fock orbitals First order property unrelaxed calculations are available with iterative CC and CI methods See Refs 16 and 18 for more details If you use DIRAC you should first prepare input files for DIRAC see http diracprogram org It is important to run a full integral transfor mation with DIRAC see the description of the MOLTRA keyword in DIRAC s manual and to use Abelian symmetry that is the C3 or C3 double groups and their subgroups Execute the pam script saving the MRCONEE and MDCINT files e g running it as pam get MRCONEE MDCINT inp Y i
78. in component of the correlation energy in spin component scaled MP2 SCS MP2 calculations 64 Options lt any real number gt the antiparallel spin component of the corre lation energy will be scaled by this number Default scsps 6 5 Example to set a scaling factor of 1 5 type scsps 1 5 80 scspt Scaling factor for the parallel spin component of the correlation energy in spin component scaled MP2 SCS MP2 calculations 64 Options lt any real number gt the parallel spin component of the correla tion energy will be scaled by this number Default scspt 1 3 Example to set a scaling factor of 0 5 type scspt 0 5 scfalg Specifies what type of SCF algorithm is to be used Options disk Conventional SCF algorithm two electron integrals are stored on disk direct Direct SCF algorithm two electron integrals are recalcu lated in each iteration step auto Based on the size and geometry of the molecule the program will automatically select the more efficient one from the above options Default scfalg auto Example to run direct SCF add scfalg direct scfdamp Specifies whether damping of the SCF density matrices is per formed Options off No damping lt any real number in the 0 1 interval gt In each SCF iteration cy cle the new and old SCF density matrices are mixed by factors 1 scfdamp and scfdamp respectively on Equivalent to scfdamp 0 7 Default scfdamp off Example to use a damping factor of 0 8 type
79. input file most of the features of MRCC can be controlled from the input files of the these programs With CFOUR the user has the option to turn off the automatic construction of the MRCC input file by giving INPUT_MRCC OFF in the CFOUR input file ZMAT In the latter case one should use this keyword 2 If you use MRCC together with COLUMBUS or DIRAC this keyword must be always given 64 Default iface none that is all calculations will be performed by MRCC Example to carry out four component relativistic calculations using the DIRAC interface give iface Dirac intalg Specifies the algorithm used for the evaluation of two electron inte grals over primitive Gaussian type orbitals Options os The e0 f0 integrals are evaluated by the Obara Saika pro cedure using the vertical and transfer recurrence relations 108 109 rys The e0 f0 integrals are evaluated by the Rys quadrature scheme 109 111 auto Depending on the angular momenta the program automati cally determines which of the two algorithms is executed For integrals of low angular momentum functions the Rys pro cedure is used while the Obara Saika algorithm is executed otherwise herm The integrals over contracted Gaussians are evaluated by the solid harmonic Hermite scheme of Reine et al 106 Notes 1 For calculations using the density fitting DF approximation intalg auto is equivalent intalg os since the Obara Saika algorithm is more efficient for any
80. irectly by CFOUR and you do not need to write any input file for Mrcc Most of the features of MRCC can be controlled by the corresponding CFOUR keyword see CFOUR s homepage at www cfour de If you use the CFOUR interface you can safely ignore the rest of this manual You also have the option to turn off the automatic construction of the MRCC input file by giving INPUT_MRCC OFF in the CFOUR input file ZMAT However it is only recommended for expert users 5 2 COLUMBUS Single point energies equilibrium geometries ground and excited state first order properties and transition moments can be computed with RHF ROHF and MCSCF reference states using the COLUMBUS interface Eval uation of harmonic vibrational frequencies is also possible via numerically differentiated analytical gradients Running MRCC with COLUMBUS requires three additional programs colto55 coldens and runc_mrcc which are available for COLUMBUS li censees from the authors of MRCC upon request To use this interface for single point energy calculations first prepare in put files for COLUMBUS using the colinp script It is important to set a calculation in the input file which requires a complete integral transforma tion e g CISD and not just MCSCF Execute COLUMBUS If you do not need the results of the COLUMBUS calculations you can stop them after com pleting the integral transformation Run the colto55 program in the WORK directory created by COLUMBUS This w
81. ith alpha spin and a relative weight of 0 1 a double excitation from orbital 5 to orbital 7 with a weight of 1 0 and another double excitation of the alpha electrons from orbitals 3 and 4 to orbitals 6 and 7 with a weight of 0 1 Notes 1 For Ms 0 states the vector is automatically spin adapted and you do not need to specify the coefficients for the corre sponding spin reversed excitations E g in the above exam ple for root 1 the 1 0 6 4 1 0 entry is unnecessary 2 The guess vector is not required to be normalized it is done automatically 3 In the case of four component relativistic calculations DIRAC interface the serial numbers of the spinors should be specified In addition the second number in the above strings must be 1 that is all excitations are formally considered as excitations of alpha electrons cmpgrp Specifies the computational point group All calculations will use the specified Abelian group See Sect 13 for more details Options auto The molecular symmetry is automatically recognized lt point group symbol gt Schonflies symbol of the Abelian point group such as C1 Ci Cs C2 C2v C2h D2 D2h Note cmpgrp C1 is equivalent to symm off Default cmpgrp auto 42 Example to use C2 point group for benzene set cmpgrp C2v core Specifies whether the core electrons are correlated Options frozen Frozen core approximation corr All core electrons are correlated lt any non negative integer n g
82. le to set a threshold of 1 10 4 type osveps 1e 4 ovirt If this keyword is set the virtual MOs will be transformed to MP2 nat ural orbitals or optimized virtual orbitals OVOs 117 Subsequently the virtual space will be truncated on the basis of the populations of the orbitals which can be controlled by keywords eps and ovosnorb See Ref 19 for more details Options off The virtual MOs are not changed MP2 MP2 natural orbitals will be used OVOS Optimized virtual orbitals will be used Default ovirt off Example to use MP2 natural orbitals give ovirt MP2 ovosnorb Specifies the retained percentage of virtual orbitals in an optimized virtual orbitals OVOs calculations ovosnorb of virtual orbitals will be retained Options lt any number between 0 and 100 gt Default ovosnorb 80 0 Example to retain only 70 of the virtuals give ovosnorb 70 0 popul This keyword controls the wave function analysis Options off No wave function analysis is performed Mulli A population analysis is also performed and Mulliken and Lowdin atomic charges as well as Mayer bond orders are com puted 118 119 IAO In addition to the above parameters intrinsic atomic orbitals IAOs are constructed and IAO partial charges are calculated 115 Default popul Mulli if dens 0 popul off otherwise Example to calculate IAO charges set popul IA0 75 refdet The reference determinant Fermi vacuum for CI CC calculations can be specified using
83. ll be displayed and the program exits with an error code if the test energy and the calculated energy differ This keyword is mainly used by the developers of the program to create test jobs to check the correctness of the computed energies See Sect 8 for the further details Options off No testing lt any real number gt The energy to be tested Default test off Example to set atest energy of 40 38235315 E type test 40 38235315 tprint Controls the printing of converged cluster amplitudes ClI coefficients if ccprog mrcc Options off No printing lt any real number gt Cluster amplitudes ClI coefficients whose ab solute value is greater than this number will be printed Note The value of the cluster amplitude ClI coefficient and the corre sponding spin orbital labels serial number of the orbital a or b for alpha or beta spin orbitals respectively will be printed The numbering of the orbitals corresponds to increasing orbital energy order Note that orbital energies are printed at the end of the SCF run if verbosity gt 3 You can also identify the orbitals using MOLDEN see Sect 14 1 Default tprint off Example to set a threshold of 0 01 give tprint 0 01 uncontract Uncontract contracted basis sets Options on or off Default uncontract off Example to uncontract the basis set add uncontract on 87 unit Specifies the units used for molecular geometries Options angs Angstroms will be used bohr Atom
84. ls and interfaces 14 Available methods 1 2 3 4 arbitrary single reference linear response CC methods Refs 1 3 and 5 LR CCSD LR CCSDT LR CCSDTQ LR CCSDTQP LR CC n linear response MRCC schemes Refs 2 3 and 5 arbitrary single reference configuration interaction methods Refs 1 3 and 5 CIS CISD CISDT CISDTQ CISDTQP Cl n full CI multi reference CI approaches Refs 2 3 and 5 Available reference states and programs RHF Mrcc only excitation energy and transition moment CFOUR COLUMBUS and MOLPRO only excitation energy ROHF standard orbitals MRCC only excitation energy and transition moment CFOUR COLUMBUS and MOLPRO only excitation energy UHF Mrcc only excitation energy and transition moment CFOUR and MOLPRO only excitation energy MCSCF COLUMBUS and MOLPRO only excitation energy Notes 1 2 So far only electric dipole transition moments have been implemented Please note that for excitation energies and geometries LR CC methods are equivalent to the corresponding EOM CC models It is not true for first order properties and transition moments With CI methods excited to excited state transition moments can also be evaluated Excited state harmonic frequencies can be evaluated for the above methods via numerical differentiation of analytical gradients using the CFOUR or COLUMBUS interface Excited state harmonic
85. ltiple line input the lines including the keyword and its input records cannot be separated Under similar conditions any line can be used for comments but the beginning of a comment line must not be identical to a keyword because that line may be identified as a keyword by the input reader and misinterpreted Thus it is recommended to start comment lines with some special character e g hash mark Please note that you can find input files for numerous test jobs in the MTEST directory created at the installation of MRCC see Sect 8 The input files have self explanatory names and also include a short description at the beginning You should look at these files for examples for the structure of the input file and the use of various keywords You can use these files as templates but please note that these files have been created to thoroughly check the correctness of the code and the installation and thus some of them contain very tight convergence thresholds as well as unusual combination of auxiliary basis sets In production calculations you should use the de fault convergence thresholds i e delete the lines including keywords itol scftol or cctol select the basis set carefully i e set the appropriate op tion for keyword basis and use the default auxiliary basis sets i e delete the lines including keywords dfbasis_scf or dfbasis_cor Please also do not forget remove keyword test and to specify the amount of memory avail able
86. ly have to prepare the input file for MOLPRO with a line starting with the mrcc label followed by the corresponding keywords and run MOLPRO The MRCC input file is then written automatically and MRCC is called directly by MOLPRO and you do not need to write any input file for MRCC Most of the features of MRCC can be controlled by the corresponding MOLPRO keywords If you use MOLPRO you also have the option to install MRcc with the makefile of MOLPRO For a detailed description of the interface point your browser to the MOL PRO User s Manual at www molpro net and then click 27 The MRCC pro gram of M Kallay MRCC If you use the MOLPRO interface you can safely ignore the rest of this manual 6 Features In this section the available features of the MRCC code are summarized We also specify what type of reference states orbitals can be used and if a particular feature requires one of the interfaces or is available with MRCC in standalone mode We also give the corresponding references which describe the underlying methodological developments 6 1 Single point energy calculations Available methods 1 conventional and density fitted resolution of identity Hartree Fock SCF Ref 22 restricted HF RHF unrestricted HF UHF and restricted open shell HF ROHF conventional and density fitted resolution of identity Kohn Sham KS density functional theory DFT Ref 24 restricted KS RKS and unrestricted
87. meters of Becke 32 EM Euler Maclaurin quadrature 33 79 Note the number of grid points is calculated by the max 20 5 3 itol 2 7 8 formula with i as the number of the row in the periodic table where the atom is located 34 To change the number of radial integration points set the value of itol Default rgrid GC Example to use the Euler Maclaurin scheme set rgrid EM rohftype Specifies the type of the ROHF orbitals See also the description of keyword scftype Options standard Standard ROHF orbitals obtained by diagonalizing the ROHF Fock matrix semicanonical Semicanonical ROHF orbitals obtained by sepa rately diagonalizing the alpha and beta UHF Fock matrices constructed using the converged ROHF orbitals Notes 1 rohftype semicanonical is required for perturbative CC meth ods if ROHF orbitals are used otherwise the expressions for the perturbative corrections are not correct Iterative CC and CI methods are invariant to the choice of ROHF orbitals 2 It is very important to give this keyword if MRCC is used to gether with another code and ROHF orbitals are used since this keyword tells MRCC what type of ROHF orbitals are taken over from the other code Default rohftype standard for iterative CC and CI methods rohftype semicanonical for perturbative methods Example to use semicanonical ROHF orbitals for iterative CC meth ods give rohftype semicanonical scsps Scaling factor for the antiparallel sp
88. ncy calculations are also possible via numerical differentiation of energies for all implemented methods with RHF ROHF and UHF orbitals 3 Using the CFOUR or the COLUMBUS interface harmonic frequency cal culations are also possible via numerical differentiation of analytic gra dients for all implemented methods for which analytic gradients are available see Sect 6 2 for a list of these methods With CFOUR the calculation of static polarizabilities is also possible using numerical differentiation 4 NMR chemical shifts can be computed for closed shell molecules using gauge including atomic orbitals and RHF reference function 6 4 Higher order properties Third order property calculations can be performed using analytic third derivative techniques quadratic response functions with the following meth ods orbitals and interfaces Available methods 1 arbitrary single reference coupled cluster methods Refs 1 3 4 11 and 12 CCSD CCSDT CCSDTQ CCSDTQP CC n 2 multi reference CC approaches using a state selective ansatz Refs 2 3 4 11 and 12 Available reference states and programs RHF CFOUR UHF CFOUR Notes 1 The analytic third derivative code has been tested for static and frequency dependent electric dipole first general second harmonic generation optical rectification hyperpolarizabilities 11 and Raman intensities 12 Please note that the orbital relaxation effects are not considered for
89. ng interfaces 1 With CFOUR analytic gradient calculations can be performed with the exact two component X2C treatment 2 With DIRAC unrelaxed first order properties can be computed using the Dirac Coulomb Hamiltonian See Ref 16 and Sect 5 3 for more details 6 8 Reduced scaling and local correlation calculations Orbital transformation techniques The computational expenses of the CC and CI methods listed in Sect 6 1 can be reduced via orbital transformation techniques Ref 19 In this framework to reduce the computation time the dimension of the properly transformed virtual one particle space is truncated Currently optimized vir tual orbitals OVOs or MP2 natural orbitals can be chosen This technique 16 is recommended for small to medium size molecules This scaling reduction approach is available with MRCC using RHF or UHF orbitals See the de scription of keywords ovirt eps and ovosnorb for more details Local correlation methods The cost of MP2 dRPA SOSEX as well as single reference iterative and perturbative coupled cluster calculations can be reduced for large molecules by the local natural orbital cluster in molecule LNO CIM CC approach Refs 20 22 26 and 27 This method combines the cluster in molecule approach of Li and co workers with the frozen natural orbital and natural auxiliary functions techniques It is available with MRCC currently only for closed shell molecules using RHF orbitals See the de
90. nians ef fective core potentials and MCSCF orbitals If MRCC is used together with the aforementioned packages the integral property integral HF MCSCF and CPHF calculations the integral and density matrix transformations etc are performed by these program systems Transformed MO property inte grals are passed over to MRCC which carries out the correlation calculation and returns unrelaxed MO density matrices if necessary In the following we describe the use of the CFOUR COLUMBUS DIRAC and MOLPRO interfaces and the features that they enable For a complete list of available features see Sect 6 See also the description of keyword iface on page 64 For the ORCA and Ps interfaces see the manual of these packages 5 1 CFOUR Most of the implemented features are available via the CFOUR interface using RHF ROHF and UHF orbitals single point energy calculations ge ometry optimizations first second and third order property calculations electronic excitation energies excited state and transition properties diago nal Born Oppenheimer correction DBOC calculations Most of the prop erties implemented in CFOUR are also available with Mrcc The interface also enables the use of several relativistic Hamiltonians The CFOUR interface is very user friendly You only have to prepare the input file ZMAT for CFOUR with the keyword CC_PROG MRCC and run Crour The MRCC input file is then written automatically and MRCC is called d
91. niques and local correla tion approaches also enable high precision calculations for medium sized and large molecules 2 How to read this manual In the following words set in typewriter font denote file names shell commands environmental variables and input records of the input file These must be typed as shown Variables that is numbers options etc which must by specified by the user will be given as lt variable gt These must be replaced by the corresponding values of the variables Optional items are denoted by brackets e g as lt variable gt 3 Authors The main authors of the MRcc code and their major contributions are as follows Mih ly K llay general design driver program dmrcc input analyzer minp automated string based many body code goldstone xmrcc mrcc domain construction for local correlation calculations mulli particular integral evaluation algorithms integ direct and density fitting Hartree Fock algorithms DFT algorithms scf density fitting MP2 and RPA algorithms drpa 4 Zolt n Rolik integral transformation and orbital optimization code ovirt domain construction for local correlation calculations mulli J zsef Csontos installation script build mrcc geometry optimization basis set optimization the MRCC homepage Istvan Ladjanszki Hartree Fock self consistent field code scf L r nt Szegedy coupled cluster singles and doubles code ccsd Bence Ladoczki atomic
92. np mol X mol where X mol and Y inp should be replaced by your input files as appropriate Then run the dirac_mointegral_export interface program which generates the files needed by MRCC It also creates a sample input file MINP for MRCC which contains the input for a closed shell CCSD calculation If you intend to run another type of calculation please edit the file as described in Sect 11 Please also note that you may need to modify the occupation vector un der the refdet keyword see the description of the keyword on page 76 and 7 you should set hamilton x2c if exact 2 component Hamiltonians are used Then run dmrcc as described in Sect 9 For relativistic property calculations define the corresponding operator in the DIRAC input file see the description of the PROPERTIES and MOLTRA keywords in DIRAC s manual Then execute the pam script as pam get MRCONEE MDCINT MDPROP inp Y inp mol X mol and edit the MINP file in particular set the dens keyword page 44 The CC property code currently does not work with double group symmetry and you need to turn off symmetry for CC property calculations that is set symm off in the MINP file Finally run dmrcc 5 4 MOLPRO With MOLPRO single point energy calculations are available using RHF UHF ROHF and MCSCF orbitals The interface also enables the use of Douglas Kroll Hess Hamiltonians as well as effective core potentials The MOLPRO interface is very user friendly You on
93. ns lt name of the grid gt the name of the quadrature as it is specified in the BASIS Grid or GENBAS file This angular quadrature will be used in each radial point LDMMMM LDNNNN An adaptive integration grid will be used For each radial point depending on its distance from the nucleus a different Lebedev grid will be selected The minimal and maximal number of points is MMMM and NNNN respectively Default agrid LD0006 LD0302 Examples 1 for a 590 point Lebedev grid set agrid LD0590 2 to use an adaptive grid with at least 110 and at most 974 angular points set agrid LD0110 LD0974 basis Specifies the basis set used in all calculations By default the basis sets are taken from the files named by the chemical symbol of the elements which can be found in the BASIS directory created at the installation The basis sets are stored in the format used by the CFOUR package see Sect 6 9 In addition to the basis sets provided by default any basis set can be used by adding it to the corresponding files in the BASIS directory Alternatively you can also specify your own basis sets in the file GENBAS which must be copied to the directory where MRCC is executed Options lt basis set label gt If the same basis set is used for all atoms the label of the basis set must be given atomtype If different basis set are used but the basis sets are identical for atoms of the same type basis atomtype should be given and the user must speci
94. odels J Chem Phys 119 2991 2003 Mih ly K llay and J rgen Gauss Analytic second derivatives for gen eral coupled cluster and configuration interaction models J Chem Phys 120 6841 2004 Mih ly K llay and J rgen Gauss Calculation of excited state proper ties using general coupled cluster and configuration interaction models J Chem Phys 121 9257 2004 Yannick J Bomble John F Stanton Mih ly K llay and J rgen Gauss Coupled cluster methods including non iterative approximate quadru ple excitation corrections J Chem Phys 123 054101 2005 92 7 Mih ly K llay and J rgen Gauss Approximate treatment of higher 10 11 12 13 14 15 16 ios eesti ear excitations in coupled cluster theory J Chem Phys 123 214105 2005 J rgen Gauss Attila Tajti Mih ly K llay John F Stanton and P ter G Szalay Analytic calculation of the diagonal Born Oppenheimer correction within configuration interaction and coupled cluster theory J Chem Phys 125 144111 2006 Mihaly K llay and J rgen Gauss Calculation of frequency dependent polarizabilities using general coupled cluster models J Mol Struct THEOCHEM 768 71 2006 J rgen Gauss Kenneth Ruud and Mihaly K llay Gauge origin inde pendent calculation of magnetizabilities and rotational g tensors at the coupled cluster level J Chem Phys 127 074101 2007 Darragh P O Neill Mih
95. omrad 12 0 drpaalg Specifies the type of the algorithm for the solution of the dRPA equations or the calculation of SOS MP2 energies See Ref 26 for more details Options fit The algorithm of Ref 31 will be used the fitting of integral lists will be performed before the dRPA iterations SOS MP2 calculation nofit The algorithm of Ref 26 will be executed the fitting of the integrals is not performed This algorithm is efficient for large molecules plasmon The dRPA correlation energy is calculated using the plasmon formula auto The algorithm is automatically selected on the basis of the size of the molecule canonical dRPA or the HOMO LUMO gap local dRPA Notes 1 For SOSEX calculations drpaalg fit is the only option which is forced by the program 2 For canonical dRPA the algorithm using the plasmon formula scales as N it is only competitive for smaller molecules but inefficient for bigger ones It avoids however the problems of the other algorithms that is convergence problems and unphysical solutions Thus it is useful for testing 3 For local dRPA drpaalg plasmon is also linear scaling but typically 2 to 4 times slower than drpaalg fit It is advan tageous for the aforementioned reasons If drpaalg auto the plasmon formula based algorithm is executed if the HOMO LUMO gap is lower than 0 05 Ep Default drpaalg fit and drpaalg auto for canonical and local dRPA respectively Example to set the secon
96. onic Gaussians will be used cart Cartesian Gaussians will be used Notes 1 For calculations using the density fitting DF approxima tion if intalg os or intalg auto the Coulomb integrals are evaluated by the algorithm of Ahlrichs 105 which only en ables the use of spherical harmonic Gaussians Consequently Cartesian Gaussians are only available with intalg rys in DF calculations see the description of keyword intalg 2 The derivative integrals are evaluated by the solid harmonic Hermite scheme 106 see the description of keyword intalg consequently differentiated integrals and thus energy deriva tives cannot be evaluated with Cartesian Gaussian basis sets Default gauss spher Example for Cartesian Gaussians the user should set gauss cart geom Specifies the format of molecular geometry The geometry must be given in the corresponding format in the subsequent lines Options zmat Usual Z matrix format In the Z matrix the geometrical parameters can only be specified as variables and the vari ables must be defined after the matrix following a blank line Another blank line is required after the variables This Z matrix format is compatible to that of CFOUR and nearly compatible to that for GAUSSIAN and MOLPRO Z matrices 60 can be generated by MOLDEN see also Sect 14 1 then the GAUSSIAN style Z matrix format must be chosen The sym bol for dummy atoms is X xyz Cartesian coordinates in xyz format
97. ons are chosen and it is not necessary to set scftype That is calc RHF is equivalent to calc SCF plus scftype RHF etc B3LYP PBEO B3PW91 B3LYP D3 B2PLYP D3 Kohn Sham SCF calculation with the specified density func tional The type of the Kohn Sham procedure i e RKS of UKS can be controlled by keyword scftype see also key word scftype The options are identical to those of keyword dft except for off user and userd see the description of 36 keyword dft Note that for a correlated calculation with KS orbitals you can only select the functional with keyword dft the value of keyword calc must be set to the desired correla tion method Note also that for DFT calculations the density fitting approximation is used by default i e dfbasis_scf is set to auto To run a conventional KS calculation set dfbasis_scf none MP2 Second order Mgller Plesset MP2 calculation the spin com ponent scaled MP2 SCS MP2 64 and the scaled opposite spin MP2 SOS MP2 65 energy will also be computed see also keywords scsps and scspt Note that efficient MP2 cal culations are only possible with the density fitting resolution of identity approximation and by default a DF MP2 RI MP2 calculation is performed that is options MP2 DF MP2 and RI MP2 are synonyms If you are still interested in the MP2 energy without DF you can e g run a CCSD calcula tion without DF where the MP2 energy is also calculated SOS MP2
98. or keyword naf_cor nchol Number of Cholesky vectors quadrature points for the Laplace inte gral in the case methods based on the decomposition of energy denom inators See also the description of keyword dendec Options auto The number of Cholesky vectors quadrature points will be automatically determined to achieve the required precision lt any positive integer gt The number of Cholesky vectors quadrature points will also be automatically determined but the maxi mum number of the vectors cannot exceed this number Default nchol auto Example to use ten Cholesky vectors quadrature points give nchol 10 nstate Number of electronic states including the ground state and excited states In non relativistic calculations for closed shell reference deter minants nstate is supposed to be the number of singlet states See also keywords nsing and ntrip Options lt any positive integer gt 71 Default nstate max 1 nsing ntrip Example for three states give nstate 3 nsing Number of singlet electronic states strictly speaking the number of of states with Ms 0 and S is even including the ground state and excited states Use this option only for non relativistic calculations and closed shell reference determinants it should be zero otherwise In the case of closed shell reference determinants a partial spin adaptation is possible see Ref 1 This enables us to search for singlet and triplet roots separately See also keywo
99. pproximation J Chem Phys 142 204105 2015 P ter Nagy Gyula Samu Zolt n Rolik and Mih ly K llay J Chem Phys 143 in preparation 2015 EMSL basis set exchange https bse pnl gov bse portal 94 29 30 37 38 39 David J Feller The role of databases in support of computational chemistry calculations J Comp Chem 17 1571 1996 K L Schuchardt B T Didier T Elsethagen L Sun V Gurumoorthi J Chase J Li and T L Windus Basis set exchange A community database for computational sciences J Chem Inf Model 47 1045 2007 Andreas He elmann Random phase approximation correlation method including exchange interactions Phys Rev A 85 012517 2012 Axel D Becke A multicenter numerical integration scheme for poly atomic molecules J Chem Phys 88 2547 1988 Christopher W Murray Nicholas C Handy and Gregory J Laming Quadrature schemes for integrals of density functional theory Mol Phys 78 997 1993 Matthias Krack and Andreas M K ster An adaptive numerical inte grator for molecular integrals J Chem Phys 108 3226 1998 Thom H Dunning Jr Gaussian basis sets for use in correlated molec ular calculations I The atoms boron through neon and hydrogen J Chem Phys 90 1007 1989 Rick A Kendall Thom H Dunning Jr and Robert J Harrison Elec tron affinities of the first row atoms revisited Systematic basis sets and wave functions
100. r OpenMP parallel execution you need to invoke the build mrcc script with the pOMP option at compilation see Sect 7 The OpenMP parallelization has been tested with PGF Intel GNU and HP compilers Please be careful with other compilers run e g our test suite see Sect 8 with the OpenMP complied executables before production calculations To run the code with OpenMP you only need to set the environmental variable OMP_NUM_THREADS to the number of cores you want to use E g under Bourne shell bash export OMP_NUM_THREADS 4 Then the program should be executed as described above 9 3 Running MRCC in parallel using MPI Currently only executable mrcc can be run in parallel using MPI technol ogy To compile the program for MPI parallel execution you need to invoke the build mrcc script with the pMPI option at compilations see Sect 7 It has been tested with the PGF Intel GNU and Solaris compilers as well as the Open MPI and local area multicomputer MPI LAM MPI environ ments To execute mrcc using MPI you should follow the following steps Prepare input files as usual Execute dmrcc The program will stop after some time 25 with the massage Now launch mrcc in parallel mode Then copy files fort 1 and fort 5 to the compute nodes and execute mrcc using mpirun E g with Open MPI for i in cat myhosts do scp fort 1 fort 5 i scr USER done mpirun nolocal hostfile myhosts wdir scr USER np
101. r an accuracy of 1078 E one must give scftol 8 scftype Specifies the type of the Hartree Fock Kohn Sham SCF procedure or the type of the molecular orbitals if the MO integrals are computed by other programs See also the description of keyword rohftype Options RHF ROHF UHF or MCSCF Notes 1 scftype MCSCF is only available if MRCC is used together with COLUMBUS or MOLPRO In that case the MCSCF calcula tion is performed by the aforementioned codes and the trans formed MO integrals are passed over to MRCC 84 2 It is very important to give this keyword if MRCC is used to gether with another code and ROHF or MCSCF orbitals are used since this keyword tells MRcc that the orbitals are not canonical HF orbitals Please also set keyword rohftype in this case 3 Ifa HF SCF calculation is run the type of the SCF wave func tion can also be controlled by keyword calc See the descrip tion of calc 4 For DFT calculations only the RHF and UHF options can be used which in that case instruct the code to run RKS or UKS calculations respectively Default scftype RHF for closed shell systems scftype UHF for open shells Example to use ROHF for open shell systems type scftype ROHF spairtol Threshold for the selection of strong pairs in local MP2 and RPA methods For each orbital pair an estimate of the pair correlation energy is calculated see the description of keyword wpairtol An orbital pair will be considered as stron
102. rds nstate and ntrip Options lt any positive integer gt Default nsing 1 for closed shell reference determinants nsing 0 oth erwise Example for two singlet states give nsing 2 ntrip Number of triplet electronic states strictly speaking the number of of states with Ms 0 and S is odd including the ground state and excited states Use this option only for non relativistic calculations and closed shell reference determinants it should be zero otherwise See the description of keywords nstate and ntrip Options lt any positive integer gt Default ntrip 0 Example for two triplet states give ntrip 2 occ Specifies the occupation of the Hartree Fock determinant Options 1 If this keyword is not given the occupation is automatically determined in the SCF calculations 2 For RHF calculations the occupation should be given in the following format occ lt ny gt lt n2 gt lt 1N gt where lt n gt is the number of occupied orbitals in irrep 7 and N is the number of irreps 3 For ROHF and UHF calculations the occupation should be given as occ lt Sig lt NA gt lt ne eee Te gt where lt n gt is the number of occupied spinorbitals in irrep 2 T2 Default occ is not specified that is the occupation is set by the SCF program Examples 1 Water RHF calculation occ 3 1 1 0 2 Water UHF calculation occ 3 1 1 0 3 1 1 0 3 Carbon atom ROHF or UHF calculation occ 2 0 0 0
103. resholds will be set so that the canonical en ergy be reproduced it is only useful for testing Note the values of the thresholds controlled by lcorthr are summa rized in the following table Note that for MP2 always naf_cor off is set and lnoepso and lnoepsv are irrelevant Loose Tight 0 bpcompo 0 985 0 985 1 0 bpcompv 0 98 0 98 1 0 lnoepso 3e 5 le 5 0 0 lnoepsv le 6 3e 7 0 0 naf_cor le 2 8e 3 off osveps le 3 le 4 spairtol ie 4 1e 5 0 0 oO jo Default lcorthr Loose Example to use tight thresholds set lcorthr Tight lmp2dens Determines whether the MP2 density matrix fragments are cal culated using the correct expressions derived for the general type of orbitals or using the expressions derived for the canonical case as described in Ref 20 66 Options on The MP2 density matrix fragments are calculated using the correct non canonical expressions off The MP2 density matrix fragments are calculated using the approximate canonical expressions as defined in Ref 20 Notes 1 To reproduce the method described in Ref 20 use lmp2dens off 2 The use of lmp2dens on is recommended since in this case the local CC energy can be corrected by the difference of the local MP2 energy and the approximate local MP2 energy calculated in the local interacting subspaces see Total CC energy correction in the output This correction usually im proves the local CC energy Default lmp2dens on Example to use t
104. rformed via numerical differentiation for all methods available in MRCC using the CFOUR interface 3 Analytic gradients are are also available with several types of relativistic Hamiltonians and reference functions see Sect 6 7 for more details 6 3 Harmonic frequencies and second order properties Harmonic frequency and second order property calculations can be per formed using analytic second derivatives linear response functions with the following methods orbitals and interfaces Available methods 1 arbitrary single reference coupled cluster methods Refs 1 3 4 9 10 and 14 CCSD CCSDT CCSDTQ CCSDTQP CC n arbitrary single reference configuration interaction methods Refs 1 3 and 4 CIS CISD CISDT CISDTQ CISDTQP CI n full CI multi reference CI approaches Refs 2 3 and 4 multi reference CC approaches using a state selective ansatz Refs 2 3 4 and 9 Available reference states and programs RHF CFOUR UHF CFOUR Notes 1 In addition to harmonic vibrational frequencies 4 the analytic Hessian code has been tested for NMR chemical shifts 4 static and frequency dependent electric dipole polarizabilities 9 magnetizabilities and ro tational g tensors 10 electronic g tensors 14 spin spin coupling con stants and spin rotation constants These properties are available via the CFOUR interface 12 2 Using the CFOUR interface harmonic freque
105. ructions in the MOLPRO manual www molpro net Examples 1 Compile MRCC for OpenMP parallel execution with Intel compiler rec ommended build mrcc Intel pOMP Compile MRCC for OpenMP parallel execution with Intel compiler and install it to the prog mrcc directory recommended build mrcc Intel pOMP f prog mrcc Compile MRcc for serial execution with Intel compiler build mrcc Intel Compile MRCC for parallel execution using MPI environment with Intel compiler for 32 bit machines build mrcc Intel i32 pMPI 7 3 Installation under Windows Under the Windows operating system the pre built binaries cannot be directly executed and the direct compilation of the source code has not been attempted so far For Windows users we recommend the use of virtualiza tion software packages such as VIRTUALBOX which allow Linux as a guest operating system In that environment MRCC can be installed in the normal way as described in the previous subsections 23 8 Testing MRCC Once you have successfully installed MRCC you may wish to test the cor rectness of the installation For that purpose numerous test jobs are at your disposal The corresponding input files can be found in the MTEST directory created at the installation where a test script mtest is also available Your only task is to change to the MTEST directory and execute the mtest script Please do not forget to add the directory where the MRCC executables are
106. s the input must include ecp MCDHF ECP 10 2 Consider the PbO molecule and use the def2 SVP basis set for both elements as well as the def2 ECP 60 pseudopotential for Pb The following inputs are equivalent Input 1 basis def2 SVP geom Pb O1R R 1 921813 Input 2 basis def2 SVP ecp atomtype Pb def2 ECP 60 geom Pb 0 1R R 1 921813 56 Input 3 basis def2 SVP ecp special def2 ECP 60 none geom Pb 0 1R R 1 921813 edisp This keyword controls the calculation of empirical dispersion cor rections for DFT and HF calculations using the DFT D3 approach of Grimme and co workers 93 94 The corrections are evaluated by the DFTD3 program of the latter authors which is available at http www thch uni bonn de tc and interfaced to MRCC You need to separately install this code and add the directory where the dftd3 executable is located to your PATH environmental variable Options off No dispersion correction will be computed auto The dispersion correction will be automatically evaluated to the KS or HF energy Note that it is only possible for particular functionals listed in the description of keyword dft and the HF method For these methods however you can also turn on the calculations of the dispersion corrections by attaching the D3 postfix to the corresponding options e g as BLYP D3 B3LYP D3 B2PLYP D3 etc see the description of keyword dft lt any options of the DFTD3 program gt You can directly give
107. scfdtol scftol 4 for correlation calculations scfdtol scftol 1 for SCF calculations Example for an accuracy of 1078 one must give scfdtol 8 scfext Specifies the number of Fock matrices used for the DIIS extrapola tion in SCF calculations 82 Options lt any positive integer gt Default scfext 10 Example to increase the number of DIIS vectors to 15 give scfext 15 scfiguess Initial guess for the SCF calculation Options sad Superpositions of atomic densities For each atom a density fitted UHF calculation is performed and the initial one particle density matrix is constructed from the averaged alpha and beta atomic densities ao Atomic density initial guess The initial one particle density matrix is constructed from diagonal atomic densities derived from the occupation of the atoms It is efficient for Dunning s basis sets core Core Hamiltonian initial guess The initial MOs are ob tained by diagonalizing the one electron integral matrix restart The SCF calculation will use the density matrices ob tained in a previous calculation and stored in the SCFDENSITIES file If the calculation is restarted from the densities obtained with another basis set the VARS file is also required Note Restarting from densities obtained with a bigger basis set is not allowed Default scfiguess sad Examples 1 For a Core Hamiltonian initial guess set scfiguess core 2 For restarting the SCF calculation from the results of
108. scription of keywords localcc lnoepso lnoepsv domrad lmp2dens dendec nchol osveps spairtol wpairtol and lcorthr for further details Natural auxiliary functions The cost of density fitting methods can be reduced using natural auxiliary functions NAF introduced in Ref 24 The approach is very efficient for dRPA but considerable speedups can also be achieved for MP2 See the description of keywords naf_cor and naf_scf for more details 6 9 Optimization of basis sets The optimization of basis set s exponents and contraction coefficients can be performed with any method for which single point energy calculations are available see Sect 6 1 The implementation is presented in Ref 25 The related keywords are basopt to turn on off basis set optimization optalg to select an algorithm for the optimization optmaxit maximum number of iterations allowed opttol convergence criterion for energy change steptol convergence criterion for parameter exponent contraction coef ficient change For their detailed description see Sect 12 For the optimization of basis sets it is important to know the format for the storage of the basis set parameters In MRCC the format used by the 17 CFOUR package is adapted The format is communicated by the following example C 6 31G Pople s Gaussian basis set 2 0 3 10 3047 5249 0018347 0140373 0688426 2321844 4679413 3623120 0000000 0
109. sis sets just type the usual name of the basis set as given above e g cc pVDZ 6 311 G etc If you employ non default basis sets you can use any label For Dunnings s aug cc p C VX Z basis sets one two or three additional diffuse function sets can be automatically added by attaching the prefix d t or q respectively to the name of the basis set To generate a d aug basis set one even tempered diffuse function is added to each primitive set Its exponent is calculated by multiplying the exponent of the most diffuse function by the ratio of the exponents of the most diffuse and the second most diffuse functions in the primitive set If there is only one function in the set the exponent of the most diffuse function is divided by 2 5 To generate t aug and q aug sets this procedure is repeated For Dunnings s basis sets to use the aug cc p C V XZ set for the non hydrogen atoms and the corresponding cc p C V XZ set for the hydrogens give aug cc p C VXZ Then the dif fuse functions will be automatically removed from the hydro gen atoms Only the conventional AO basis set can be specified with this keyword For the fitting basis sets used in density fitting approximations see the description of keywords dfbasis_ The cc pVDZ RI JK basis set has been generated from cc pVTZ RI JK by dropping the functions of highest angular momentum The aug cc pVX Z RL JK basis sets are constructed automatically from the correspondin
110. sis sets i e 6 311G 6 311G etc the cc pVTZ RI basis set will be used as the auxiliary basis if the basis also includes dif fuse functions i e 6 31 G 6 3114 G etc the aug cc pVDZ RI and aug cc pVTZ RI basis sets are employed by default Notes 1 For the available fitting basis sets see the notes for keyword basis on page 32 2 The density fitting approximation can also be invoked by at taching the prefix DF or RI to the corresponding option of keyword calc see the description of calc Default dfbasis_cor auto for local correlation calculations i e localcc off dfbasis_cor none otherwise Examples 1 To use the cc pVTZ RI fitting basis in the correlated calcu lation for all atoms the input must include dfbasis_cor cc pVTZ RI 2 Consider the water molecule and use the cc pVTZ RI fitting basis set for the hydrogens and aug cc pVTZ RI for the oxy gen The following inputs are equivalent dfbasis_cor atomtype O aug cc pVTZ RI H cc pVTZ RI or dfbasis_cor aug cc pVTZ RI 3 Consider the water molecule and use the cc pVTZ cc pVTZ RI basis set fitting basis set for the hydrogens and aug cc pVTZ aug cc pVTZ RI for the oxygen in a local correlation calculation The following inputs are equivalent calc CCSD T localcc on basis aug cc pVTZ 46 dfbasis_scf aug cc pVTZ RI dfbasis_cor aug cc pVTZ RI or calc LCCSD T basis aug cc pVTZ 4 To run a DF HF calculation with the c
111. st and second row atoms the thresholds are excrad and 2 excrad respectively while the threshold is 2 5 excrad for heavier elements Options lt any positive real number gt Radius of the local fitting domains in bohr inf Infinite radius will be applied i e a conventional direct DF HF calculation will be executed Notes 1 Local fitting domains are only available for RHF and RKS wave functions 2 For average organic molecules with localized electronic struc ture excrad 5 0 is a good choice For more complicated sys tems bigger thresholds are recommended Default excrad inf Example to set a threshold of 5 0 bohr type excrad 5 0 excrad_ fin In DF HF calculations if excrad and excrad_fin differ an ex tra iteration is performed to get an accurate HF energy excrad fin specifies the radius of local fitting domains for the exchange contribu tion in this iteration step Options See the description of keyword excrad Default excrad_fin 1 5 excrad 59 Example to avoid the use of local fitting domains in the extra iteration step give excrad_fin inf freq Frequency for frequency dependent properties in atomic units avail able only with CrourR See Refs 9 and 11 for more details Options lt any real number gt Default freq 0 0 Example to set a frequency of 0 1 a u give freq 0 1 gauss Specifies whether spherical harmonic or Cartesian Gaussian basis func tions will be used Options spher Spherical harm
112. t The lowest according to orbital energy order n pieces of spatial orbitals the lowest n pieces of alpha and n pieces of beta spin orbitals for UHF semicanonical ROHF reference will be dropped Default core frozen Example to correlate all core electrons set core corr or core 0 dboc Diagonal Born Oppenheimer correction DBOC available only with CFOUR Options on or off Default dboc off Example for a DBOC calculation set dboc on dendec Selects the algorithm for the decomposition of energy denominators Cholesky decomposition or Laplace transform for canonical SOS MP2 and dRPA also required for SOSEX as well as for local MP2 and dRPA calculations The dRPA calculation is performed using the mod ified algorithm of HeBelmann 31 based on the decomposition of energy denominators For the calculation of the SOS MP2 energy in practice one dRPA iteration is performed with the aforementioned algorithm In the case of local MP2 and dRPA calculations the correlation energy contributions are also evaluated with the aid of the decomposition of en ergy denominators see Ref 26 The algorithm for the decomposition can be set using this keyword in all of the above cases The number of retained Cholesky vectors quadrature points can be controlled by keyword nchol Options Cholesky Cholesky decomposition will be used Laplace Laplace transform will be used Default dendec Laplace for SOS MP2 dendec Cholesky otherwise Notes
113. t d group 13 15 elements J Chem Phys 119 11099 2003 Kirk A Peterson Detlev Figgen Erich Goll Hermann Stoll and Michael Dolg Systematically convergent basis sets with relativistic pseudopotentials I Small core pseudopotentials and correlation con sistent basis sets for the post d group 16 18 elements J Chem Phys 119 11113 2003 Kirk A Peterson and Cristina Puzzarini Systematically convergent basis sets for transition metals II Pseudopotential based correlation 97 64 65 consistent basis sets for the group 11 Cu Ag Au and 12 Zn Cd Hg elements Theor Chem Acc 114 283 2005 Kirk A Peterson Detlev Figgen Michael Dolg and Hermann Stoll Energy consistent relativistic pseudopotentials and correlation consis tent basis sets for the 4d elements Y Pd J Chem Phys 126 124101 2007 Detlev Figgen Kirk A Peterson Michael Dolg and Hermann Stoll Energy consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf Pt J Chem Phys 130 164108 2009 James W Boughton and Peter Pulay Comparison of the Boys and Pipek Mezey localizations in the local correlation approach and auto matic virtual basis selection J Comp Chem 14 736 1993 Stefan Grimme Improved second order Maller Plesset perturbation theory by separate scaling of parallel and antiparallel spin pair corre lation energies J Chem Phys 118 9095 2003 Yousung Jung Rohini C Loch
114. t fifth rung functionals blending DFT and perturbation theory J Comp Chem 34 2327 2013 Pal Mezei Gabor I Csonka Adrienn Ruzsinszky and Mih ly K llay Construction and application of a new dual hybrid ran dom phase approximation J Chem Theor Comp 11 in press dx doi org 10 1021 acs jctce 5b00420 2015 Functionals were obtained from the Density Functional Repository as developed and distributed by the Quantum Chemistry Group CCLRC Daresbury Laboratory Daresbury Cheshire WA4 4AD United King dom contact Huub van Dam h j j vandam dl ac uk or Paul Sher wood for further information 100 92 R Strange F R Manby and P J Knowles Automatic code gen 93 94 95 96 i 97 98 99 100 101 eration in density functional theory Comp Phys Comm 136 310 2001 Stefan Grimme Jens Antony Stephan Ehrlich and Helge Krieg A consistent and accurate ab initio parametrization of density functional dispersion correction DFT D for the 94 elements H Pu J Chem Phys 132 154104 2010 Stefan Grimme Stephan Ehrlich and Lars Goerigk Effect of the damping function in dispersion corrected density functional theory J Comp Chem 32 1456 2011 Jeppe Olsen Poul Jorgensen and Jack Simons Passing the one billion limit in full configuration interaction FCI calculations Chem Phys Lett 169 463 1990 Mihaly K llay and P ter R Surj n Computing
115. tes in bohr atoms are specified by atomic symbols unit bohr geom tmol 4 0 00000000 0 00000000 0 00000000 H 1 82736517 0 00000000 0 00000000 O 2 41444411 2 68807873 0 00000000 0 3 25922198 2 90267673 1 60610134 H ghost Ghost atoms can be specified using this keyword e g for the purpose of basis set superposition error BSSE calculations Options none There are no ghost atoms serialno Using this option one can select the ghost atoms spec ifying their serial numbers The latter should be given in the subsequent line as lt ny gt lt Ng gt lt Nk gt lt N gt a where n s are the serial numbers of the atoms Serial num bers separated by dash mean that lt nz gt through lt n gt are ghost atoms Note that the numbering of the atoms must be identical to that used in the Z matrix or Cartesian coordinate specification but dummy atoms must be excluded Default ghost none 62 Examples 1 Rectangular HF dimer the atoms of the second HF molecule are ghost atoms geom H Fi RI H 2 R21A F3 R12A1iD R1 0 98000000 R2 2 00000000 A 90 00000000 D 0 000000000 ghost serialno 3 4 2 Ammonia the third hydrogen is a ghost atom note that the serial number of the hydrogen is 4 instead of 5 because of the dummy atom geom X NiR H 2 NH 1 AL H 2 NH 1AL3A H 2 NH 1 AL3B R 1 00000000 NH 1 01000000 AL 115 40000000 A 120 00000000 B 120 00000000 ghost serialno 4 gtol Threshol
116. the basis sets which are added to the GENBAS file will be optimized 18 You can perform unconstrained optimization when all the exponents and contraction coefficients are optimized except the ones which are exactly 0 0 or 1 0 Alternatively you can run constrained optimizations when particular exponents coefficients or all exponents and coefficients for a given angular momentum quantum number are kept fixed during the optimization The parameters to be optimized can be specified in the GENBAS file as follows 1 Unconstrained optimization no modifications are needed by default all exponents and contraction coefficients will be optimized except the ones which are exactly 0 0 or 1 0 2 Constrained optimization by default all the exponents and coefficients will be optimized just as for the unconstrained optimization To op timize freeze particular exponents or coefficients special marks should be used Examples e 2 use the mark without quotes if you want to keep an ex ponent or coefficient fixed during the optimization You should put this mark right after the fixed parameter no blank space is allowed If this mark is attached to an angular momentum quan tum number none of the exponents coefficients of the functions in the given shell will be optimized except the ones which are marked by use the mark without quotes if you want a parameter to be optimized Then you should put this mark rig
117. the electric field These properties are available via the CFOUR interface 13 2 Using the CFOUR interface anharmonic force fields and the correspond ing spectroscopic properties can be computed using numerical differen tiation techniques together with analytic first and or analytic second derivatives at all computational levels for which these derivatives are available see Sect 6 2 and 6 3 for a list of these methods 6 5 Diagonal Born Oppenheimer corrections Diagonal Born Oppenheimer correction DBOC calculations can be per formed using analytic second derivatives techniques with the following meth ods orbitals and interfaces Available methods 1 arbitrary single reference coupled cluster methods Refs 1 3 4 and 8 CCSD CCSDT CCSDTQ CCSDTQP CC n 2 arbitrary single reference configuration interaction methods Refs 1 3 4 and 8 CIS CISD CISDT CISDTQ CISDTQP CI n full CI 3 multi reference CI approaches Refs 2 3 4 and 8 4 multi reference CC approaches using a state selective ansatz Refs 2 3 4 and 8 Available reference states and programs RHF CFOUR UHF CFOUR 6 6 Electronically excited states Excitation energies first order excited state properties and ground to excited state transition moments can be computed as well as excited state geometry optimizations can be performed using linear response theory and analytic gradients with the following methods orbita
118. the inverse of the two center integral matrix is used Default dfalg invsqrt Example to use Cholesky decomposition set dfalg Cholesky dfbasis_cor Specifies whether the density fitting approximation will be used in the correlated calculations and also specifies the fitting basis set Options none The density fitting approximation is not used for the corre lated calculation lt basis set label gt atomtype special The density fitting approx imation is invoked and the specified basis set is used as fit ting basis set For the specification of the basis the same rules apply as for keyword basis see the description of keyword basis auto This option can only be used if Dunning s aug cc pVX Z Weigend and Ahlrichs def2 Peterson s cc pV X Z F 12 or aug ec pV X Z PP or Pople s basis sets are used as the normal ba sis set In this case if dfbasis_cor auto the density fitting approximation is invoked For the aug cc pV_X Z PP basis sets the corresponding aug cc pV_X Z PP RI basis sets will 45 be used automatically as the fitting basis sets while for a cc pV X Z F12 basis set the corresponding aug cc pV_X Z RI basis will be taken For the def2 basis sets also the corresponding RI basis sets will be used e g def2 TZVPP RI for def2 TZVPP def2 QZVPP RI for def2 QZVPP etc For Pople type mini mal and double basis sets i e STO 3G 3 21G 6 31G etc the cc pVDZ RI basis set while for triple ba
119. ty Amsterdam for the develop ment and maintenance of the DIRAC interface and for the permission to distribute the interface code e Professor P ter R Surj n E tv s University Budapest for his support at the early stages of the code development e Janos Br t n TU Budapest for continuous technical support Financial support to the development of the MRCC suite has been provided by the 91 Hungarian Scientific Research Fund OTKA Grant Agreement Nos T023052 T035094 T047182 T49718 D048583 NF72194 K108752 and PD108451 European Research Council ERC under the European Community s Seventh Framework Programme FP7 2007 2013 ERC Grant Agree ment No 200639 Hungarian Science and Technology Foundation Grant Agreement Nos IND 5 2001 and IND 04 2006 Bolyai Research Scholarship of the Hungarian Academy of Sciences Grant Agreement No BO 00593 07 New Hungary Development Plan project ID TAMOP 4 2 1 B 09 1 KMR 2010 0002 Lendiilet Program of the Hungarian Academy of Sciences References 1 Mih ly K llay and P ter R Surj n Higher excitations in coupled cluster theory J Chem Phys 115 2945 2001 Mih ly K llay P ter G Szalay and P ter R Surj n A general state selective coupled cluster algorithm J Chem Phys 117 980 2002 Mih ly K llay J rgen Gauss and P ter G Szalay Analytic first derivatives for general coupled cluster and configuration interaction m
120. ul optimization 7 Installation 7 1 Installation of pre compiled binaries After registration at the MRcc homepage pre built statically complied binaries are available in the download area To install these executables 20 Linux operating system and the 2 10 or later version of the GNU C Li brary glibc is required The binaries are provided in a gzipped tar file mrcc YYYY MM DD binary tar gz where YYYY MM DD is the release date of the program Note that you will find several program versions on the homepage Unless there are overriding reasons not to do so please always download the last version To unpack the file type tar xvzf mrcc binary tar gz Please do not forget to add the name of the directory where the executa bles are placed to your PATH environmental variable 7 2 Installation from source code To install MRCC from source code some version of the Unix operating system Fortran 90 and C compilers as well as BLAS basic linear al gebra subprograms and LAPACK linear algebra package libraries are re quired Please be sure that the directories where the compilers are located are included in your PATH environmental variable Please also check your LD_LIBRARY_PATH environmental variable which must include the directories containing the BLAS and LAPACK libraries After registration at the MRCC homepage the program can be down loaded as a gzipped tar file mrcc YYYY MM DD tar gz where YYYY MM DD is the release date
121. upied molecular orbitals Options off No orbital localization boys Boys localization is performed 113 pm Pipek Mezey localization is performed 114 IBO intrinsic bond orbitals of Knizia are constructed 115 cholesky localized orbitals are calculated by the Cholesky de composition of the one particle density matrix 116 Default orbloco off in the general case orbloco boys for local cor relation calculations Example to carry out Pipek Mezey localization for the occupied or bitals type orbloco pm orblocv Specifies what type of orbital localization is performed for virtual molecular orbitals Options All the options introduced for keyword orbloco excepting IBO also work for orblocv see the description of keyword orbloco for details In addition for local correlation calculations there is one more option pao Projected atomic orbitals Default orblocv off in the general case orblocv pao for local cor relation calculations Example to carry out Boys localization for the virtual orbitals type orblocv boys osveps Threshold for the occupation numbers of orbital specific virtual or bitals OSVs used at the evaluation of pair correlation energies in local MP2 and RPA calculations See the the description of keyword wpairtol for more details Options 74 lt any real number in the 0 1 interval gt Orbitals with occupation numbers smaller than this number will be dropped Default osveps 1e 3 Examp
122. vectors see Refs 95 96 and 1 useful for very large CI LR CC vectors follow Davidson diagonalization with root following recommended for excited state calculations if the initial guess is given man ually or the calculation is restarted Default diag david Example for root following type diag follow domrad Radius of atom domains for local correlation methods For each localized MO LMO using the Boughton Pulay procedure 63 we assign those atoms to the LMO on which it is localized Then for each LMO an atom domain is constructed in two steps the LMO is called the central LMO of the domain In the first step those atoms are included in the domain whose distance from the atoms assigned to the central LMO is smaller than domrad In the second step those LMOs are identified which are localized on the atoms selected in the first step and the domain is extended to include all atoms assigned to these LMOs Options lt any positive real number gt In the first step of the construction of atom domains all atoms whose distance from the atoms assigned to the central LMO is smaller than this number in bohr will be included in the domain inf Infinite radius will be applied i e there is only one atom domain including all atoms 53 Default domrad 10 0 Note To use the local CC methods as defined in Ref 20 set domrad inf that is use only one atom domain including all atoms Example to set a threshold of 12 0 bohr type d
123. y correlated wavefunc tions The atoms H He B Ne and Al Ar J Chem Phys 128 084102 2008 Thom H Dunning Jr and P Jeffrey Hay Gaussian basis sets for molec ular calculations in Methods of Electronic Structure Theory edited by Henry F Schaefer II volume 2 Plenum New York 1977 Florian Weigend Marco H ser Holger Patzelt and Reinhart Ahlrichs RI MP2 optimized auxiliary basis sets and demonstration of efficiency Chem Phys Lett 294 143 1998 Florian Weigend Andreas Kohn and Christof Hattig Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations J Chem Phys 116 3175 2002 Florian Weigend Hartree Fock exchange fitting basis sets for H to Rn J Comp Chem 29 167 2008 P Jeffrey Hay and Willard R Wadt Ab initio effective core potentials for molecular calculations Potentials for the transition metal atoms Sc to Hg J Chem Phys 82 270 1985 Willard R Wadt and P Jeffrey Hay Ab initio effective core potentials for molecular calculations Potentials for main group elements Na to Bi J Chem Phys 82 284 1985 P Jeffrey Hay and Willard R Wadt Ab initio effective core poten tials for molecular calculations Potentials for K to Au including the outermost core orbitals J Chem Phys 82 299 1985 Kirk A Peterson Systematically convergent basis sets with relativis tic pseudopotentials I Correlation consistent basis sets for the pos

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