CRYSCOR07 Beta Version 0.94 User's Manual C. Pisani(1), S
Contents
1. LMP2 Lagrangian orbital nonrelaxed Density matrix tolerance for evaluating the density matrix Lennard Jones contribution to energy only reducible WFf pairs with distance from the reference cell greater than DLJ1 and lower than d are used to calculate the L J coeff the contribution from all flower pairs between d and DLJ3 is evaluated L J calculation stops when the k th g star s energy contrib is smaller than 1 71 level of printing 15 2 11 Two electron integrals 2 11 1 Exact two electron integrals rec variable value meaning e A8 SCHWARZ Ko 2 el integrals Schwarz screening e 3I TS1 TS2 TS3 10 Schwarz tolerances 107 7 10 10 A8 DSCREEN Ko 2 el integrals coeff pre screening 3I TDi TD2 TD3 4 4 Density screening tolerances 10 7P 4 A8 INTREA Ko Read integrals from fortran unit f84 A8 AMPREA Ko Read amplitudes from fortran unit f91 A8 ASYMDOM Ko only vertical excitations are considered 2 11 2 Multipolar Expansion rec variable value meaning e A8 MULTIPO Ko Multip calc of 2 el intgrls for d lt dww lt da e I NMULTIP 4 Max multipole moment e A8 MULTDIST Ko optional redef of d e F DISTI 4 d A 2 11 3 Density Fitting For the DF theory in CRYSCOR see reference 10 11 15 2 12 Printing and plotting It may be useful to obtain printed or graphical information on some quantities of in terest Here are some suggestions for the use of the printing options The IPRINT variable controls the ge2. 0 00000038 0 00000038 0 00000029 0 00000029 0 00000029 0 00000022 l 0 00000023 0 00000023 0 00000017 0 00000023 0 00000023 0 00000017 l 0 00000015 0 00000015 0 00000011 l 0 00000012 0 00000012 0 00000009 l 0 00000010 0 00000010 0 00000008 Cycle Delta l ecorr e2 e2 grimme eio 3 0 00000079 0 03103997 0 03104076 0 03429214 It can be noticed that ecorr and e2 coincide within the assigned tolerance CONTOL 0 00001 and the calculation is terminated B 2 Lennard Jones contribution Lennard Jones extrapolated energy contributions LJ MP2 0 0000861623 LJ GRIMME 0 0000660520 HF ENERGY 8 0592434162E 00 HF MP2 LJ EN 8 0593295785E 00 HF GRIMME LJ EN 8 0593094681E 00 WARNING with the chosen tolerance on energy for at least one fl fl type all g stars have been used to calculate L J contributions 26 Bibliography 1 C Pisani M Busso G Capecchi S Casassa R Dovesi L Maschio C Zicovich Wilson and M Sch tz J Chem Phys 122 094113 2005 www cryscor unito it 2 www crystal unito it 3 G H Wannier Phys Rev 52 191 1937 4 C M Zicovich Wilson R Dovesi and V R Saunders J Chem Phys 115 9708 2001 5 P Pulay Chem Phys Letters 100 151 1983 S Saebg and P Pulay Chem Phys Lett 113 13 1985 6 www molpro net 7 R Dovesi V R Saunders C Roetti R Orlando C M Zicovich Wilson F Pascale B Civalleri K Doll N M Harrison P
3. 3130 0 1829 0 0050 2 10 2 20 BOND C 5 1 C 1 1d I 0 0007 0 3130 0 1829 0 0050 2 11 3 5 BOND C 8 18 C 4 1 I 0 0007 0 3130 0 1829 0 0050 2 11 3 6 BOND C 8 18 C 4 1 I 0 0007 0 3130 0 1829 0 0050 2 11 3 9 BOND C 8 18 C 4 1 I 0 0007 0 3130 0 1829 0 0050 2 12 4 3 BOND C 7T 2 C 3 4 I 0 0007 0 3130 0 1829 0 0050 2 12 4 4 BOND C 7 2 C 3 4 I 0 0007 0 3130 0 1829 0 0050 2 12 4 8 BOND C 7 2 C 3 4 I 0 0007 0 3130 0 1829 0 0050 Since in ACE there are 40 electrons per cell the total number of WnFs is 20 The symmetrization procedure generates two bunches of SAWnFs Bunch 1 comprises 8 single petal flowers which transform into each other through space group operation They are classified as of ATOMIC type and are associated to the 8 carbon atoms In fact they correspond to the CH bonds but since most of the charge is on the carbon atom this bonding character is not recognized this would happen by setting the variable TOLB activated by the KW TOLBON to a larger value than the default e g 0 4 Bunch 2 comprises 4 three petal flowers Each flower is centered in the middle of the bond of one of the 4 molecules and its three petals describe the triple bond The type of these SAWnFs is obviously BOND It is possible in this case to better clarify the 22 meaning of the symmetry labels Consider for instance the last WnF 2 12 4 8 BOND C 7 2 C 3 4 I 0 0007 0 3130 0 1829 0 0050 This WnF belongs to bunch 2 and to flower 12 in
4. 8 NOSYM12 11 NPAOSREA 15 OPERTOL 8 Output examples 19 OVLMETR 13 PAIR 8 PCALC 11 PGNEW 8 Plotting option 11 POLECORR 13 PRINPLOT 11 Printing option 11 SCHWARZ 12 SELECINT 14 STAR 8 STARDSTR 10 Symmetry adapted WF 6 SYMMFLAG 7 SYMMWEF 7 SYMVER 7 TESTDOM 10 Tests 23 TOBJ 8 TOLBON 7 TOLEAMPS 11 TOLEQPRS 11 TOLPRO 7 TOLSHL 7 Truncation criteria 8 Truncation tolerances 8 Two electron integrals 12 WPROJE 8 29
5. 99 0 888 END DSCREEN 0 001 0 001 888 ENDDF PRINPLOT MULTIPO 1 4 END PAIR END 8 12 TOBJ 0 001 0 001 END 20 General information In the output the number of AOs and WnFs is first reported followed by a list of the most important CRYSCOR parameters adopted in the calculation The case of ACE is reported below xo MP2 CORRELATION ENERGY Number of AOs 152 Number of WFs 20 2A 2A 2 2 kk ok 2A K 2 ok ok k koe ok ok ok ok ok 3K 2 22 oko ok ok ok kc oko ok ok k ok ajajajaja K gt K OE Input Parameters MAX N OF CYCLES 50 CONV ON ENERGY 1 0000E 05 PAIR DISTANCE WEAK 2 0000E 00 DISTANT 2 0000E 00 PAOs COEF TOLL 1 0000E 02 WFs COEF TOLL 1 0000E 02 ADJ GTF EXP FOR P g TRUNCATION 4 0000E 02 SCHWARZ TOL STRONG WEAK DISTANT 10 8 8 8 DSCREEN TOL STRONG WEAK DISTANT 10 8 8 8 MONKHORST SHR FACTORS 8 8 8 LEVEL OF PRINTING 1 EXCLUDE PAOs WITH NORM LESS THAN 10 1 DOMAINS DEFINED BY INPUT aggiungere la keyword FESO ORI 3k 2k 2k ak ak a 2K k ODIO ak alaba ak k 2K 2K 2K ak ak ak ak 2K ak 2K 9K K 9K ak ak kak a K K K Note that e the tolerance on the energy convergence is tight anyway it can be modified by the KW CONTOL e the meaning of PAIR PAIR DISTANCE is discussed in depth below e the WnF and PAO coefficient truncations are set to 10 7 KW TOBJ as previ ously explained which corresponds to rather poor tolerances for LiH the much better level 10 is adopted e the adjoined
6. GTF exponent k word PGNEW used in the recalculation of the one electron density matrix for generating PAOs is set to 0 04 which corresponds to high accuracy e the domains are defined by input KW MOLDOM the default being DOMCOE as used here for LiH e the other parameters are more technical see the Manual for information Information on WnFEs Basic information on the symmetry adapted WnFs provided by the Properties part of CRYSTAL is next reported as shown below for the case of ACE 21 aK 2k ak K 2k 2k ake gt K 2k k ad oleada 2 1 ok 1 222A ad gt K 2K ad 2A kk lea 2 2 2A ad 1 ad ad ad 2K ad EE 2 2 ad 2K ad EK ad al 2K 2K ad lle oe WF INFORMATION bunch flower flower petal type atom g atom g abs rel l 1 1 1 10 ATOMIC C 2 12 I 0 0011 0 3718 0 2109 0 0029 1 2 2 14 ATOMIC C 1 1 I 0 0011 0 3718 0 2109 0 0029 1 3 3 13 ATOMIC C 4 1 I 0 0011 0 3718 0 2109 0 0029 1 4 4 16 ATOMIC C 3 4 I 0 0011 0 3718 0 2109 0 0029 1 5 5 15 ATOMIC C 6 1 I 0 0011 0 3718 0 2109 0 0029 1 6 6 19 ATOMIC C 5 1 I 0 0011 0 3718 0 2109 0 0029 1 7 7 17 ATOMIC C 8 18 I 0 0011 0 3718 0 2109 0 0029 1 8 8 11 ATOMIC C 7 2 I 0 0011 0 3718 0 2109 0 0029 2 9 1 1 BOND C 6 1 C 2 12 I 0 0007 0 3130 0 1829 0 0050 2 9 1 2 BOND C 6 1 C 2 12 I 0 0007 0 3130 0 1829 0 0050 2 9 1 7 BOND C 6 1 C 2 12 I 0 0007 0 3130 0 1829 0 0050 2 10 2 12 BOND C 5 1 C 1 1d I 0 0007 0 3130 0 1829 0 0050 2 10 2 18 BOND C 5 1 C 1 1d I 0 0007 0
7. MP2 Equations mtb dr da d o PETI ce e 13 2 IMD2SEHSEBI 2o 209 S eh A et NA 3o eh e RE B aon d e Ss as 14 29 1 Paus Partitioning S Sauce dose E UR AR Med ard de Rm 14 2 9 2 Freezing of Indices uie oso Iu ouo oe RE ee B we 14 2 10 Beyond MP2 energy L1 6x9 ER Ge DRE ERR a ee 15 2 11 Two electron integrals u i293 e y fees E eer S reed gts 16 2 11 1 Exact two electron integrals 16 2 11 2 Multipolar Expansion 33 39x24 ge hb A DA 16 2 l 3 Density Fitting lt secou S ece dinen g an edet od 16 2 12 Printing and plotting sida go ee a 16 A Input Examples 18 B Output Examples 20 B 1 Commented Output esa A OSE OE DS ES ERE ES 20 B 2 Lennard Jones contribution 0 0 20 002 00 26 Chapter 1 Introduction CRYSCOR isa post Hartree Fock HF local correlation program for non conducting crystals 1 It can be considered as the post HF option of the CRYSTAL program 2 since the good reference HF solution for the crystalline systems is provided by this code The post HF method currently implemented is a perturbative method namely M ller Plesset at the second order MP2 Well localized symmetry adapted Wannier functions 3 4 WnF are adopted instead of delocalized Bloch functions this permits the exploita tion of the short range nature E x R of electron correlation following the general Pulay scheme 5 as implemented in the molecular MOLPRO code 6 Its generaliza tion to periodic 3 dimensional syst
8. a total counting and 4 within its bunch it is found at the 8 th place in a list including the 20 WnFs The two atoms involved in the bond the main atoms of this WnF are C 7 in the crystal cell 2 and C 3 in the crystal cell 4 For each WnF the participation according to a Mulliken partition of the various shells of its main atoms in its definition is provided in the line below For instance in the first WnF bunch 1 flower 1 petal 20 which has only one main atom C 2 in the crystal cell 12 the participation of the 4 shells of C 2 are 0 0011 0 3718 0 2109 0 0029 showing that this WnF has a hybrid sp character The case of LiH is much simpler in the present respect since it has only two va lence electrons per cell hence only one WnF of atomic type and centered in H essentially of s character 1 1 1 1 ATOMIC H 1 1 I 0 0858 0 1675 0 7537 0 0000 0 Information on the shape of WnF domains is next reported Since all petals in the same flower have the same domain this information concerns the different flowers Consider first the case of ACE FLOWERS DOMAINS FLOW n 1 Atom 2 C n of G 1 12 Atom 6 C n of G 1 gt 1 Atom 10 H n of G 1 gt 12 Atom 14 H n of G 1 gt 1 FLOW n 2 Atom 1 n of G 1 gt 1 Atom 5C n of G 1 1 Atom 9H n of G 1 gt 1 Atom 13 H n of G 1 gt 1 FLOW n 3 Atom 4 C x n of G 1 1 Atom 8 C n of G 1 18
9. atom at point B BL BM BN indices direct lattice input as reals of the cell where the atom is located IC label of the atom at point C CL CM CN indices direct lattice input as reals of the cell where the atom is located 17 Appendix A Input Examples 1 Input barebone NEWK 888 Monkhorst shrinking factors for CRYSTAL eigenvalues calculation 10 Fermi Energy recalculation and no printing option switched on MEMORY 1000000 END 2 Suite Input NEWK 16 16 16 00 MEMORY 1000000 COREQ 1 CONTOL 10 0 0001 DOMPUL 0 98 PAIR 4 4 TOBJ 0 005 0 005 SCHWARZ 888 DSCREEN 888 END 3 Input for the Domain definition NEWK 888 10 MEMORY 1000000 DOMDEF ATOMS 16 1 15 123456789 10 11 12 14 15 16 domain are defined in terms of atoms number of flowers first flower 15 atoms selected atoms in distace order from the HHHH flower centroid 2 15 123457815 16 10 24 27 23 26 29 3 15 16 15 123456780910 11 12 13 14 15 PAIR 4 6 TOBJ 0 005 0 005 END 18 4 Printing and Plotting Input PRINPLOT 1 WF 43 1258 END ATOMS Level of printing KW WnF printing and plottinf of the Wannier functions AQs coef are printed in 4 g vectors WnFs are plotted including AOs coef of the first 3 stars of g vectors selected g vectors printing see CRYSTAL manual MAPN option end of CRYSTAL MAPN option 5 Density Fitting Input DFITTING 8 12 STDBASIS VTZ ENDDF Inpu
10. description without modifying the HF or DFT solution The last item refers to the possibility of freezing the SCF procedure no need to go to convergence and is essential for CRYSCOR It can be activated by inserting in the third last CRYSTAL input block the keyword as follows rec variable valuemeaning e A8 GUESSDUAL Ko activate the option e 2I NFRAG number of insertions as classified below CYCLZ 0 for a complete calculation and 1 if the calculation is stopped at the zero cycle no diagonalization of the Fock matrix is performed for each I 1 NFRAG insert the following keywords e NI IRRAT I label of the irreducible atom geometry input order whose basis is changed STSH I number of the shell of the atom IRRAT I after which the insertion is made NUMSH I number of shells added if NUMSH is positive or deleted if NUMSH is negative after the shell STSH I WARNING Note that being a restart option the GUESSDUA keyword needs the fortran unit fort 20 which is a copy of the fort 9 to restart the calculation of the modified basis from the original one WARNING To run CRYSCOR calculation the GUESSDUA option has to be used by freezing the SCF procedure at the zero cycle CYCLZ 1 For further information on the GUESSDUA option refer to the CRYSTAL 2 manual 2 7 2 DUALBAS The dual basis set option in CRYSCOR is activated by the keyword DUALBAS it is mandatory to put the DUALBAS keyword before the NEWK one To r
11. domains used in the generation of WW pairs e F mindom pop 0 1 only those atoms are included whose WnF population is gt mindom pop e A8 MAXDOM Ko Setting the maximal number of atoms in the WnFf do mains e F maxdom 60 maximal number of atoms that can be included in a single WnFf domain 2 6 2 DOMCOE The domain of the i th WnF is specified as comprising all atoms which contain at least an AO x such that the coefficient c is larger in absolute value than a prescribed value by default TDOM 0 01 TDOM can be changed by activating the keyword DOMCOE This default setting is usually inadequate on the other hand assigning very low values to TDOM may lead to domains which are too large with very high computational cost or have strange shapes rec variable value meaning e A8 DOMCOE Ko standard domains DEFAULT e F TDOM 0 01 include atom if at least one of its coeff is gt TDOM 2 6 3 DOMPUL A definition which is chemically more sensible is provided by the Boughton Pulay BP criterion a sort of Mulliken population analysis is performed for each WnF by looking how much of it out of a total of 1 is provided by the different atoms these are included in the domain in order of decreasing contribution until the domain contains a preset fraction WFPOP of the total WnF population Note that atoms which are equivalent by symmetry with respect to the WnFf and contribute therefore the same population are all included
12. meaning A8 OPERTOL Ko active region F I TOLOR NFAC 0 01 6 tolerance for cutting the coefficients multiplication fac tor for the distance A8 STAR Ko MMMCGO redefinition I NSTAR n star of g vectors 2 6 WnF domain definition The definition of the WnF domains that is the atoms and consequently the PAOs associated to each WnF is crucial to the accuracy and cost of the calculation Several definitions are possible Note however that WnFs which belong to the same flower have the same domain Therefore the definition concerns only the different flowers their reference number and the relevant information is printed by PROPERTIES at the end of the localization procedure look at the string WnF INFORMATION Several possibilities exist to properly define the WnFf domains as will be commented in the paragraphs below 2 6 1 General definition Flower domains can be defined according to different criteria e atomic coefficients in the WFs expansion DOMCOE see 2 6 2 e atomic population in the WFs DOMPUL see 2 6 3 e atom distacences from the WF centroids DOMDEF see 2 6 4 e molecular domain MOLDOM see 2 6 5 In all the cases flower kernel domains are defined and used for the generation of WW pairs According to the ATOMIC or BOND flower character these domains contain one single atom or the two atoms involved in the bond respectively There are two general keywords rec variable value meaning e A8 MINPOP Ko Design minimal
13. AR 1 NSTAR Which stars from WnFf center 2 7 Dual Basis Set In the study of extended systems the use of diffuse basis sets is limited by the incoming of linear dependencies in the overlap matrix On the other hand a correct description of the virtual manifold often achieved with extended basis sets plays a crucial role in electron correlation calculations To overcome this problem a dual basis set option has been implemented in which two different basis set are used the first one called ref is used for the calculation of the HF reference solution that is to generate the WFs the second one improved with as many diffuse functions as we want called mod is used in the correlation calculation to generate PAOs and to perform the MP2 equations The procedure is the following 1 a CRYSTAL PROPERTIES calculation with the ref basis set to obtain the reference WFs fort 80 2 a CRYSTAL calculation with the mod basis set and the GUESSDUA keyword on see 2 7 1 to get all the quantities of interest in the new basis set fort 9 3 a CRYSCOR calculation with the DUALBAS keyword on see 2 7 2 for details 2 7 1 GUESSDUA The keyword GUESSDUA is a restart option of CRYSTAL that could be useful in the following cases 1A Meyer Simulazione di epi layer ossidici su superfici metalliche con tecniche quanto meccaniche periodiche 2006 2007 Thesis 11 e in a basis set optimization procedure e to improve the virtual manifold
14. Atom 12 H n of G 1 gt 1 Atom 16 H n of G 1 18 FLOW n 11 Atom 4 C n of G 1 gt 1 Atom 8 C n of G 1 18 Atom 12 H n of G 1 1 Atom 16 H n of G 1 18 FLOW n 12 Atom 3 C n of G 1 gt 4 Atom 7 C n of G 1 2 Atom 11 H n of G 1 gt 4 Atom 15 H n of G 1 gt 2 23 Since the KW MOLDOM has been used the domain of each of the 12 flowers coincides in this case with the molecule to which its main atoms belong For instance the domains of flowers 8 and 11 coincide because they are located on the same molecule For the case of LiH the output is as follows xx FLOWERS DOMAINS FLOW n 1 Atom 1H n oG 13 1 3 13 9 7 5 10 11 4 6 8 12 2 Atom 2 Li on of G 6 8 12 2 40 26 30 Here the KW DOMDEF has been used From the input we see that just one domain has to be defined the WnF 1 is involved the only one to which three stars of neigh bors are assigned they are specified in the following card star 1 which contains one H atom star 2 which contains six Li atoms star 3 which contains twelve H atoms for a total of 19 atoms The list of the atoms of either type in the domain and the crystal cell to which they belong are reported Classification of WnF pairs As previously said PAIR serves to classify WnF pairs according to the distance Dist between the corresponding core domains This classification concerns in fact pairs of
15. CRYSCORO7 Beta Version 0 94 User s Manual C Pisani 1 S Casassa 1 L Maschio 1 M Halo 1 M Schiitz 2 D Usvyat 2 1 Theoretical Chemistry Group Universit di Torino Torino Italy 2 Institute for Physical and Theoretical Chemistry Universit t Regensburg Regensburg Germany September 11 2008 Contents 1 Introduction 2 LI E netianality 375 2 S047 le dem acu sai Sk Ie ee 2 T2 Howto run GRY SCOR 4 ei ied En degree ORIS Ner y WEM a 2 13 Notes on the Beta Version s 3 1 4 Acknowledgments ur Sue ia a dod XT eee 3 2 Input instructions 4 2 L Input format 202a PA UEXq s Lut ca Erin ees Qs tk 4 2 1 1 Typographical conventions and acronyms 5 2 2 Symmetry adapted WnF o 6 2 3 General CRYSCOR keywords 8 2 4 Truncation criteria and tolerances 8 2 5 Active Spatso ias E S A Boe ades 8 2 6 WF domain definition 4 4 mu weg RU CE e xr EP dens 9 2 6 1 General definition subo vox EG ORE ex eee sh de 9 203 DOMCOE i zw bue grotte ese STEIN E k 9 20 30 DOMPUL 0 he ee ata e SALA S APO P3 10 264 IDIOOMDEBEL 2 oS nae Revie E rrr e er eee ec RE eame 10 20 57 MOLDOM os es ato Hla dae ck Gg PIE Me Edu ux d 10 2 0 0 TES DOM era uter eoe a ag eae Be Boe e AA 10 Zw Dual Basis Sell ouis temm Beg Tem Schau PS PER Him E 11 20654 GUESSDUA a a M gates zoe Roue lei g tebe gie SPR 11 25 2 DUALBAS wel s amt bn ds EH nA 12 2 5
16. WnF flowers since the domains of all WnFs in a flower coincide Also only the symmetry irreducible pairs are classified In the case of ACE the core domain is either the C atom to which the CH bond belongs for atomic WnFs or the two bound C atoms for bond WnFs and we have set from input disti 2 A dist2 8 A The part of the output which reports the classification by distance is as follows Strong pairs 3 Weak pairs 7 Distant pairs 9 n of irr pairs classified 19 Flower Flower Pairs summary pair fi f2 ig npi np2 Dist DistC Type Integrals 1 1 1 1 1 1 0 0000 0 0000 Strong Exact 2 1 9 1 1 3 0 0000 1 2964 Strong Exact 3 9 9 11 3 3 0 0000 20 0000 Strong Exact 4 1 3 1 1 1 3 2886 3 7387 Weak Exact 5 1 5 tg 1 1 1372 2 4944 Weak Exact 6 1 8 1 1 1 3 0980 3 4502 Weak Exact 7 1 11 1 1 3 3 9336 4 7133 Weak Exact 8 1 12 1 1 3 3 8784 4 6621 Weak Exact 9 3 9 1 1 3 3 0980 3 1529 Weak Exact 10 9 10 1 3 3 3 8784 3 9373 Weak Exact 11 1 2 1 1 1 4 8462 5 6172 Distant Multipolar 12 1 6 11 1 1 4 8016 5 4295 Distant Multipolar 13 1 10 1 1 3 4 8016 5 0726 Distant Multipolar 14 1 1 2 1 1 5 5682 6 1020 Distant Multipolar 15 1 5 2 1 1 4 9921 5 0874 Distant Multipolar 16 1 9 2 1 3 5 1617 5 1615 Distant Multipolar 17 3 2 2 1 1 5 3656 5 7997 Distant Multipolar 18 3 10 2 1 3 5 7211 6 5340 Dista
17. alue meaning e A8 MOLDOM Ko molecular domain 2 6 6 TESTDOM It may sometimes be useful to have a preliminary look at the possible shapes of the domains without performing a calculation This possibility is provided by activating 10 the keyword TESTDOM The coordinate and types of the atoms in each domain are stored on Fortran unit 17 in xyz format for visualization and the computation stops Moreover the composition of the different stars their distance from the WnFf center etc are printed in the output file so allowing further selection look at the string DOMAIN INFORMATION Two choices are possible Either the same number of stars and the same sequence are used for each domain keyword ALLEQ or differences are allowed between the different domains keyword NONEQ In the former case only one variable NSTAR and one vector ISTAR must be defined In the latter case domains are generated following the same criterion as for DOMDEF rec variable value meaning e A8 TESTDOM Ko Test run for WnFf domains domain STOP after defin ing WnFf domains insert one of the following set of cards I or Il _______ e A8 ALLEQ all WnFf domains are equal eI NWFDOM N WnFf domains to define e I NSTAR number of stars e 201 ISTAR 1 NSTAR which stars from WnFf center CST e A8 NONEQ different WnFf domains eI NWFDOM N WnFf domains to define LL for each WnFEf N 1 NWFDOM insert the following keywords e 21 NWF NSTAR Which WnFf nunmber of stars 201 IST
18. c proce dure read WnFs from a previous run fort 88 default value save WnFs on fortran unit fort 88 after symm adap do not perform the re wannierization step after symm adap do not perform the re wannierization and re orthogonalization steps redefinition of the tolerance to classify WnFs as bond or atomic if abs pop 1 pop 2 lt tolb then it is a bond WnF where pop is the atomic population and 1 2 are the two main atoms WnF symmetry is verified by means of scalar products per formed in a number of crystal cells defined by g max MMMGO value of g max 1 define the level printing level end of SYMMWE block With reference to the input file some comments can be done e The last two options of the SYMMFLAG keyword IFSAVE 2 3 are intended to maximally preserve the WnF symmetry to a small detriment of the local character 2 3 General CRYSCOR keywords rec variable value A8 NEWK KM I IS I ISP I IFE 0 1 NPR A8 MEMORY KM I IMEM A8 PGNEW Ko F EXAD A8 WPROJE KT A8 END KN meaning CRYSTAL HF eigenvectors calculation at a number of k point in the reciprocal space shrinking factor for reciprocal space net Monkhorst net The num ber of k points where the Fock KS matrix is diagonalized is roughly proportional to 15 P M MYV F where IDIM denotes the periodic di mensionality of the system and MVF denotes the number of point symmetry operators shrinking factor of the secondary recipro
19. cal space net Gilat net for the evaluation of the Fermi energy and density matrix no Fermi energy calculation is performed Fermi energy is computed by performing integration on the new k points net number of printing options to switch on not active memory allocation allocation in KBytes recompute the CRYSTAL Density Matrix P according to the given tolerance adjoned GTF exponent for P truncation density matrix P from PAO projection to end main input stream 2 4 Truncation criteria and tolerances rec variable e A8 CONTOL e IF MAXC CONV e A8 TOBJ e 2F TWF TPAO e A8 PAIR e 2I DIST1 DIST2 e A8 COREQ e I JNORM e A8 LONTOL e F TOLS e A8 DELPAO e I N e NI NP 1 N 2 5 Active Space value meaning Ko SCF convergence criteria 10 0 000001 Max number of cycles tol on energy difference Ha Ko Truncation of WnFs and PAOS 0 001 0 001 Ko strong weak distant WW pairs 5 11 0 0 es d d d di da A Ko exclude evanescent PAOs 1 elimin PAOs with norm 10 7NORM Ko truncation of LON 0 01 tolerance on the LON overlap matrix Ko exclude the selected PAOs from the virtual space num of PAOs to eliminate PAOS to eliminate These keywords reduce the dimension of the active space that is the extension of the crystalline system with a sensitive saving of computational cost However both the keywords are delicate especially in the case of periodic Density Fitting DFP rec variable value
20. d SYMMWF The related information is stored in fortran unit fort 80 that must be saved at the end of the run properties lt crystal input3 filename gt properties output3 filename C the CRYSCOR calculations are to be run in the directory containing the fort 9 and fort 80 fortran units as follows cryscor lt cryscor input filename gt cryscor output filename Suggested file extensions for input and the output are summarized in table 1 1 ipu e Tompu e crystal properties ju cryscor 84 91 sec 2 11 f131 sec 2 9 2 Table 1 1 Input and output standard file names 1 3 Notes on the Beta Version CRYSCOR is linked to the public version of CRYSTAL pub 1 0 1 With respect to the standard release this source contains the DUAL BASIS option see manual 2 7 2 and an update version of the localy_sym subroutine d The density fitting option is in progress a reliable version will be provided soon 1 4 Acknowledgments The authors are greatful to Prof Claudio Zicovich Wilson and to Prof Roberto Dovesi Chapter 2 Input instructions 2 1 Input format The Input consists in a series of keywords KW possibly followed by the respective arguments to be written in separate cards card 1 card 2 in free format as shown in the following sections Not all KWs are necessary the ones that are mandatory are marked as KM the others as Ko The ones marked with KT are technical keywords used by the
21. developers of the code For the parameters defined by optional Keywords Ko default values are provided by CRYSCOR as indicated in square brackets A typical CRYSCOR input file looks as follows table 2 1 the order of KWs is practically free but some conditions must be NEWK CRYSTAL eigenvalue calculation 12 12 12 00 MEMORY gt Memory required kbytes 1200000 DOMDEF gt Definition of the virtual space 1 13 123 PATR gt Definition of the occupied space 22 TOBJ gt Tolerances 0 01 0 01 END END Table 2 1 CRYSCOR input sample respected e g 1 NEWK must be the first Input card 2 MEMORY must be the second keyword 3 DFCHECK requires DFITTING to be present and exact integrals to be available on F84 unit 4 INTREA requires integrals to be available on F84 unit 5 AMPREA requires amplitudes to be available on F91 unit The description of the input is subdivided into sections which control different parts of the code Inside each sections the meaning of KWs and of the respective parameters is summarily indicated in an input deck then detailed explanations suggestions and comments are added and some input examples are provided 2 1 1 Typographical conventions and acronyms In the description of the input data which follows the following typographical conven tions are adopted e new record default values il suggested values Moreover some acronyms will be used AO Atom
22. ems requires a full use of both point and transla tional symmetry Actually the localization procedure and the MP2 method itself are not suitable for conducting systems 1 1 Functionality e density fitting technique for the evaluation of 2 electron integrals 10 11 e use of dual basis set e evaluation of long range energy contributions by means of Lennard Jones ex trapolation technique e two different schemes to perform the MP2 correction to HF density matrix 12 13 1 2 How to run CRYSCOR To execute a CRYSCOR job you ought to run before two CRYSTAL calculations for more details about the CRYSTAL code please refer to Crystal User s Manual 7 and CRYSTAL web site www crystal unito it On Unix systems CRYSCOR and CRYSTAL is accessed using directly the cryscor executable crystal and properties Syntax and procedure are outlined in the following paragraphs A crystal executable performs a wave function calculation Geometry and symme try information Fock and density matrix canonical eigenvalues and eigenvectors are stored on fortran unit fort 9 that must be saved at the end of the run 2 crystal lt crystal input12 filename gt crystal_output12_filename properties executable calculates on request a number of quantities of inter est By means of the LOCALI keyword localized Wannier functions WnF are calculated from the subset of occupied delocalized crystalline orbitals and sym metrized 9 keywor
23. h D Arco M Llunell CRYSTAL06 User s Manual Universit di Torino Torino 2006 8 C Pisani G Capecchi S Casassa L Maschio Mol Phys 103 2527 2005 9 S Casassa C Zicovich Wilson and C Pisani Theor Chem Acc 116 726 2006 10 L Maschio D Usvyat C Pisani F Manby S Casassa and M Sch tz Phys Rev B 76 075101 2007 11 D Usvyat L Maschio F Manby M Sch tz S Casassa and C Pisani Phys Rev B 76 075102 2007 12 C Pisani S Casassa L Maschio Zeit Phys Chemie 220 913 2006 13 S Casassa M Halo L Maschio C Roetti and C Pisani Theor Chem Acc 117 781 2007 14 S Grimme J Chem Phys 118 9095 2003 15 L Maschio and D Usvyat Phys Rev B 78 073102 2008 27 Index AMPREA 12 ASYMDOM 12 CONTOL 8 COREQ 8 COVVV 12 DELPAO 8 Density Fitting 12 DENSMAT 11 DF performance 14 DFCHECK 14 DFITTING 13 DFSCHW 13 DOMCOE 9 DOMDEF 10 DOMDEF2 10 DOMONLY 15 DOMPUL 9 DOMREA 15 DSCREEN 12 END 7 8 ENVPAIR 15 EQALG 11 FIXDOM 15 FIXNPAOS 15 FORCE 7 Freezing of Indices 15 Gilat net 8 Input example 16 Input instructions 4 INTREA 12 LENJONES 11 Local periodic MP2 theory 2 LONTOL 8 MAXDOM 9 MEMORY 8 MINPOP 9 MOENPAIR 15 MOLATOMS 15 28 MOLDOM 10 MOLPAIR 15 Monkhorst net 8 MP2 equations 11 MP20LD 11 MPREAD 12 MULTDIST 12 MULTIPO 12 Multipolar Expansion 12 NEWK
24. ic Orbital centered on atom obtained as a linear combination of Gaussian type orbitals GTO WnF Wannier Functions basis set of the occupied manifold WnFf Flower of Wannier Functions group or single WnF which form a basis for a representation of point group operators and share the same center 9 PAO Projected Atomic Orbitals basis set of the virtual space FF Fitting Function for the Density Fitting approximation of two electron integrals 2 2 Symmetry adapted WnF An input file for the properties part of CRYSTAL namely those with the extension d3 see section 1 2 step B and table 1 1 has to be prepared in order to obtain well localized and symmetry adapted WnFs The definition of WnFs is controlled by an input block opened by LOCALWF and containing a set of keywords as VALENCE explained in the Crystal User s Manuall7 The a posteriori symmetrization procedure mandatory in the case of a subsequent MP2 calculation is activated by SYMMWTF The procedure 9 can be briefly outlined as follows 1 WnFs are classified depending on the number of atoms that most contribute to it on the basis of the atomic population analysis in particular WnFs will be defined bond or atomic if the charge density is mainly concentrated on one or two atoms respectively These atoms will be referred in the following as main atoms according to both shell population and symmetry properties of the main atoms WnFs are grouped int
25. in the domain or all excluded The BP criterion is adopted by activating the keyword DOMPUL rec variable value meaning e A8 DOMPUL Ko Boughton Pulay BP domains e F WFPOP 0 98 total WnF pop in BP domain 2 6 4 DOMDEF A more specific tailoring of WnFf domains is possible by activating the following key words For each WnFf stars of equivalent atoms are included in the domain the total number of stars and the identification labels of the different stars included in order of increasing distance from the WnFf center are indicated by the variable NSTAR and the vector ISTAR respectively see examples in the Appendix A very useful keyword in the case of molecular crystals is MOLDOM for each WnF it defines on the basis of atomic connectivity a domain corresponding to the molecular unit rec variable value meaning e A8 DOMDEF Ko Design WnFf domains by stars of atoms e I NWFDOM number of WnFf domains to define for each WnFEf N 1 NWFDOM insert the following keywords e 21 NWF NST Which WnFf n stars to be included 201 ISTAR 1 NST which stars of atoms according to a distance criteria with respect to the WnFf center A8 DOMDEF2 Ko Design WnFf domains by atoms I NWFDOM number of WnFf 201 IATS 1 NWFDOM how many atoms closest to the WnF s centers to be included in the domains If needed additional atoms are automatically added to fill the stars of atoms 2 6 5 MOLDOM Recommended for molecular crystals rec variable v
26. neral level of printing It is advisable to keep it at its default value 1 If IPRINT is set to gt 1 however Detailed information on some specific items can be collected if one of the follow ing KWs general name item is activated after the IPRINT card WF FWF PAO SPAO FPAO LON SLON FLON as illustrated below An item END card must be inserted to end the printing section of the Input either immediately after the IPRINT card or group of the other item s cards 16 rec variable value meaning A8 PRINPLOT Ko Define printing options I IPRINT 1 General level of printing A8 item Ko Print plot info on item END WF FWF PAO SPAO FPAO LON SLON FLON DOMAIN if item END then end print sect else read in a sequence 21 NPRG IGPLT the AOs coeff of N P RG crystal cells are printed in the output file n of star of g vectors to be used in the plot data stored on fort 25 nl NG 1 NG 2 selected crystal cells for the printing option if IGPLT 0 then insert MAPNET cards see also Crystal User s manual 7 I3 NPY number of points on the B A segment enter a keyword to choose the type of coordinates_____________ COORDINA XA YA ZA cartesian coordinates of point A XB YB ZB cartesian coordinates of point B XC YO ZC cartesian coordinates of point C or O ATOMS IA label of the atom at point A AL AM AN indices direct lattice input as reals of the cell where the atom is located IB label of the
27. nt Multipolar 19 9 9 2 3 3 5 5241 6 1020 Distant Multipolar There are three strong pairs d 0 seven weak pairs 0 lt d lt dist1 nine distant pairs disti d lt dist2 for a total of 19 irreducible pairs Pairs separated by more 24 than dist2 are considered very distant and they are neglected in the local approach The table provides information on the pairs considered the label which identifies each pair pair the first 1 and second 2 flower involved the number of the cell where the latter is located ig the first flower is always in the reference 1 cell the number of petals np1 and np2 of each flower Apart from the distance between the two core domains Dist also the distance between the respective centers DistC is reported For instance pair 2 involves an atomic flower 1 petal and a bond flower 3 petals belonging to the same molecule For them Dist 0 DistC 1 2964 A half the length of the C C bond Finally their classification according to distance Type and the way the respective integrals are treated Integrals are reported Concerning this point it can be observed that strong and weak pairs are always treated in the same approximation so that this distinction is purely formal for the moment being In the present case since the DFITTING option has not been activated these integrals are evaluated exactly while in the LiH case they are calculated with the DF tech nique On the co
28. ntrary the integrals of distant pairs are evaluated in a multipolar approximation because in both cases the MULTIPO option has been activated SCF information The SCF MP2 calculation is next started Cycle by cycle the contribution to the MP2 correlation energy from each pair is re ported along with the total energy This is exemplified below for the case of ACE first cycle Cycle number 1 SO ee fine a3 Sh eee ee eee ee et pair deg petals ecorr e2 e2 grimme rn 1 8 0 02349892 0 02351009 0 02819870 2 16 0 01497798 0 01441493 0 01249024 3 4 0 13324567 0 12853852 0 13285143 ea 4 48 0 00001406 0 00001393 0 00001082 5 8 0 00046131 0 00041999 0 00038185 6 48 0 00002349 0 00002356 0 00001826 7 48 0 00002082 0 00001951 0 00001601 8 48 0 00002201 0 00002067 0 00001691 l 0 00011116 0 00010614 0 00008839 l 0 00010512 0 00009339 0 00008167 0 00000141 0 00000137 0 00000108 0 00000158 0 00000153 0 00000121 0 00000584 0 00000539 0 00000448 l 0 00000068 0 00000067 0 00000052 l 0 00000177 0 00000175 0 00000135 l 0 00000455 0 00000426 0 00000349 l 0 00000095 0 00000094 0 00000072 0 00000244 0 00000229 0 00000187 l 0 00000914 0 00000817 0 00000701 Cycle Delta l ecorr e2 e2 grimme ero 1 0 02908339 0 97965131 0 95056792 0 97187614 This table provides the local MP2 correlation energy fo
29. o subsets the symmetry of each subsets is verified in the case of subsets composed of non symmetry related WnFs the WnFs are projected into the sub space defined by the point group of the subsets a sub group of the crystal point group Each WnF becomes a representative function of one of the rows of the irreducible representation IRREP of the sub group As a result of this procedure each WnF is classified by four index b f p g bunch flower petal and crystal cell such that a general symmetry operator W of the crystal applied to a WnF gives W b p 8 E Ty A new set of optional keywords permits us to control and optimize the procedure so bsp ye that an input file for the acetyl crystal can look like this NEWK 444 10 LOCALWF SYMMWF END VALENCE CYCTOL 234 BOYSCTRL 8 8 100 WANDM 24 1 FULLBOYS 6 END END begin of the localiz the symm adap proc is switch on end of the symm input block localiz keywords db dk Gt HHH end of the local input block end of the properties input block rec variable e A8 SYMMWF e A8 SYMMFLAG e I IFSYM I IFSAVE A8 TOLBON F TOLB e AB SYMVER I MMG A8 PRINT I NPRINT A8 END value Ko Ko 0 a w NR 0 2 Ko meaning symmetry adaptation of WnFs activate symmetrization options Foster Boys loc procedure followed by WnFs symmetry adap WnFs symmetry adaptation and then Foster Boys lo
30. pe are included strong weak distant WW pairs where both WnFs do not have the molecule atoms in the domains environment WnFs 0d dizda da oo d da A If DIST1 DIST2 are 0 no pairs of this type are included strong weak distant WW pairs between the environment and molecule WnFs 0 d d d2 d2 00 d d2 A If DIST1 DIST2 are 0 no pairs of this type are included 2 9 2 Freezing of Indices All these keywords can be used for consistency in geometry optimization and work correctly if the order of WnFs in different geometries is the same rec variable A8 FIXDOM Ko A8 FIXNPAOS Ko A8 DOMREA Ko A8NPAOSREA Ko A8 DOMONLY Ko value meaning Saving the information on the domains and on the number and type of the pairs in the file fort 131 Saving the number of the redundant PAOs for each pair in the file fort 132 Reading the information on the domains and on the number and type of the pairs from fort 131 Reading the number of the redundant PAOs for each pair from fort 132 Does not perform the actual LPM2 calculations Obtains the information on the domains pairs redundant PAOs and stops 14 2 10 Beyond MP2 energy rec A8 PCALC 21 IFFPAIR TOL_P A8 DENSMAT F THR DENS A8 LENJONES F di DLJ1 lt d variable F DLJ3 F TOLLJ I IPRINT value Ko Ko 1078 Ko 20 meaning MP2 Density matrix n of WnFf pairs in local space and Tol on Wannier coeff
31. r each pair deg is the de generacy of the pair due to the symmetry classification petals is the product of the number of petals of the two flowers ecorr and e2 are the pair correlation energies at the given SCF cycle the latter includes the contribution of the residues the former not see equation 7 of Ref 1 at convergence the two must coincide e2 grimme is the correlation energy obtained after a straightforward correction according to the Grimme method 14 The sum of the contributions from the different pairs of flowers multiplied by the respective degeneracy deg is reported in the last line Delta ecorr e2 gives an indication of the distance from convergence 25 The corresponding section of the ouput for the last cycle of the LiH calculation is as follows Cycle number 3 iini Ak cung ed eel SETI e o A a e aere en ena mers pair deg petals ecorr e2 e2 grimme uM uei m I EN UE ee ee ee ae ee ee EMI 00 1 1 0 02392389 0 02392476 0 02870867 00 2 12 0 00046675 0 00046675 0 00036717 00 3 6 0 00008184 0 00008184 0 00006416 00 4 24 0 00002373 0 00002373 0 00001841 ee 5 12 0 00001152 0 00001152 0 00000895 00 6 24 0 00000515 0 00000515 0 00000397 00 T 8 0 00000270 0 00000270 0 00000208 00 8 48 0 00000169 0 00000169 0 00000130 l 0 00000103 0 00000103 0 00000079 l 0 00000071 0 00000071 0 00000055 l 0 00000072 0 00000072 0 00000055 0 00000052 0 00000052 0 00000040 l
32. t for DF estimate of LiF integrals shrinking factor of k net for DF FT fitting radius A Basis Set Input Card Basis Set type End of DF Input deck H dk dk dk dk OH 19 Appendix B Output Examples B 1 Commented Output In the following we comment the output files of two MP2 calculations for an acetyl ACE and a Lithium hydride LiH crystal respectively The former one refers to a rather complicated system and poor tolerances are adopted the latter one is ex tremely simple and the computational conditions are very good These two cases will allow us to comment on specific aspects of the output files ACE is a molecular crystal of cubic symmetry space group pa comprising four acetylene molecules HC CH per unit cell All C and H atoms are symmetry equiv alent to each other The basis set adopted for C comprises one s two sp and one d shell for H two s and one p shell LiH is an ionic crystal of cubic symmetry rocksalt structure space group Fm3m with only one lithium and one hydrogen per cell The basis set adopted for Li com prises two s one p and one d shell for H three s one p and one d shell The two CRYSCOR calculations are performed with the following inputs ACE LiH NEWK NEWK 888 888 0 0 0 0 MEMORY MEMORY 10000000 1200000 COREQ DOMDEF 1 1 CONTOL 13 50 0 00001 123 MULTIPO DFITTING 4 8 PAIR 20 40 4 6 1 12 MOLDOM 0011 TOBJ 4 242065 1 0 01 0 01 density fitting basis set SCHWARZ
33. un a MP2 calculation the following fortran units have to be provided the fort 9 unit of the modified calculation the fort 80 of the reference one rec variable valuemeaning e A8 DUALBAS Ko activate the option 12 2 8 MP2 Equations rec A8 A8 A8 I A8 F A8 variable MP2OLD NOSYM12 EQALG int_alg TOLEQPRS thr_eq TOLEAMPS thr_eq2 value KT KT KT 2 KT 10 7 KT 10 meaning Invoking the old code for the equations Switching off the symmetry i with respect to permuta tions of the WnFs i and j in the ij pairs Evaluation of the beta terms in the LMP2 equations Algorithm 1 or 2 Prescreeining in the evaluation of the beta terms in the LMP2 equations Threshold for prescreeinig Prescreeining for evaluating the updates in the LMP2 equations Threshold for prescreeinig 13 2 9 MP2 Energy 2 9 1 Pairs Partitioning rec variable A8 MOLATOMS Ko I n molpairs 0 nl imol 1 n_molec A8 MOLPAIR Ko 2F DIST1 DIST2 A8 ENVPAIR Ko 2F DIST1 DIST2 A8 MOENPAIR Ko 2F DIST1 DIST2 value meaning Activating the partitioning of the crystal into molecules and environment number of atoms which are considered to be molecules the list of the atoms belonging to the molecules strong weak distant WW pairs with both WnFs having at least one molecule atom in their domains each molecule WnFs 0 d dy d2 d2 00 d dz A If DIST1 DIST2 are 0 no pairs of this ty
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