Home

User Manual

Contents

1. 2 DD 5 Di wz Fav 5 5 DF eee VEJ iv 3 13 2 I pvel I lt J uvEeIJ 3 13 13 lt cmp2 gradient fmo 2 hartree hohr gt x y z Values of x y and z compornent of the FMO2 MP2 gradient of each atom Sum with the FMO2 RHF gradient is printed out together with the correlation contribution This the correlation contribution includes the terms of the external electrostatic potential o pHF ert Z o corr Abra aa MRa 3 13 3 A fmo2 44 CHAPTER 3 OUTPUT cmp2 corr o corr M P2 aa 3 13 4 3 13 14 lt ri cmp2 gradient fmo 2 hartree hohr gt x y z Values of x y and z compornent of the FMO2 RI MP2 gradient of each atom Sum with the FMO2 RHF gradient is printed out together with the correlation contribution This the correlation contribution includes the terms of the external electrostatic potential 0 AF ext Z 0 corr RI MP ie gee We 2 3 13 5 ri cmp2 corr o corr RI M P2 aie 3 13 6 3 13 15 lt rhf electron density fmo 2 gt density Electron density of the FMO2 RHF at the positions defined by the input PPn rm 3 13 16 lt cmp2 electron density fmo 2 gt density Electron density of the FMO2 MP2 at the positions defined by the input Pood kia cmp2 corr MP2 fot Em 3 13 17 lt ri cmp2 electron density fmo 2 gt density Electron density of the FMO2 RI MP2 at the positions defined by the input RI MP P fm
2. Pair Interaction Molecular Orbital Method an Approximate Computational Method for Molecular Interactions K Kitaura E Ikeo T Asada T Nakano M Uebayasi Chem Phys Lett 312 1999 319 324 Fragment Molecular Orbital Method an Approximate Computational Method for Large Molecules K Kitaura E Ikeo T Asada T Nakano M Uebayasi Chem Phys Lett 313 1999 701 706 Fragment molecular orbital method application to polypeptides T Nakano T Kaminuma T Sato Y Akiyama M Uebayasi K Kitaura Chem Phys Lett 318 2000 614 618 Fragment molecular orbital method use of approximate electrostatic potential T Nakano T Kaminuma T Sato K Fukuzawa Y Akiyama M Uebayasi K Kitaura Chem Phys Lett 351 2002 475 480 Extending the Power of Quantum Chemistry to Large Systems with the Frag ment Molecular Orbital Method D G Fedorov K Kitaura J Phys Chem A 111 2007 6904 6914 Theoretical study of the prion protein based on the fragment molecular orbital method T Ishikawa T Ishikura K Kuwata J Comput Chem 30 2009 2594 2601 Fragment molecular orbital method analytical energy gradients K Kitaura S I Sugiki T Nakano Y Komeiji M Uebayasi Chem Phys Lett 336 2001 163 170 Derivatives of the approximated electrostatic potentials in the fragment molec ular orbital method T Nagata D G Fedorov K Kitaura Chem Phys Lett 475 2009 124 131 Energy gradie
3. sub LMP correlatoin energy of the FMO2 Correlation energy and sum with the RHF energy are printed out p Be eS i sum LMP2 correlatoin energy of the FMO2 Correlation energy and sum with the RHF energy are printed out corr LM P2 sum BHF est Z go per EM Rao fmo2 fmo fmo2 3 13 9 lt rhf mulliken population fmo 2 gt pop Mulliken population of the electron density of the FMO2 RHF Nfmo2 A charge Sum of the pop and nucleus charge NF A Za 3 13 FMO 2 RESULT 43 3 13 10 lt cmp2 mulliken population fmo 2 gt pop Mulliken population of the electron density of the FMO2 MP2 Njrmoa A charge Sum of the pop and nucleus charge Njmo2 A Za cmp2 corr Correction by the MP2 correlation Neorr MP2 A fmo2 3 13 11 lt ri cmp2 mulliken population fmo 2 gt pop Mulliken population of the electron density of the FMO2 RI MP2 NBIGMPACA charge Sum of the pop and nucleus charge Nimo A Za cmp2 corr Correction by the MP2 correlation corr RI MP Nios A 3 13 12 lt rhf gradient fmo 2 hartree hohr gt x y z Values of x y and z compornent of the FMO2 RHF gradient of each atom see section 4 2 2 4 2 5 4 2 6 This value includes the terms of the external electrostatic potnetial Eq 4 2 40 and nucleus potential Eq 4 2 41 aa Phat DF ae ee er Teg o N
4. dr 4 3 8 OF en ira 4 3 8 Since the electron density of the FMO method are 4 3 3 and 4 3 7 we obtain the following expressions for the electrostatic potentials of the FMO1 and FMO2 1 Pnor Im gt 5 DF TA Paea V X 4 3 9 I pvel m 1 PF rn02 Pm PF nor rm 5 yD ADF eA Pape ce v 4 3 10 I gt J weld m Here we introduce a new matrix ux rm defined as 1 yv lm a eae E 4 3 11 uxye tm Hv 4 3 11 Using this value the following expressions is obtained GRE tm 23 Tr D Fur tm 4 3 12 OFF oltm Fea tm gt Tr ADE urs tm 4 3 13 I gt J Note that the second term of the FMO2 RHF electrostatic potential is two body correction on the FMO1 RHF electrostatic potential 64 CHAPTER 4 THEORY 4 3 3 Electric field The electric field at position r is written as the following equation B x 2 4 r 4 3 14 Or GP Since the electrostatic potential obtained from the FMO method are 4 3 12 and 4 5 16 we obtain the following expressions for the electric field of the FMO1 and FMO2 EHE tm Tr DEF uren 4 3 15 I m BEE tm EEE rm Tr api P s urs tm 4 3 16 I gt J Note that the second term of the FMO2 RHF electric field is two body correction on the FMO1 RHF electric field 4 3 4 Mulliken population analysis The total electron number is written as the following equation NEF fete dr 4 3 17 Since the electron density of the FMO method a
5. defined by the input Pfmo2 Em esp nuc Electrostatic potential by the nucleus charge at the positions defined by the input In the case that the calculated position is exactly overlapped to the nucleus position the contribution of this nucleus is excluded is attached esp sum The sum of the esp elec and esp nuc The contribution of the external potential is not included 46 CHAPTER 3 OUTPUT ri cmp2 corr Orr ea at rm 3 13 8 fmo2 3 13 21 lt rhf electric field fmo 2 gt ele Electric field by the electron density of the FMO2 RHF at the positions defined by the input Ee o2 m nuc Electric field by the nucleus charge at the positions defined by the input In the case that the calculated position is exactly overlapped to the nucleus position the contribution of this nucleus is excluded is attached sum The sum of the elec and nuc The contribution of the external potential is not included 3 13 22 lt cmp2 electric field fmo 2 gt ele Electric field by the electron density of the FMO2 MP2 at the positions defined by the input Efmoa Em nuc Electric field by the nucleus charge at the positions defined by the input In the case that the calculated position is exactly overlapped to the nucleus position the contribution of this nucleus is excluded is attached sum The sum o
6. int Dynamic update is used for acceleration of the monomer SCC convergence 1 not used O used Default value is 0 14 CHAPTER 2 INPUT e frag_calc_pair int list Selection of the fragment pairs whose dimer calculations are performed If not all the dimer calculations are performed the total properties can not be evaluated only interaction energies of the selected pairs are evaluated This keyword is used as the follow frag_calc_pair number of the list of fragment pairs list 1 list 2 The list is a description specifying the fragment pairs For example ifrag jfrag gt pair of ifrag and jfrag ifrag jfragi jfrag2 gt pairs of ifrag and jfragi jfrag2 ifrag ALL gt all pairs including ifrag See example input 2 3 6 2 2 3 Molecular integral e eritv double Threshold value used for screening by Ka in the two electron integral evaluations Default value is 1 0E 12 e eri cauchy_tv double Threshold value used for screening by Cauchy Schwarz inequality in the two electron inte gral evaluations Default value is 1 0E 10 2 2 4 RHF e rhf int RHF calculation is performed 1 performed O not performed The default value is 1 e rhf grad int RHF gradient calculation is performed 2 2 KEYWORDS 15 1 performed O not performed The default value is 0 rhf_no_int_buff Two electron integrals are buffered on memory in RHF calculat
7. the superscript FT MP2 is ommited Note that derivative of the dimer RI MP2 correlation energy includes the environmental electrostatic potential term In the case that external electrostatic potnetial exists the following term is added corr RI M P2 corr RI M P2 o e Ny 25 Xs Dy ie Vina 5 Do Dry pv are 4 5 11 I pvel I lt J pveld 70 CHAPTER 4 THEORY 4 5 4 Electron Density Electron density of the FMO2 RI MP2 is RI MP RI M P2 e ala oe E cote car pa res where the correlation term is written as RI MP RI MP Oras eye Se Dey A tien Ear I pvel corr RI M P2 D ADT wm vem VEX where ADOT MP2 is defined as corr RI M P2 _ pcorr RI M P2 corr RI M P2 corr RI M P2 AD gt D7 D K D3 4 5 5 Electrostatic potential The electrostatic potential of the FMO2 RI MP2 is RI MP2 RI MP2 pe eG Sgr sma on Mess where the correlation term is written as gor RI MP2 y E r o por RI MP2 1 tm fmo2 a gt Tr AD Yim I gt J 4 5 6 Electric field The electric field of the FMO2 MP2 is corr RI MP Be MEAG Bae tn Er Drm where the correlation term is written as po MP2 aoe Tr p pir RI MP2 ulem Dia s urs tm k 4 5 7 Mulliken population Mulliken population of the FMO2 RI MP2 is corr RI MP ME IENEN D A where the correlation term is written as corr RI M P2 pee RI M P2 N fmo gt gt D S Ein I pea 4 D 5 ADA HEKE Srs pu
8. 5 Example input fmo gly5 inp qd 2 mpi_np 1 3 mem mbyte 1792 5 ri_cmp2 1 6 7 ATOM 8 38 1 9 2 of cc pVDZso_007 8 627555 4 276962 2 760481 10 2 6 cc pVDZso_006 8 859925 2 857283 0 461630 i i ees 3 6 cc pVDZso_006 6 396634 1 768013 0 560757 12 4 8 cc pVDZso_008 4 376048 2 217524 0 372588 13 5 1 cc pVDZso_001 7 403302 5 700198 2 541971 42 34 1 cc pVDZso_001 2 627541 0 136631 0 932746 43 35 1 cc pVDZso_001 5 491791 4 541737 1 266959 44 36 1 cc pVDZso_001 4 745658 2 453913 3 720098 45 37 8 cc pVDZso_008 8 395797 0 629437 0 701933 H 38 1 cc pVDZso_001 10 133232 1 059911 0 772473 48 49 FRAGMENT 50 3 5 52 FRAG_ATOM 0 13 0 PE 1 2 345 6 7 8 91013 14 15 55 FRAG_ATOM 0 14 1 56 11 12 16 17 18 19 20 21 22 23 24 27 28 29 57 10 58 59 FRAG_ATOM 10 11 1 60 25 26 30 31 32 33 34 35 36 37 38 61 24 62 is line 02 This line sets the number of cores user for each monomer or dimer calcula tion In this case all the monomer and dimer calculations are performed with one core and individual calculations are progressed at the same time line 03 This line sets the size of memory per core used for calculation in Mbyte line 05 This line sets performing RI MP2 calculation line 07 08 These lines mean that atomic numbers coordinat
9. These results are obtained without any change of the input file in the distribution e h20 4 inp 12 atoms 96 basis functions 1 fragment RHF and RI MP2 energy XeonE5429 1 core 2 0 GByte memory per core time 3 61 sec e fmo h2o 4 inp 12 atoms 96 basis functions 4 fragments RHF and RI MP2 energy XeonE5429 1 core 2 0 GByte memory per core time 2 56 sec e trp2 inp 51 atoms 516 basis functions 1 fragment RHF and RI MP2 gradient XeonE5429 1 core 2 0 GByte memory per core time 13052 98 sec 6 CHAPTER 1 COMPILE AND EXECUTE Figure 1 1 Examples of script to run PAIC S lt in the case directly using mpirun paics run sh gt bin bash export PAICS_ROOT home ishi program paics INP 1 NCPU 2 DIR pwd mpirun np NCPU PAICS_ROOT main exe DIR INP This script is executed as paics run sh input filename number of cores gt amp output filename amp lt in the case using LSF paics run lsf sh gt bin bash export PAICS_ROOT home ishi paics paics 20080703 2 DIR pwd BSUB_DIR DIR INP_FILE 1 OUT_FILE 2 NCPU 3 rm f BSUB_DIR bsub log rm f BSUB_DIR bsub out bsub o BSUB_DIR bsub out e BSUB_DIR bsub log n NCPU mpijob mpirun PAICS_ROOT main exe DIR INP_FILE gt amp DIR 0UT_FILE This script is executed as paics run lsf sh input filename output filename number of cores 1 3 TEST CALCU
10. automatically selected cc pVDZri cc pVDZ cc pVDZso 6 31G 6 31G cc pVTZri cc pVTZ ri cmp2_grad int RI MP2 gradient calculation is performed 1 performed O not performed Default value is 0 ri cmp2_lprint 1 int Print level of monomer RI MP2 calculation Default value is 1 which give a normal printing e riccmp2_Iprint_2 int Print level of dimer RI MP2 calculation Default value is 1 which give a normal printing 2 2 7 Local MP2 e Imp2_chk int Local MP2 calculation is performed 18 CHAPTER 2 INPUT O not performed 1 performed Default value is 0 The local MP2 calculation in the PAICS is used not for speed up but for fragment interaction analysis based on local MP2 FILM Imp2_Iprint_1 int Print level of monomer local MP2 calculation Default value is 1 which gives a normal printing Imp2_Iprint_2 int Print level of dimer local MP2 calculation Default value is 1 which gives a normal printing Imp2_loc int Method of localization O Pipek Mezey 1 Boys 2 not perform localization Default value is 0 the value of 2 is used only for the debug Imp2_max itr int Maximum iteration number for solving linear equation Default value is 30 Imp2th_1 double Threshold value used for determination of the domain Default value is 0 02 Imp2th_1_dim double Threshold value used for determination of the domain Default
11. calculation the progress of the calculatons are printed out by the following order e dimer rhf e dimer cmp2 e dimer ri cmp2 e dimer Imp2 e dimer field property 40 CHAPTER 3 OUTPUT 3 13 FMO 2 result After the following keyowrd walues evaluated using the monomer and dimer calculations are printed out 3 13 1 lt rhf ifie gt rhf The IFIE including the nucleus potential and the interaction energy with the external potential see the section 4 1 1 and 4 1 2 AEPF Tr ADE V9 EZ rhf cp The value obtained by subtracting the estimated BSSE form the rhf see the section 4 1 8 AEF Tr ADEF VG EZ Epp PG 3 13 2 lt cmp2 ifie gt normal not scs Contribution to the IFIE of the MP2 correlation In the case performing the BSSE correc tion the corrected value is additionally printed out see the section 4 4 1 and 4 4 2 hee Ape ee ae aac 3 Grimme s scs Contribution to the IFIE of the SCS MP2 correlation with Grimme s factor In the case performing the BSSE correction the corrected value is additionally printed out see the section 4 4 3 AB TG I E cha EATI Jung s scs Contribution to the IFIE of the SCS MP2 correlation with Jung s factor In the case performing the BSSE correction the corrected value is additionally printed out see the section 4 4 3 7 a a Aes _ pBSSE corr MP2 2 Ery Hill s scs Contribution to t
12. following quantum chemical calculations Additionally names of the variables which use the memory more than 1024 Kbyte 3 5 Fragment information After the following keyword information about echa fragment is printed out Informations of the fragments are printed out to order with large size which include number of the basis functions electrons and projection orbitals The number of fragments treated in three approximation levels i e 4 center integrals 3 center integrals and point charge when calcu lating the environmental electrostatic potential are printed out for each fragment Additionally the number of fragments calculated with and without dimer es approximation when performing dimer calculation are also printed out for each fragment 3 6 Fragment pair information After the following keyword several informations about the fragment pairs are printed out Numbers of the fragment pairs whose dimer caluclations are performed with and without dimer es approxmation are printed out Additionally the information is also given with divided into the size of basis function 3 7 Monomer SCC calculation After the following keyword progress of the monomer SCC calculations is printed out 36 CHAPTER 3 OUTPUT 3 7 1 lt monomer scc cycle gt For each iteration the FMO1 RHF energy and its difference the maximum difference of monomer energy and its sequential number of fragment and the computational times are printed out He
13. gt J where A ea le is Aner en Bee _ pee Beer 4 4 5 The IFIE of MP2 is evaluated as corr MP AEMP NEE AE 4 4 6 66 CHAPTER 4 THEORY 4 4 2 BSSE correction As is the case with HF calculation the BSSE is estimated only for the IFIE of the pair not sharing the basis set under the vaccume condition For BSSE correction the following values are additionally needed pecorr M P2 vac IIJ the monomer correlation energy of the J th fragment under the vacuum condition including the basis set of the J th fragment prr MP2 vac JIJ the monomer correlation energy of the J th fragment under the vacuum condition including the basis set of the I th fragment PEA the monomer correlation energy of the J th fragment under the vacuum condition ee the monomer correlation energy of the J th fragment under the vacuum condition With these values the BSSE of the IFIE of he fragments J and J is written as the following equation EBSSE corr MP2 2 Cou B aac es IJ I IJ corr M P2 vac corr M P2 vac Hoses vac __ By i 4 4 7 Thus the corrected IFIE is AEMP2 0P AE F OP 4 Ae a P D AE 4 4 8 4 4 3 SCS MP2 energy In the case using the spin compornent scaled MP2 SCS MP2 the monomr or dimer correlatoin energy scaled with specific factor is used instead of the normal correlation energy In this text the superscript of MP2 is replaced as follows In the case us
14. is equivalent to the total In the case that the external potential dose not exist this value is zero see the section 4 5 3 textsf4 1 6 and 4 1 7 do rr DFP VE BF O Tr ADEF VES I I gt J 3 13 6 lt cmp2 total energy fmo 2 gt normal MP2 correlatoin energy of the FMO2 Correlation energy and sum with the RHF energy are printed out see the section 4 4 1 MP2 HF eat Z MP2 Emo gt Efmos pine 42 CHAPTER 3 OUTPUT Grimm s scs MP2 correlatoin energy of the FMO2 scaled with factors developed by Grimme Correlation energy and sum with the RHF energy are printed out see the section 4 4 3 M P2 1 HF ext Z corr M P2 1 E pno E fmo2 E fmo Jung s scs MP2 correlatoin energy of the FMO2 scaled with factors developed by Jung Correlation energy and sum with the RHF energy are printed out see the section 4 4 3 ie ae ea ie OR Hill s scs MP2 correlatoin energy of the FMO2 scaled with factors developed by Hill Correlation energy and sum with the RHF energy are printed out see the section 4 4 3 M P2 3 HF ext Z corr M P2 3 E pmo E fmo2 E fmo 3 13 7 lt ri cmp2 total energy fmo 2 gt normal RI MP2 correlatoin energy of the FMO2 Correlation energy and sum with the RHF energy are printed out see the section 4 5 1 orr RI M P2 corr RI M P2 HF ext Z E E mo2 c fmo2 fmo2 Ey 3 13 8 lt Imp2 total energy fmo 2 gt
15. repulsion integral derivative of electron repulsion integral environmental electrostatic potential projection operator fragmentation monomer scc calculation monomer monomer calculation dimer_es dimer es calculation dimer dimer calculation rhf RHF cmp2 canonical MP2 riccmp2 RI MP2 localize localization of orbital Imp2 local MP2 e basis Data files of basis set are stored The following files exist user definition STO 3G 1 1 COMPILE 631g dat 6 31G 631lgdp dat 6 31G cc pVDZ dat cc pVDZ cc pVTZ dat cc pVTZ cc pVQZ dat cc pVQZ cc pVDZso dat cc pVDZ segmented opt cc pVTZso dat cc pVTZ segmented opt cce pVDZri dat auxiliary basis function for cc pVDZ cce pVTZri dat auxiliary basis function for cc pVTZ cc pVQZri dat auxiliary basis function for cc pVQZ e sample Examples of the input and output are stored The following files exist h20 4 inp conventional calculation of tetramer of HzO h2o0 4 out result of calculation fmo h20 4 inp FMO calculation of tetramer of H20 fmo h2o0 4 out result of calculation trp2 inp conventional calculation of TPR TRP trp2 out result of calculation c12h26 inp conventional calculation of C12H26 c12h26 out result of calculation fmo c12h26 inp FMO calculation of C12H26 fmo c12h26 out result of calculation gly5 inp conventional calculation of GLYs gly5 out result of calculation fmo gly5 inp FMO calculation of GLYs fmo gly5 out re
16. the electrostatic potential with 4 center integrals gt The first term of Eq 4 1 36 is evaluated from the electron aa of the K4 th fragment PK4 cay 2H erat eR K4 v 4 1 37 where the p 4 r is evaluated with the density matrix of the K4 th fragment determined by the monomer SCC calculation that is PKL gt Dki roA r o r 4 1 38 AcE Ka Thus the first term of Eq 4 1 36 can be written with the 4 center integrals as the following equation DUR Cra DO DEF uy do 4 1 39 K4 0 K4 lt evaluation of the electrostatic potential with 3 center integrals gt The second term of Eq 4 1 36 is evaluated from the electron ae of the K3 th fragment PK3 X vko eat oat v 4 1 40 K3 where p r is approximately evaluated with the density matrix of the K3 th fragment deter mined by the monomer SCC calculation that is pral D Die Sroa JACA 4 1 41 ACK3 oe K3 Thus the second term of Eq 4 1 36 is written with the 3 center integrals as the following equation So ces gt gt DESx uv 4 1 42 K3 K3 AEK3 caution In the program Eq 4 1 42 is calculated with the normalization factor as DVX Y DE Si a x rla 4 1 43 K3 AEK3 52 CHAPTER 4 THEORY lt evaluation of the electrostatic potential with point charges gt The third term of Eq 4 1 36 is evaluated from the electron density of the K th fragments
17. value is 0 001 Imp2th_2 double Threshold value used for selection of the orbital pair Default value is 4 0 Imp2th_2_dim double Threshold value used for selection of the orbital pair Default value is 8 0 Imp2th_3 double Threshold value used for integral transformation Default value is 0 004 Imp2th_4 double Threshold value used for integral transformation Default value is 1 0E 12 2 2 KEYWORDS 2 2 8 atom keyword Atoms are defined using atom keyword where each column is a Number of atoms b Type of basis set O cartesian type 1 spherical type c Sequential serial number d Atomic number e Name of basis function x X coordinate y Y coordinate z Z coordinate 19 The name of basis function is defined with basis_def keyword The coordinates of the atoms are give in the unit which is defined with coord_unit keyword See example inputs 2 3 20 CHAPTER 2 INPUT 2 2 9 frag_atom keyword Number of the fragment is defined using fragment keyword and each fragment is defined using frag_atom keyword Thus the number of frag_atom keywords in the input should be same as the number of the fragments The format is FRAGMENT number of fragment FRAG_ATOM a e oar Wu py FRAG_ATOM a e m a uau p FRAG_ATOM a b c where each column is a Formal charge of the fragment b Number of atoms in the fragmen
18. 0 Fragment molecular orbital based molecular dynamics FMO MD method with MP2 gradient Y Mochizuki T Nakano Y Komeiji K Yamashita Y Okiyama H Yoshikawa H Yamataka Chem Phys Lett 504 2011 95 99 Analytic energy gradient for second order Moeller Plesset perturbation theory based on the fragment molecular orbital method T Nagata D G Fedorov K Ishimura K Kitaura J Chem Phys 135 2011 044110 Fragment molecular orbital calculation using the RI MP2 method T Ishikawa K Kuwata Chem Phys Lett 474 2009 195 198 Acceleration of fragment molecular orbital calculations with Cholesky decom position approach Y Okiyama T Nakano K Yamashita Y Mochizuki N Taguchi S Tanaka Chem Phys Lett 490 2010 84 89 Application of resolution of identity approximation of second order Moeller Plesset perturbation theory to three body fragment molecular orbital method M Katouda Theor Chem Acc 130 2011 449 453 RI MP2 gradient calculation of large molecules using the fragment molecular orbital method T Ishikawa K Kuwata J Phys Chem Lett 3 2012 375 379 Fragment interaction analysis based on local MP2 T Ishikawa Y Mochizuki S Amari T Nakano H Tokiwa S Tanaka K Tanaka Theor Chem Acc 118 2007 937 945 An application of fragment interaction analysis based on local MP2 T Ishikawa Y Mochizuki S Amari T Nakano S Tanaka K Tanaka Chem Phys Lett 463 2
19. 008 189 194
20. 057410 76 048248 80 942639 123 2 1 cc pVDZso_001 44 179907 75 949983 82 482766 13 3 3 1 cc pVDZso_001 43 216147 74 423084 79 954312 14 4 1 cc pVDZso_001 41 247052 76 295803 81 494439 15 3 5 6 cc pVDZso_006 43 828418 78 174190 79 332592 1735 1725 1 cc pVDZso_001 74 517570 59 611411 109 392466 1736 1726 1 cc pVDZso_001 75 199761 58 160101 112 366895 1737 1727 6 cc pVDZso_006 76 511231 56 081402 109 069323 1738 1728 1 cc pVDZso_001 77 344601 54 760484 110 420477 1799 1729 1 cc pVDZso_001 77 996556 57 143428 108 103673 1741 1742 FRAGMENT 1743 106 1744 1745 FRAG_ATOM 1 7 0 1746 5 123 467 1747 1748 FRAG_ATOM 0 19 1 1749 12 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 8 9 I 30 CHAPTER 2 INPUT calculations are performed with 1 core and 8 individual calculations are progressed at the same time line 0005 This line sets the size of memory per core used for calculation in Mbyte line 0007 This lines sets performing RI MP2 calculations line 0009 1739 These lines give the atomic numbers coordinates basis functions of 1792 atoms and spherical type basis sets are used line 1742 2186 These lines give the definitions of 106 fragments If only the interaction energies between prion protein and GN8 are needed just perform i
21. 1 1 941777 2 463141 0 002634 18 10 1 cc pVDZso_001 4 427776 2 291180 1 463833 19 11 1 cc pVDZso_001 2 463453 1 941764 0 002780 20 12 1 cc pVDZso_001 2 291353 4 428135 1 463364 22 FRAGMENT 23 3 4 24 25 FRAG_ATOM o 3 o 26 1 5 6 ya fares 28 FRAG_ATOM o 3 o 29 2 Fi 8 30 31 FRAG_ATOM o 3 o 32 3 9 10 33 34 FRAG_ATOM o 3 o 35 4 11 12 36 BH 3 meaning of each line of the input line 02 This line sets the number of cores user for each monomer or dimer calcula tion In this case all the monomer and dimer calculations are performed with one core and individual calculations are progressed at the same time line 03 This line sets the size of memory per core used for calculation in Mbyte line 05 This line sets performing RI MP2 calculation line 07 08 These lines mean that atomic numbers coordinates basis functions of 12 atoms are given in the following lines and spherical harmonic basis functions are used line 09 20 These line give the atomic number coordinates basis functions of the atoms line 22 23 These lines give the number of fragment In this case 4 fragments are given in the following lines line 25 35 These lines give the definition of the 4 fragments 26 CHAPTER 2 INPUT 2 3 3 FMO calculation of GLY In Figure 2 5 input for FMO calculation of GLY is given The meaning of each line Figure 2
22. 2 pc inp il R 2 mem mbyte 1792 3 mpi_np 1 4 5 cmp2_grad 1 6 ri_cmp2_grad 1 T 8 ATOM 9 40 10 1 8 cc pVDZso_008 1 2 6 cc pVDZso_006 12 c 3 1 cc pVDZso_001 13 2 4 1 cc pVDZso_001 15 ex_point_charge 16 2 36 17 1 0 295544 103300 i 18 2 0 204929 317599 19 3 0 180917 521898 50 34 0 558942 972834 51 35 0 210549 238241 52 36 0 236426 455521 53 54 position 55 36 56 1 0 103300 5 492608 57 2 0 317599 7 022772 oF 3 2 521898 6 514663 Lo 89 34 1 972834 503713 90 35 2 238241 671106 91 36 2 455521 946313 93 FRAGMENT 1 96 FRAG_ATOM 1 a o 0 319322 0 904629 0 117246 2 682198 ono 492608 022772 514663 503713 671106 946313 334387 412113 099571 637485 162132 359779 1 256692 0 106102 0 307596 1 387482 1 047770 3 137662 0 940018 0 700446 334387 412113 099571 637485 162132 359779 ro AK f x line 08 13 These lines give the atomic numbers coordinates basis functions of the 4 atoms in HCO molecule line 15 16 These lines mean that 36 external point charges are given in the following lines line 17 52 These lines give the 36 external point charges corresponding to 12 water molecules line 54 55 These lines mean that 36 position are given in the followin
23. 99810 7 4950000 7 0 1272620 2 7970000 8 0 5445290 0 5215000 0 1 1 1 0000000 0 1596000 1 3 1 0 0381090 9 4390000 2 0 2094800 2 0020000 3 0 5085570 0 5456000 1 1 1 1 0000000 0 1517000 2 1 1 1 0000000 0 5500000 In this example the name of the definition is cc pVDZ_006 When cc pVDZ_006 is used in atom keyword this basis set is applied The basis sets ready defined in the PAICS are shown in the following table basis set name of definition available atoms STO 3G STO 3G_ 2 001 053 6 31G 6 31G_ 001 030 6 31G 6 31G _ 001 030 cc pVDZ cc pVDZ_ 001 018 020 036 cc pVTZ cc pVTZ_ 001 018 020 036 cc pVQZ cc pVQZ_ 001 018 020 036 cc pVDZso cc pVDZso_ 001 018 031 036 cc pVTZso cc pVTZso_ 001 018 031 036 cc pVDZri cc pVDZri_ 001 018 031 036 cc pVTZri cc pVT Zri_ 001 018 031 036 2 3 Example In this section some examples of the input are given These input files are included in the distribution of the PAICS 24 CHAPTER 2 INPUT 2 3 1 Conventional calculation of tetramer of water molecules In Figure 2 3 input for the conventional calculation of tetramer of water molecules is given In the case of a conventional calculation not FMO calculation one definition of the fragment must be given When performing such a calculation one monomer calculation is performed on the other
24. F is approximately written as ABETS p PP a Bees Ee 4 1 32 Consequently by substituting Eq 4 1 30 to Eq 4 1 32 we obtain the following equation AEF 5 DPI uvt Eg Jo D77 uvYJ I uv uvEI pve Td 5 So DET DIe mw Ao 4 1 33 pvel AcE T This is the IFIE for the dimer es pairs 4 1 5 Environmental electrostatic potential The matrix of the environmental electrostatic potential V x is written as sum of the attractive potential and repulsive potential form the other fragments i e Vx 5 ux K 5 VxX K gt 4 1 34 KX KX where the first term of this equation is calculated as gt ixni Hl OY ETEN Sa 4 1 35 K X Kx Ack VA 1 On the other hands the second term of this equation is evaluated using three types of manner 1 evaluated without any approximation i e 4 center electron repulsion integrals are used 2 approximately evaluated with 3 center integrals which is called esp aoc approximation 3 approximately evaluated with point charges which is called esp ptc approximation 4 1 FMO RHF ENERGY 5l Here we write the potential from the electron density in the form of the summation over the contributions of the three types of manner as the following equation 4 S vx Do Yxa Yxa DOV KK 4 1 36 K4 K3 Kp KX where K4 K3 and K indicate the fragments whose potential are evaluated with 4 center integrals 3 center integrals and point charges respectively lt evaluation of
25. I gt JuEA 4 5 12 4 5 13 4 5 14 4 5 15 4 5 16 4 5 17 4 5 18 4 5 19 4 5 20 4 6 FMO LMP2 ENERGY 71 4 6 FMO LMP2 energy In this section the theory related to the LMP2 is explained making it be related to the output of the PAIC S The formulation basically follows the previous publications reporting the theory and method of the FMO scheme 23 24 4 6 1 Energy The LMP2 total energy of one body approximation FMO1 LMP2 and two body approximation FMO LMP2 is corr LM P2 Be Se ee 4 6 1 corr LM P2 Ee a Erio ae o a 4 6 2 Here a TAR and fee are defined with the LMP2 correlatoin energy of the monomer or dimer as corr LM P2 corr LM P2 Bee Ee 4 6 3 I corr LM P2 corr M P2 corr LM P2 By Be sey be 4 6 4 I I gt J where Ape is N a Bee EMBA per _ POTEM RA 4 6 5 The IFIE of the FMO LMP 2 is evaluated as APTME2 Ae fs Ap OMe 4 6 6 Here A is calculated using the pair correlation energies between local orbitals of the dimer LMP2 calculation as Ape ee Ss Eij 4 6 7 tel jEJ Here is the pair correlation energy Thus we can define the correlation energy of the FMO2 LMP2 as corr LM P2 sum corr M P2 corr LM P2 sum B ON Beh oy eee en 4 6 8 I I gt J Bibliography 12 The FRAGMENT MOLECULAR ORBIAL METHOD Practical Applications to Large Molecular Systems G Fedorov and K Kitaura Eds CRC Press Boca Raton FL 2009
26. K p r2 Y iram l fa E v 4 1 44 Kp Kp 1 2 where px r is approximately treated as the point charges determined by the monomer SCC calculation Thus the third term of Eq 4 1 36 is written with the point charge as the following equation qB pain a 5x H ba Roar v 4 1 45 Kp Kp BEKy 4 1 6 Energy including external potential In the case that the external potential exists the Fock operator of Eq 4 1 1 is modified as fE fxt 5 uxx Ux K Py V3 4 1 46 K X where the last term is the operator associated with the external potential Here we define the matrix of the external potential as Vin u V v 4 1 47 In this case contribution of the external potential is added to the E 4 E XE gt E RP 4 Tr DEF VE 4 1 48 Thus the FMO1 energy is written as rope _ Ser a S_Tr DFF vs 4 1 49 T T With considering Eq 4 1 26 the FMO2 RHF energy is written as BHF est _ SD ieee Be Bee BI HF _ nee 527 r ADH FV 17 fmo2 I I gt J I gt J E2 DEEV So Tr DEF Vis Tr DEP VE Tr DFF Ve I gt J 4 1 50 For the matrix of the external potential the following equations are satisfied Tr D7 V5 Tr Diy Vis 4 1 51 Thus we can obtain the FMO2 RHF energy as r2 SOBFF S E FF EPF E HF 52 Tr ADH PV 17 I I gt J I gt J S 0Tr Di Ve So Tr ADFF VR I I gt J 4 1 52 4 1 FMO RHF ENERGY 53 and this equation is written using the FMO1 RHF ener
27. LATION 7 c12h26 inp 38 atoms 298 basis functions 1 fragment RHF and RI MP2 energy XeonE5429 1 core 2 0 GByte memory per core time 250 80 sec fmo c12h26 inp 38 atoms 298 basis functions 3 fragments RHF and RI MP2 energy XeonE5429 1 core 2 0 GByte memory per core time 288 36 sec gly5 inp 38 atoms 379 basis functions 1 fragment RHF and RI MP2 energy XeonE5429 1 core 2 0 GByte memory per core time 1242 73 sec fmo gly5 inp 38 atoms 379 basis functions 3 fragments RHF and RI MP2 energy XeonE5429 1 core 2 0 GByte memory per core time 1034 30 sec fmo h2co water12 inp 40 atoms 326 basis functions 13 fragments RHF RI MP2 and MP2 gradient XeonE5429 1 core 2 0 GByte memory per core time 302 36 sec h2co water12 pc inp 4 atoms 38 basis functions 1 fragment RHF RI MP2 and MP2 gradient XeonE5429 1 core 2 0 GByte memory per core time 2 59 sec fmo h2co water128 inp 388 atoms 3110 basis functions 129 fragment RHFand RI MP2 gradient electric field XeonE5429 1 core 2 0 GByte memory per core time 1276 88 sec fmo h2co water128 pc inp 22 atoms 182 basis functions 7 fragments RHFand RI MP2 gradient electric field XeonE5429 1 core 2 0 GByte memory per core time 51 32 sec h2co water128 pc inp 22 atoms 182 basis functions 1 fragment RHFand RI MP2 gradient electri
28. Parallelized ab initio calculation system based on FMO PAICS User Manual Chapter 1 Compile and Execute 1 1 Compile How to compile the PAICS is explained in this section 1 1 1 Directory and file in the distribution Directories and files included in the distribution of the PAICS are listed e Makefile_paics Makefile for compiling the PAICS e make inc File used for compiling the PAIC S This file should be arranged according to your com puter system e make sh Script to compile the PAICS e clean sh Script to clean up e main c Source code of the main function of the PAICS e paics run sh An example of the script to run the PAICS with MPICH This file should be arranged according to your computer system 1 CHAPTER 1 COMPILE AND EXECUTE e paics run sf sh An example of the script to run the PAICS with LSF This file should be arranged according to your computer system e man Manuals PDF are stored The following file exists manual pdf e src Source codes are stored The following directories exist include parallel_control memory _control header parallelization control memory control paics overall PAICS input input output output fmt error function oneint one electron integral oneint_grad eri eri_grad esp projection fragment monomer scc user dat sto3g dat derivation of one electron integral electron
29. RAG_ATOM o 3 o 58 5 6 8 90 FRAG_ATOM o 3 o 91 38 39 40 i 92 line 02 This line sets the number of cores user for each monomer or dimer calcula tion In this case all the monomer and dimer calculations are performed with one core and individual calculations are progressed at the same time line 03 This line sets the size of memory per core used for calculation in Mbyte line 05 06 This lines sets performing canonical MP2 and RI MP2 gradient calculations By these two lines energy and gradient calculations of RHF canonical MP2 RI MP2 are performed line 08 49 These line give the atomic numbers coordinates basis functions of the 40 atoms line 51 91 These lines give the definition of the 13 fragments one H2CO and 12 water molecules 2 3 5 Conventional calculation of HCO with external point charges In Figure 2 7 input for the conventional calculation of HyCO in water molecules is given where the water molecules are treated as external point charge The meaning of each line of the input line 02 This line sets the number of cores user for monomer calculation line 03 This line sets the size of memory per core used for calculation in Mbyte line 05 06 This lines sets performing canonical MP2 and RI MP2 gradient calculations By these two lines energy and gradient calculations of RHF canonical MP2 RI MP2 are performed 28 CHAPTER 2 INPUT Figure 2 7 Example input h2co water1
30. RI M P2 Es Me SoBe L J AE a 4 5 4 I I gt J where Kp ere is Te UTMRR Eee MER E PETI MED PPT RITME 4 5 5 The IFIE of MP2 is evaluated as AERI MP2 L A BEF 4 A See 4 5 6 4 5 FMO RI MP2 69 4 5 2 BSSE correction The BSSE correction in the FMO RI MP2 is evaluated by the exactly same say as that in the FMO MP2 Thus the discussion and formulaton are obtained by the following replacement of the superscript in the section 4 4 2 MP2 RI MP2 4 5 3 Gradient The derivative of the FMO2 RI MP2 energy is RI M P2 HF 0 corr RI M P2 OA fmo2 7 54 Eime oT BA fmo2 4 5 7 er MP2 where derivative of the RI MP2 correlation energy Ep is written with the derivative of the monomer or dimer RI MP2 correlation energy a o corr RI M P peor RI MP corr RI MP re aD 5 ree 24 a a D 4 5 8 E the derivative of the monomer and dimer correlation energy is corr corr corr jae 4 gt PE Plu 2 Pea Plg OA xa uvPEI PQEI corr I weer I 2 X Di ahh 2 Wi a pvel corr corr 2 5 2D aD ro D7 HO Tv 5g el 4 5 9 pv rAoET Bere corr corr BAY 4 5 Petia P uv 2 by Tony PIQ uvPEIJ E a corr IJ weerr IJ corr IJ 2 gt DY ye 3 Wa ee DY eve pvel ds pvEIJ pvEIJ X corr corr 2 2059 nu DIF ro Diz ro DF xa 74 BY Aa 4 5 10 pvrAoEL I where the matrixes of D W T and 7 are calculated by the same way as a normal RI MP2 gradient alcilation
31. agments in F lt the number of fragments in F gt much computational time can be reduces because the majority of the dimer calculation is those of the fifth term Thus this restriction is useful for the case that only the interaction energies related to the fragment of F are required For example in the case that the interaction of a ligand molecule with a protein is examined In the PAICS such a restricted calculations are performed with the frag_calc_pair keyword lt definition of the partial energy gt The first and second terms in Eq 4 1 67 give the internal energy of the fragments of F and the third term give the interaction energy between the fragments of F and Fy Thus we define the partial energy of F as the following equation EFino2 Fr a Ay Pea AB 4 1 68 gt This is used for the definition of the partial energy gradient 4 2 FMO RHF GRADIENT 55 4 1 9 BSSE correction In the FMO method an correction of the basis set super position error BSSE is not simple because the monomer and dimer calculations include the environmental electrostatic potential Additionally in the case including the cut of covalent bonds the BSSE correction becomes still more difficult because several basis sets are shared by the two fragments Thus in the PAICS amount of the BSSE is estimated under the vacuum condition for the IFIE of the pairs not sharing the basis sets For the estimation of the BSSE of the fragment pai
32. and IJ for monomer and dimer calculations respectively The first term of this operator is a normal Fock operator fx hx 2 Jx Kx 4 1 2 where hx is one electron operator 1 ZA hx 3V gt _ 4 1 3 2 AEX Ra r and J and K are coulomb and exchange operators respectively The second term of the Eq 4 1 1 is electrostatic potentials from the other fragments which are defined as Za ux a 4 1 4 00 gt 2 Ram K UX K far E 4 1 5 i ri r 48 CHAPTER 4 THEORY where ux x is attractive potential of X from the nuclei of the K th fragment and vx x is repulsive potential of X from the electron density of the K th fragment The electron density of each fragment is determined with an iterative procedure called monomer self consistent charge SCC calculation and potential from the other fragment is called environmental electrostatic potential The third term is the projection operator related to cut of covalent bonds in the fragmentation Px BY 0 0 4 1 6 k where Ok is a component excluded from the variational space of the monomer and dimer calcu lations and B is a sufficiently large positive value 4 1 2 Definition of matrixes Here we define the several matrices associated with above operator hxw u hx v 4 1 7 Ux K wy Hux 4 1 8 Ux K uy LIUx K Y 4 1 9 Pxy u Px v 4 1 10 Jxw eH Ix v 4 1 11 Kx u Kx v 4 1 12 wh
33. c field 8 CHAPTER 1 COMPILE AND EXECUTE XeonE5429 1 core 2 0 GByte memory per core time 112 41 sec e fmo prp gn8 inp 1792 atoms 16736 basis functions 106 fragments RHF and RI MP2 XeonE5429 8 cores 2 0 Gbyte memory per core time 114628 66 sec 31 8 hours e fmo hiv Ipv inp 3225 atoms 30224 basis functions 203 fragments RHF and RI MP2 XeonE5429 8 cores 2 0 Gbyte memory per core time 195976 17 sec 54 4 hours e fmo dna inp 638 atoms 6898 basis functions 40 fragments RHF and RI MP2 XeonE5429 8 cores 2 0 Gbyte memory per core time 28736 74 sec 8 0 hours 1 3 2 Check of result Outputs correspoinding to these inputs are also contained in distribution of the PAICS Thus you should compare between the your results and them O caution FMO calculation is progressed in order of the monomer SCC calculation the monomer calculation and the dimer calculation The FMO 1 and FMO 2 properties are printed out with the time of the monomer and dimer calculations being finished respectively On the other hands in conventional calculation the monomer SCC and dimer calculations are not performed and only one monomer calculation is performed You should check that the tests calculations are progressed in such order by checking the output from a head and confirm that the results of your calculations is in agreement with those of the output contained in th
34. culation of each fragment in monomer calculation If this keyword is not set value of mpi np keyword is used In analogy with the mpi np the total number of cores used for calculation must be divisible by this value mpi np dim int The number of cores used for calculation of each fragment pair in dimer calculation If this keyword is not set value of mpi np keyword is used In analogy with the mpi np the total number of cores used for calculation must be divisible by this value print rank int MPI rank printing the results of calculation to standard output Default value is 0 This keyword is used only for debug mem mbyte int Size of memory per core used for calculation Mbyte Default value is 128 Since the default value is too small this keyword should be set in every calculations Iprint int General print level You can decide the print level of each part of the calculation separately using the other keywords see the following keywords coord_unit int Unit of the coordinates used in the input O bohr 1 angstrom Default is 0 w result_file char String used for name of the file into which some information is written during calculation w log file int Write the results of calculation to the file by each core separately O not write 1 write 2 2 KEYWORDS 11 Default value is 0 The file name is automatically determined as w_result_file _ mpi_rank log Thus when this
35. d the last term of this equation 4 2 FMO RHF GRADIENT 57 lt Derivative of Tr D 7 Vis gt We note the following relation 5 Diy Visz 5 DIV DIEVI I lt J I lt J 5 ma D Vv Ta J DEEV i DH Vi I amp I I lt J Ny 1 J oN X X DF Vw I I J Ny 1 S DFV X D7 Vv I I N 2 gt DIF Vi 4 2 11 I Using this relation the derivative of the term including Tr Di Vrz in Eq 4 2 17 is 5 T DES DVI I gt J o E E DE gaVe N D E aP Viw 4212 I gt J pvel ds pvel lt Terms including the derivative of density matrix gt Terms including the derivative of density matirx are the last terms of Eq 4 2 8 and the last term of Eq 4 2 12 i e o o N y 5g 0th Vi N 2 Y 542th Vin 0 4 2 13 pvel pvel Thus they are canceled lt Terms including the environmental electrostatic potential gt Terms including the derivative of environmental electrostatic potential is the last term of Eq 4 2 10 and the first term of Eq 4 2 12 i e bp Dry Fa aqVisw pa DG D ww gq Visw 5 ADF lagi 4 2 14 pvels pvels lt definition GF A gt Here we introduce the following values G F A ap D HE ie o 5 5 DEED Fio Di DDF gal Pee 2 w a 4 2 15 pvel 58 CHAPTER 4 THEORY Ow A hime pveld 1 1 HF t3 DEF u DIF o T O vA DTJ A za Ac pv rAo a WHE opStaw gt ADE E Viri 4 2 16 pvEIJ pvEIJ Using th
36. d term of Eq 4 2 21 can be expressed as the following equation 3 a ADX wW BA a K3 uvEX 3 5 ADE Tal 5 DEP ySrxon mw IAA VEX K3 ACKs o K3 20 pD f gt DEE an T Ka A IXA DRT oa K3 a bEKs AcE K3 73 pF s s 4 2 34 9 X K3 aa K3 a OA Xap 4 where Zaa gt ADE uv 4 2 35 VEX 4 2 FMO RHF GRADIENT 61 lt derivative of v KGET The derivative of Ux Kp uv is a ad Da riw De 2 CHU menh p BEKp o 1 pa gall pl 4 2 36 If we neglect the first term of this equation the fourth term of Eq 4 2 21 can be expressed as the following equation gt ADE ToD VEX Kp PB l S RE E AA a VEX Kp BEK Uma Ee hma o 4 2 37 4 2 5 External electrostatic potential In the case that external electrostatic potential exists h is modified as hy hy Va 4 2 38 Thus the following electrostatic term is added to G F A y DIF O yest 4 2 39 e X uv aA V uv uV Consequently the following value is added to the FMO2 RHF gradient o N 25 y Df wp fet 5 DFF 7 Vif av 4 2 40 I pvel I lt J uvEeIJ 4 2 6 Nucleus potential The expression of the FMO2 RHF gradient including the external electrostatic potential and nucleus potential is the following equation 0 O pHFlert Z _ o A fmo2 ga Efmoz o W Di ag fet 5 D Ve I pvel I lt J pveld o ZZ Zext EENE BEZZ Y E V a er 4 2 41 62 CHAPTER 4 THEORY 4 2 7 Restriction of di
37. d with factors developed by Hill Correlation energy and sum with the RHF energy are printed out see the sections 4 4 1 and 4 4 3 poor M P2 1 HF ext Z corr M P2 3 fmol E fmol Ey mol 3 11 DIMER ES APPROXIMATION 39 3 10 7 lt ri cmp2 total energy fmo 1 gt normal RI MP2 correlatoin energy of the FMO1 Correlation energy and sum with the RHF energy are printed out see the sections 4 5 1 corr RI M P2 HF ext Z corr RI M P2 E fmol y E fmol F E fmol 3 10 8 lt Imp2 total energy fmo 1 gt normal LMP2 correlatoin energy of the FMO1 Correlation energy and sum with the RHF energy are printed out see the sections 4 6 1 peorr LMP2 pHFlert z as poor LM P2 f fmol fmol mol 3 11 Dimer es approximation After the following keyword progress of the dimer es approximation are printed out 3 11 1 lt energy gt progress of dimer es calculation contribution to energy is printed out 3 11 2 lt gradient gt progress of dimer es calculation contribution to gradient is printed out 3 12 Dimer calculations After the following keyword progress of each dimer calculation is printed out where A and B are sequential serial numbers of the dimer calculations and the fragment pairs respectively dimer calculations are performed to oder widh large size Note that only the dimer calculations performed with core whose mpi_rank is 0 are printed out For each dimer
38. e distribution of the PAICS Chapter 2 Input 2 1 General rule The value of each keyword is set by writing a keyword name and value s separated with space or new line x mpi_np 4 Don t use O mpi_np 4 II Use space The line started with is treated as a comment 2 2 Keywords In this section keywords of the PAIC S which are used in input are summarized 2 2 1 General control e mpi_np int The number of cores used for calculation of each fragment or fragment pair Default value is 1 For example in the case that the total number of cores used for calculation is 8 and this keyword is set to 2 each calculation of fragment or fragment pair is parallelized with 2 cores and 4 individual calculations are progressed at the same time Thus the total number of cores must be divisible by this value You can set this value separately for monomer SCC calculation monomer calculation and dimer calculation using the following keywords The total number of cores used for calculation is determined with MPI options when performing the calculation e mpi_np_scc int 10 CHAPTER 2 INPUT The number of cores used for calculation of each fragment in monomer SCC calculation If this keyword is not set value of mpi_np keyword is used In analogy with the mpi_np the total number of cores used for calculation must be divisible by this value mpi np mon int The number of cores used for cal
39. e sets performing RI MP2 calculation Note that RHF calculation is performed by default line 07 08 These lines mean that atomic numbers coordinates basis functions of 12 atoms are given in the following lines The number of 1 in this line indicates that spherical harmonic type of basis function is used line 09 20 These line give the atomic numbers coordinates basis functions of the atoms line 22 23 These lines give the number of the fragment In this case only one fragment is given because the conventional calculation is performed 2 3 EXAMPLE 25 line 25 26 These lines give the definition of the fragment In this case only one defi nition of the fragment is given 2 3 2 FMO calculation of tetramer of water molecules In Figure 2 4 input for FMO calculation of tetramer of water molecules is given The Figure 2 4 Example input fmo h2o 4 inp T 2 mpi_np 1 3 mem_mbyte 1792 5 ri_cmp2 1 7 ATOM 8 12 1 9 1 8 cc pVDZso_008 3 486380 1 544957 0 147898 10 2 8 cc pVDZso_008 1 544970 3 486131 0 147941 at 2 3 8 cc pVDZso_008 3 486367 1 544968 0 147896 12 4 8 cc pVDZso_008 1 544966 3 486182 0 147916 13 2 5 1 cc pVDZso_001 1 941779 2 463103 0 002632 14 6 1 cc pVDZso_001 4 427908 2 291387 1 463627 15 3 1 cc pVDZso_001 2 463369 1 941622 0 003213 16 8 1 cc pVDZso_001 2 291661 4 428602 1 462845 17 9 1 cc pVDZso_00
40. ere u v A o are indices of the basis functions of X Using these matrices we introduce the other matrices Vx K Ux K Vx K 4 1 13 Vx gt gt Vx 4 1 14 K X hy hy Vx Px 4 1 15 Fx hy 2Jx Kx 4 1 16 The molecular orbitals determined by the Fock equation with the operator of Eq 4 1 1 are defined as x5 DWE OX hi 4 1 17 L and the density matrix is defined as DE o 2 CH CHE 4 1 18 4 1 FMO RHF ENERGY 49 4 1 3 Energy The HF energies of the monomer and dimer are 1 B 5Tr D hx Fx 4 1 19 Here we introduce a new energy which is obtained by excluding the contribution of the environ mental electrostatic potential from the Bee that is E a BEF _Tr D F Vx 4 1 20 The total energy of the one body approximation of the FMO method FMO1 is defined as PaA EGS 4 1 21 I and the total energy of the two body approximation of the FMO method FMO2 is defined as EEE YO BHP Ny 2 0 BFF 4 1 22 I lt J I This FMO2 energy can be written as eee ERP 4 BPF BPF BY 4 1 23 I gt J Here we introduce a new matrix D whose dimension is same as that of the density matrix of dimer IJ and the matrix elements are defined as metlandvel DIG u DF fy gt HF the others Di ps Using this matrix the FMO2 RHF energy is written as BRT y BPP S er EPP E 7 I I gt J 5 Tr DEF Vi Tr Di Vrs Tr Did Vi i 4 1 24 I gt J Add
41. es basis functions of 38 atoms are given in the following lines and spherical harmonic basis functions are used line 09 46 These line give the atomic number coordinates basis functions of the atoms line 49 50 These lines give the number of fragment In this case 3 fragments are given in the following lines line 52 61 These lines give the definition of the 3 fragments 2 3 4 FMO calculation of HCO in water molecules In Figure 2 6 input for FMO calculation of HzCO in water molecules is given The meaning of each line of the input 2 3 EXAMPLE 27 Figure 2 6 Example input fmo h2co water12 inp mem_mbyte 1792 mpi_np 1 cmp2_grad 1 ri_cmp2_grad 1 40 1 cc pVDZso_008 0 319322 1 cc pVDZso_006 0 904629 0 307596 1 387482 cc pVDZso_001 0 117246 1 047770 3 137662 cc pVDZso_001 2 682198 o 940018 0 700446 cc pVDZso_008 0 103300 492608 4 334387 x 256692 0 106102 sa455 RONACOHUOTAWN gt ps jo akon CO OO 2 45 36 1 cc pVDZso_001 8 052276 2 267906 0 972153 46 37 1 cc pVDZso_001 5 366306 1 949235 2 692752 47 38 8 cc pVDZso_008 1 972834 2 503713 7 637485 48 39 1 cc pVDZso_001 2 238241 0 671106 7 162132 a 49 40 f cc pVDZso_001 2 455521 3 946313 6 359779 50 51 FRAGMENT 52 13 5S 54 FRAG_ATOM o 4 o 55 1 2 3 4 2 5G N lt a 57 F
42. ese values the FMO2 RHF gradient is written as o ga Efm N 2 X GF A X GI A 4 2 17 I I gt J 4 2 3 Dimer es approximtion In the case of the dimer es pairs EPF is written as BEEP RHP 4 Tr DESV I 4 2 18 Thus we need to calculate the following value Da 4 2 19 E F 7 is given as Eq 4 1 30 Because parts including the derivative of density matrix is canceled we need to calculate the remaining parts Thus in the case of the dimer es pairs GTJ A GF A GF A 2 K FE gato t2 a Fv gat X SO DPED 7 hoz q Hy AZ 4 2 20 vel Noe T 4 2 4 Environmental electrostatic potential Because the environmental electrostatic potential is evaluated with the three types of manner as shown in Eq 4 1 34 and 4 1 36 this is written as the following equation 5 ADF T iai pve x 5 ADJE uv n 2 ux K uv 5 ADX iw 5a D Arow pve xX pve xX T o HF HF h J 5 AD BTA Vikapu gt ADE ey X Kp uv 14221 uvEX K3 vEX Kp lt derivative of ux K gt The derivative of ux x is a aa SO uxw az Hl OS Ros a v 4 2 22 K X K X BEK 4 2 FMO RHF GRADIENT 59 Thus the first term of Eq 4 2 21 is expressed as 5 AD eo 5 UX K u HVEX KAX n acta la pvVEX KAX BEK atl pe a Saree 4 2 23 4 lt derivative of VX Ka gt The derivative of ve Kaju is JA DM gt 5 BRE a Ka AocK4 Dif aa Blur 4 2 24 The first term of this e
43. f the elec and nuc The contribution of the external potential is not included 3 13 23 lt ri cmp2 electric field fmo 2 gt ele Electric field by the electron density of the FMO2 RI MP2 at the positions defined by the input BR MPA nuc Electric field by the nucleus charge at the positions defined by the input In the case that the calculated position is exactly overlapped to the nucleus position the contribution of this nucleus is excluded is attached sum The sum of the elec and nuc The contribution of the external potential is not included Chapter 4 Theory 4 1 FMO RHF energy In this section the theory related to the calculation of the FMO RHF energy is explained making it be related to the output of the PAICS The formulation basically follows the previous publications reporting the theory and method of the FMO scheme 1 2 3 4 5 6 7 4 1 1 Definition of operators In the FMO method a target molecule is divided into small fragments and only calculations of the fragments referred to as monomer and pairs of the fragments referred to as dimer are performed The total energy could be evaluated using the results of monomer and dimer calculations In these calculations the modified Fock operator is used which is fx fxt 5 uxu vx Px 4 1 1 K X where X is index of the fragment or pair of fragments i e X is replaced by J
44. g lines line 56 91 These lines give the 36 positions where the electron density electrostatic potential and electric field are calculated line 93 97 These lines give the definition of one fragments of H2CO 2 3 6 FMO calculation of print protein with GN8 molecule In Figure 2 8 input of the FMO calculation of print protein and GN8 molecule is given in which each amino acid residue is treated as a single fragment and GN8 molecule is divided into 4 fragments The meaning of each line of the input line 0002 0004 These lines set the number of cores user for the monomer SCC calcula tion the monomer calculation and the dimer calculation In this case all monomer calculations are performed with 8 cores in the monomer SCC procedure On the other hands if the total cores used for this calculation is 8 all monomer and dimer 2 3 EXAMPLE Figure 2 8 fmo prp gn8 inp 1750 5 2177 FRAG_ATOM 0 14 2 2178 1700 1701 1702 1703 1709 1707 1705 1706 1708 1710 1711 1712 1713 1704 2179 1697 1714 2180 2181 FRAG_ATOM 0 17 1 2182 1683 1684 1685 1686 1687 1688 1689 1690 1696 1694 1692 1693 1695 1697 1698 1699 1691 2183 1680 2184 2185 FRAG_ATOM 0 16 0 2186 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1 2 mpi_np_scc 8 3 mpi_np_mon 1 4 mpi_np_dim 1 a mem_mbyte 1792 7 ri_cmp2 1 8 9 ATOM 10 1729 1 A t 7 cc pVDZso_007 43
45. ge the FMO 1 energy change become smaller than this value the iteration is judged to be converged Default value is 1 0E 6 Both the values of scc_tv_1 and scc_tv_2 must be fulfilled for the convergence Idimer double Threshold value used for determination of the dimer es approximation pairs This value is given by the multiple of the van der Waals radius When the distance of the nearest atoms between two fragments is larger than this value its dimer calculation is performed using dimer es approximation Default value is 2 0 Iptc double Threshold value used for determination of the fragments treated with point charge approx imation in calculation of the environmental electrostatic potential This value is given by the multiple of the van der Waals radius Default value is 2 0 laoc double Threshold value used for determination of the fragments treated with three center approx imation in calculations of the environmental electrostatic potential This value is given by the multiple of the van der Waals radius Default value is 0 0 projection_tv double Positive value used in the projection operators for the fragmentation Default value is 1 0E 6 cp_corr int BSSE correction with the counter poise method is applied for evaluations of the IFIE 1 apply O not apply Default value is 0 BSSE correction could be applied only for the IFIE of the fragment pairs not sharing covalent bonds scc_no_dyn
46. gy as Bima Eimi O E I B E EUG I gt J Tr ADEP Vis Tr ADEF VE 4 1 53 The second term of this equation is the two body correction on the FMO1 energy Thus we can define the IFIE including the external potential as the following equation ABEF c t _ E HF gt HF _ BAP 4 Tr ADEFV Tr ADEF V3 4 1 54 4 1 7 Energy including nucleus potential The monomer or dimer HF energy including the external electrostatic potential and nucleus Ee ee potential is written as pE leet EEF 4 Tr DEF ve EZ 4 1 55 Zo ZAZB ZAZLC EX D Ra Rg EA Dar Ds Ra R A lt B EX K X AEX CEK D3 D dr EZ 4 1 56 KAX AEX where E is the interaction energy between the nuclei and external potential The first term is the repulsive potential among the nuclei in X and the second term is the repulsive potential between the nuclei in X and the K th fragment The third term is the attractive potential between the nucleus in X and the electron density of the K th fragment Here we introduce some values defined as the following equations ZAZB E XY 4 1 57 A lt B EX Ra Re ZalZo gt gt Ra Ro 4 1 58 Acxcek A Si Eze Zapn t 4 1 59 2 Ra r 1 Using these values Eq 4 1 56 is written as prenn _ pur Tr DE vet EZZ 5y E o 5y EX EX 4 1 60 K X K X The FMO1 RHF energy is defined by excluding the contribution of the other fragments from sum of the monomer energies Th
47. hands monomer scc and dimer calculations are skipped The meaning of each line of the input Figure 2 3 Example input h2o0 4 inp 1 2 mpi_np 1 3 mem_mbyte 1792 4 5 ri_cmp2 1 6 7 ATOM 8 12 1 9 1 8 cc pVDZso_008 3 486380 1 544957 0 147898 10 2 8 cc pVDZso_008 1 544970 3 486131 0 147941 11 3 8 cc pVDZso_008 3 486367 1 544968 0 147896 12 4 8 cc pVDZso_008 1 544966 3 486182 0 147916 13 5 1 cc pVDZso_001 1 941779 2 463103 0 002632 14 6 1 co pVDZso_001 4 427908 2 291387 1 463627 15 7 1 cc pVDZso_001 2 463369 1 941622 0 003213 16 8 1 cc pVDZso_001 2 291661 4 428602 1 462845 17 9 1 cc pVDZso_001 1 941777 2 463141 0 002634 18 10 1 cc pVDZso_001 4 427776 2 291180 1 463833 19 11 1 cc pVDZso_001 2 463453 1 941764 0 002780 20 12 1 cc pVDZso_001 2 291353 4 428135 1 463364 21 22 FRAGMENT 23 1 24 25 FRAG ATOM 0 12 o0 2 1 2 3 4 5 6 7 8 9 10 11 12 27 28 line 02 This line sets the number of cores user for monomer or dimer calculation In the case of a conventional calculation only one monomer calculation is performed Thus this number should be same as the total number of cores used in calculation The total number of cores is given when performing calculation with the MPI option line 03 This line sets the size of memory per core used for calculation in Mbyte In this case 1729 Mbyte is used per core line 05 This lin
48. he IFIE of the SCS MP2 correlation with Hill s factor In the case performing the BSSE correction the corrected value is additionally printed out see the section 4 4 3 ARMER Ape Fe ee 3 13 FMO 2 RESULT Al 3 13 3 lt ri cmp2 ifie gt normal not scs Contribution to the IFIE of the RI MP2 correlation In the case performing the BSSE correction the corrected value is additionally printed out see the section 4 5 1 and 4 5 2 APES MER AE ITUM SMER gt EE RAAE ITM 3 3 13 4 lt Imp2 ifie gt Imp2 ifie Contribution to the IFIE of the LMP2 correlation AR een 3 13 1 3 13 5 lt rhf total energy fmo 2 gt total FMO2 energy in the RHF calculation including the nucleus potential and the interaction energy with the external potential see the section 4 5 3 textsf4 1 6 and 4 1 7 De FF Tr DEF ver ae EZ Epo I E EF EN PF BAP I gt J Tr AD F Vis Ef Tr ADF VE internal The value obtained by excluding the interaction energy with the external potential from the total Thus in the case that the external potential dose not exist this value is equivalent to the total see the section 4 5 3 textsf4 1 6 and 4 1 7 Sie FE BF 0 BEF E EF E YF Tr ADEFV 13 BF I I gt J external Only the contribution of the interaction energy with the external potential in the total Thus sum of the internal and external
49. hf_orthtv double Threshold value used for canonical orthognalization Default value is 1 0E 6 This value is applied for all monomer and dimer RHF calculations e rhf_engtv double Threshold value of the energy used for the convergence test Default value is 1 0E 8 This value is applied for all the monomer and dimer RHF calculations 2 2 5 Canonical MP2 e cmp2 int Canonical MP2 calculation is performed O not performed 1 performed Default value is 0 e cmp2_grad_ int MP2 gradient calculation is performed 1 performed O not performed Default value is 0 e cmp2_Iprint_1 int Print level of monomer canonical MP2 calculation Default value is 1 which gives a normal printing e cmp2 lprint 2 int Print level of dimer canonical MP2 calculation Default value is 1 which gives a normal printing e cmp2 th_iajs double Threshold value used for screening of the integral transformation Default value is 1 0E 8 2 2 KEYWORDS 17 e cmp2 th_iars double Threshold value used for screening of the integral transformation Default value is 1 0E 8 e cmp2 th pqrs double Threshold value used for screening of the integral transformation Default value is 1 0E 8 2 2 6 RI MP2 e ricmp2 int RI MP2 calculation is performed O not performed 1 performed Default value is 0 In RI MP2 calculation auxiliary basis function is used In the PAICS auxiliary basis function is
50. ing Grimm s factor MP2 SCS1 M P2 In the case using Jung s factor MP2 SCS2 M P2 In the case using Hill s factor i MP2 SCS3 M P2 4 4 4 Gradient Derivative of the FMO2 MP2 energy is MP2 BHF 0 peert MP2 gg imo2 gg fmo t jg fmo 4 4 9 where the term of the MP2 correlation energy EA is written with the derivatives of the monomer and dimer correlation energy as pcorr MP2 _ N 2 y O pony te y 9 peorr MP2 4 4 10 A fmo2 f A I e A IJ or 4 4 FMO MP2 67 The derivatives of the monomer and dimer correlation energy is corr corr corr OB D DPZ Sine We rq Stu vel aes 2 ww do 4 4 11 pvrAo ELT Ey 5 DEP E 5 Wee ore pvEIJ pvEIJ 0 IJ Ds Pat wise iv IAe aD D we Bae 4 4 12 pvrAoEL I pvels where the matrixes of DQ WS and 9 are evaluated by the same way as a normal MP2 gradient calculation the superscript MP2 is ommited Note that only the derivative of the dimer correlation energy includes the environmental electrostatic potential term In the case that external electrostatic potnetial exists the following term is added corr M P2 yez corr M P2 ex Ny 2 _ 5 D T AS Dp Diz i A ie 4 4 13 I pvel I lt J pvel ds 4 4 5 Electron density Electron density of the FMO2 MP2 is corr M P2 pee ta a E a T 4 4 14 where the correlation term is written as corr M P2 corr M P2 P fmo2 r gt 5 Di uv u r m V rm I pvel co
51. ion 1 buffered O not buffered Default value is 0 This value is applied for all monomer and dimer RHF calculations This keyword is used only for checking performance of the program in development rhf Iprint 1 int Print level of monomer RHF calculation Default value is 1 which gives a normal printing rhf_lprint 2 int Print level of dimer RHF calculation Default value is 1 which gives a normal printing rhf_maxit int Maximum number of RHF iteration Default value is 999 This value is applied for all monomer and dimer RHF calculations rhf_ndiis int Number of Fock matrices recorded for DIIS acceleration Default value is 4 This value is applied for all monomer and dimer RHF calculations rhf_diis_tv double Threshold value used for DIIS acceleration When the maximum value of the DIIS error vectors become smaller than this value DIIS acceleration is started Default value is 2 0 This value is applied for all monomer and dimer RHF calculations rhf_orth int Method used for the orthogonalization of the basis function O canonical orthogonalization 1 symmetric orthogonalization Default value is 1 This value is applied for all monomer and dimer RHF calculations rhf_init_mo int Method for making initial orbitals 16 CHAPTER 2 INPUT O hcore 1 projection from orbitals using sto 3g Default value is 1 This value is applied for all monomer and dimer RHF calculations e r
52. itionally we introduce a new matrix ADF Diy Dis Dir I 4 1 25 Using this matrix the FMO2 RHF energy is written as Epo gt BFP O B EF gees Eee 52 Tr AD FVH ae 4 1 26 I I gt J I gt J Here we introduce a new value AERP BBP E PF gt BP Tr ADEF VE 4 1 27 and using this value the FMO2 RHF energy is written as the following equation Eo Ero 5 AEF 4 1 28 I gt J Thus we can consider that the second term of this equation is the two body correction on the FMO1 RHF energy and which is called inter fragment interaction energy IFIE or pair interaction energy PIE 50 CHAPTER 4 THEORY 4 1 4 Dimer es approximation For the dimers constructed with largely separated fragments the E 77 is approximately calcu lated by considering only the electrostatic interaction between the two fragments This treatment is called dimer es approximation In this approximation the E 7 is evaluated as the fol lowing equation eS EPE EGP I cera R ae ER r a Te ae T14 f AERE asda 4 1 29 AEJ ACI Roen r r This equation can be written with the density matrices as PPr apang B YF4 DEF win A DE usw A DrD who 4 30 uvEI pvEJ pvEI oe I Additionally for the dimer es pairs the following equation is satisfied Tr ADFF Vis Tr D77 Vis Tr DIG Vis Tr Dyy Vrs 0 4 1 31 Thus by combining this equation with Eq 4 1 27 the AE
53. keyword is set to 1 w_result_file keyword must be set Since the results of each core is written separately the file is made by the number of cores e w scc int Write the monomer density determined by the monomer scc calculation O not write 1 write Default value is 0 The file name is automatically determined as w_result_file scc Thus when this keyword is set to 1 w_result_file keyword must be set The electron density written to this file can be used as an initial density of the monomer SCC calculation when performing the other calculations e rresult_file char String used for name of the file from which some information is read during calculation e rscc int Read the monomer electron density from the file as an initial density of monomer scc calculation O not read 1 read Default value is 0 The file name is automatically determined as r_result_file scc Thus when this keyword is set to 1 r_result_file keyword must be set e atom Atoms are defined This keyword must be given in every calculations How to use this keyword is described in the following subsection e fragment int Number of the fragments This keyword must be given in every calculations In the case of conventional calculation i e not FMO calculation this keyword is set to 1 How to use this keyword is described in the following subsection 12 CHAPTER 2 INPUT frag_atom Fragment is defined This keyword m
54. l The contribution of the environmental electrostatic potential is excluded see the sections 4 1 1 and 4 1 5 E FP Tr DEP Ve TAA Rp rhf E The value obtained by excluding the interaction energy with the external potential from the rhf E ext Thus in the case that the external potential dose not exist this value is equivalent to the rhf E ext see the sections 4 1 4 HF Z Ely EF 3 10 2 lt monomer cmp2 corr energy gt cmp2 normal The MP2 correlation energy of each monomer see the sections 4 4 1 Bee cmp2 grimme The SCS MP2 correlation energy of each monomer with Grimme s factor see the sections 4 4 1 and 4 4 3 pocorn M P2 1 I cmp2 jung SCS MP2 correlation energy of each monomer with Jung s factor see the sections 4 4 1 and 4 4 3 pers cmp2 hill SCS MP 2 correlation energy of each monomer with Hill s factor see the sections 4 4 1 and 4 4 3 peor M P23 T 3 10 3 lt monomer ri cmp2 corr energy gt ri cmp2 normal The RI MP2 correlation energy of each monomer see the sections 4 5 1 poor RI MP2 I 3 10 4 lt monomer Imp2 corr energy gt Imp2 The LMP2 correlation energy of each monomer see the sections 4 6 1 Pertwee I 38 CHAPTER 3 OUTPUT 3 10 5 lt rhf total energy fmo 1 gt total FMO1 energy in the RHF calculation including the nucleus potential and the interaction energ
55. lation Progress of each dimer calculation Only dimer calculations performed with the core whose mpi_rank is 0 are printed out 12 fmo 2 result Values evaluated using the results of monomer and dimer calculations i e the results of two body approximation of the FMO method 3 2 Input information After the following keyword information about the input are printed out e lt memory gt mpi parallel gt parameters and thresholds gt rhf gt cmp2 gt lt lt lt e lt ri cmp2 gt lt Imp2 gt lt read basis set definition gt lt input coordinate of nucleus charge gt lt input coordinate of basis sets gt lt input fragment gt 3 3 Make projection operator In the PAICS before beginning the monomer SCC calculation RHF calculations and orbital localizations of a CH molecule are performed for every fragmentations including cut of a covalent bond to make a projection operator After the following keyword information about the making projection orbital are printed out If the fragmentations including cut of a covalent bond exist information about the RHF calcu lation and the localization to make projection operator is printed out 3 4 MEMORY INFORMATION 35 3 4 Memory information After the following keyword information about the global variables of the PAICS are printed out The size of the memory used for the global variables is printed out The remaining memory can be used for the
56. mer calculation When dividing the fragments into two groups F and Fz we defined the partial energy of Fi as Eq 4 1 68 Thus the partial energy gradient of the atoms in F can be defined as the following equation a giim Np 2 G7 P A 7 GT AJH I I gt J SOSO GK A Np XO GH A Np XO GH A 4 2 42 I K I K where IJ and KL are the indexes of the fragments in F and F respectively and A is the geometrical parameters of the atoms of the fragments in F Difference between the normal energy gradient Eq 4 2 17 and partial energy gradient is Np 2 S GHY A So GHEY A 4 2 43 K K gt L As show in the previous section the terms including derivative of the density matrix dose not need to be calculated in the case of the normal energy gradient i e the last term of Eq 4 2 8 and the second term of Eq 4 2 12 are canceled with each other But in the case of the partial energy gradient the following terms are remained because of the above difference o aes DE VKw 4 2 44 K I pveKk If we want to calculate the partial energy gradient exactly this term must be evaluated But this term is treated as zero in the PAICS It is consider that when using the partial energy gradient for geometry optimizations or molecular dynamics simulations we need the gradient close to the total gradient rather than the exact partial gradient 4 3 FMO RHF density In this sectio
57. n the theory related to the calculation of the electron density electrostatic potential and electric field of the FMO RHF is explained making it be related to the output of the PAICS The formulation basically follows the previous publications reporting the theory and method of the FMO scheme 1 4 3 1 Electron density The electron density of the monomer or dimer is written as occ oe rm gt m OF Em Hlm 4 3 1 iEX where r is the molecular orbital of monomer or dimer and n is occupation number i e 2 in the case of RHF calculation Using the density matrix this equation is written as PX tm Dey ultm v t 4 3 2 VEX 4 3 FMO RHF DENSITY 63 FMO1 density is defined as Pfmor Pm po Pr tm 4 3 3 FMO2 density is defined as P mo2l rm gt of pri rm a rm 4 3 4 I gt J The FMO2 density is rewritten as ofr oa tm Pfton Em O PLT Om OFF em oF em b 438 I gt J Here we introduce Ap r defined as Apri tm pri tm p a oF Em E gt D ADT w Lm Vem 4 3 6 pvEIJ Consequently the FMO2 density is written as Diro Em Pfinor Tm gt A Ca 4 3 7 I gt J We should note that the second term of the FMO2 RHF electron density in Eq 4 3 7 is two body correction on the FMO1 RHF electron density 4 3 2 Electrostatic potential The electrostatic potential at position rm is written as the following equation HF HF p r m
58. ng the selected dimer calculations is enough Using frag_calc_pair keyword only selected dimer calculations are performed In this case prion protein and GN8 is assigned to 1 102 and 103 106 fragments respectively Thus the following descriptions should be added to the input frag_calc_pair 1 103 106 1 102 This is equivalent to the following descriptions frag_calc_pair 4 frag_calc_pair 408 103 1 102 103 1 104 1 102 103 2 105 1 102 106 1 102 103 102 104 1 104 2 104 102 105 1 105 2 105 102 106 1 106 2 106 102 2 3 7 The other examples of input The other examples are included in the distribution of PAICS which are listed as follows e trp2 inp conventional calculation of TRP 2 2 3 EXAMPLE 31 c12h26 inp conventional calculation of Cy2H26 molecule fmo c12h26 inp FMO calculation of C12H26 molecule gly5 inp conventional calculation of GLY s fmo h2co water128 inp MO calculation of HCO in water molecules fmo h2co water128 pc inp FMO calculation of H2CO in water molecules with point charges h2co water128 pc inp conventional calculation of HyCO in water molecules with point charges fmo hiv lIpv inp FMO calculation of HIV1 protease and lopinavir molecule fmo dna inp FMO calculation of DNA 2 3 8 Development of the program for making the input Paics View As shown in this section it is not easy to make an input manually in the case of the FMO calculation of a protein o
59. nk This keyword depends on your computer system Usually this is not needed to be set 2 run make sh Run make sh in the root directory of the PAICS If it is successful main exe is created The c 1 2 ompile takes time considerably Execute How to execute the PAICS is explained in this section 1 3 TEST CALCULATION 5 1 2 1 Make input file When performing the PAICS you need to make an input file see the section of input of this manual 1 2 2 Run calculation 1 You must set an environmental variable PAICS_ROOT in which the root directory of the PAICS is set This environmental value is referred to during calculation 2 Run the main exe using MPI command together with one argument of the input filename Examples of the script to run the PAICS are shown in Figure 1 1 1 2 3 Results of calculation Results are printed out into standard output so they could be recorded using redirection After the calculation you should check whether the WARNING has come out or not 1 3 Test calculation After the compilation it is recommended to perform the test calculations and check the computational results as follows 1 3 1 Execution of test calculations To perform the test calculations is recommended with example inputs after the compi lation Since manner of the execution is depends on your computer systems some trial and error may be needed As a reference computational times of the examples are shown below
60. nts in combined fragment molecular orbital and polarizable con tinuum model FMO PCM calculation H Li D G Fedorov T Nagata K Kitaura J H Jensen M S Gordon J Comp Chem 31 2010 778 790 Importance of the hybrid orbital operator derivative term for the energy gra dient in the fragment molecular orbital method T Nagata D G Fedorov K Kitaura Chem Phys Lett 492 2010 302 308 Fully analytic energy gradient in the fragment molecular orbital method T Nagata K Brorsen D G Fedorov K Kitaura M S Gordon J Chem Phys 134 2011 124115 73 74 BIBLIOGRAPHY 13 Partial energy gradient based on the fragment molecular orbital method ap 14 15 16 17 18 19 20 21 23 24 plication to geometry optimization T Ishikawa N Yamamoto K Kuwata Chem Phys Lett 500 2010 149 154 A parallelized integral direct second order Moller Plesset perturbation theory method with a fragment molecular orbital scheme Y Mochizuki T Nakano S Koikegami S Tanimori Y Abe U Nagashima K Kitaura Theor Chem Acc 112 2004 442 452 Large scale MP2 calculations with fragment molecular orbital scheme Y Mochizuki S Koikegami T Nakano S Amari K Kitaura Chem Phys Lett 396 2004 473 479 Second order Moller Plesset perturbation theory based upon the fragment molecular orbital method D G Fedorov and K Kitaura J Chem Phys 121 2004 2483 249
61. o2 rm ri zcmp2 corr RI MP2 rae em 3 13 FMO 2 RESULT 45 3 13 18 lt rhf electrostatic potential fmo 2 gt esp elec Electrostatic potential by the electron density of the FMO2 RHF at the positions defined by the input P mo2 rm esp nuc Electrostatic potential by the nucleus charge at the positions defined by the input In the case that the calculated position is exactly overlapped to the nucleus position the contribution of this nucleus is excluded is attached esp sum The sum of the esp elec and esp nuc The contribution of the external potential is not included 3 13 19 lt cmp2 electrosatic potential fmo 2 gt esp elec Electrostatic potential by the electron density of the FMO2 MP2 at the positions defined by the input Pf mod rm esp nuc Electrostatic potential by the nucleus charge at the positions defined by the input In the case that the calculated position is exactly overlapped to the nucleus position the contribution of this nucleus is excluded is attached esp sum The sum of the esp elec and esp nuc The contribution of the external potential is not included cmp2 corr ge ies 3 13 7 3 13 20 lt ri cmp2 electrstatic potential fmo 2 gt esp elec Electrostatic potential by the electron density of the FMO2 RI MP2 at the positions
62. quation is written using the Us as 400 XO UA A uv im 4550 Sous A uv lim 4 2 25 Ka i Kame Ka Ka i Ka me Ka If we neglect the second term this is written as occ Occ o Se o O88 2 Sra yuv lim 4 2 26 K4 i K4meK4 aBEek When using the density matrix this is written as 25 SY i a4 pi See DEE po b wy do 4 2 27 K4 c0 CK4 aBe Kk Consequently the second term of Eq 4 2 21 can be expressed as the following equation D gt ADX pv ies w T K4 pve x o OO AO OE y guno vVEX K4 30C Ka 1 25D f D PE aTtaeDH oshsa 0228 Ka aBEKa ocK4 where Ty Kyo gt ADE nv 4 2 29 VEX 60 CHAPTER 4 THEORY lt derivative of Vx gt The derivative of vx Ka uv S pak Doda E DES Fo Sxoal py AX K3 K3 o Ks o o DR yg sq xen ny dA DEF ASX pg uv w 4 2 30 The first term of this equation is written using the Ug as OCC OCC 4 gt x gt Ufi CH5m CHa Sxaol AY AA K3 o K3 i K3 mEK3 occ vir 450 SO SO SS UB CH im CH 5 Sxrc uv AA 4 2 31 Ks o K3 ic K3 MEK3 If we neglect the second term this is written as Occ Occ A met 2y DD 2 ye gt CR i CR mq SXa8 X K3 c K3i K3meK3 a EK3 OF mm Ch ot Sxoal pv AX 4 2 32 When using the density matrix this is written as 2 gt D be DR es T Sxap DEP Bo Sxoa py AX 4 2 33 K3 A K3 0 K3 a EK3 Consequently the thir
63. r IJ the following values are additionally needed B ac gt the monomer energy of the J th fragment under the vacuum condition including the basis set of the J th fragment Eo the monomer energy of the J th fragment under the vacuum condition including the basis set of the J th fragment p T Oa the monomer energy of the I th fragment under the vacuum condition Ha Ee the monomer energy of the J th fragment under the vacuum condition Using these values the BSSE of the IFIE between the fragments I and J is written as the following equation BSSE HF _ pHF vac HF vac HF vac HF vac E EP G gi perO _ ph 4 1 69 Thus the corrected IFIE is ABAOE 2 AEE pPSs2F 4 1 70 4 2 FMO RHF gradient In this section the theory related to the calculation of the FMO RHF gradient is explained making it be related to the output of the PAICS The formulation basically follows the previous publications reporting the theory and method of the FMO scheme 1 8 9 10 11 12 13 4 2 1 Definition of the UA We write the derivative of the orbital coefficients as a all aq Ox wi gt Vins OR 4 2 1 A Xom mEX where the following equation is satisfied o A A HF HF Ui T Uji R 5 Cx pi Cx vj 57Sxu 4 2 2 VEX 4 2 2 Derivative of the FMO energy From Eq 4 1 26 the following equation is obtained Pe aN SO BEY BF Tr ADEFV 4 2 3 T I gt J 56 CHAPTER 4 THEORY Here we introduce a new mat
64. r nuclic acid Now we have developed the program Paics View which supports creation of an input of the PAICS In the near future the source code of Paics View is going to be open to the public Chapter 3 Output 3 1 Overall of the output In the PAICS progress and result of calculation are printed out to the standard output by the following order 1 input information Values of the keyword definitions of the basis set coordinates of the nuclie and basis functions and definition of the fragment are printed out make projection operator Information about making projection operators used for fragmentation In the PAICS the projection operators are created in every calculations Memory information Size of the memory for the global variables of the PAICS fragment information Information of the fragments fragment pair information Information of the fragment pairs monomer scc calculation Progress of the monomer SCC calculation monomer scc result Results of the monomer SCC calculation monomer calculation Progress of each monomer calculation Only monomer calculations performed with the core whose mpi _rank is 0 are printed out 34 CHAPTER 3 OUTPUT 9 fmo 1 result Values evaluated using the result of monomer calculations i e the results of one body approximation of the FMO method 10 dimer es approximatoin Progress of the dimer es approximation 11 dimer calcu
65. re the FMO1 RHF energy is the following value see the section 4 1 y Tii 4 Tr DEF ver ms EZ zg I 3 8 Monomer SCC result After the following keyword results of the monomer SCC calculation are printed out 3 8 1 lt monomer scc charge center gt charge center The center of the positive charge of each fragment These values just depend on the coordinates of the nuclei charge center The center of the negative charge of each fragment These values depend on the electron density determined by the monomer SCC calculation 3 9 Monomer calculation After the following keyword progress of each monomer calculation is printed out A and B is sequential sequential number of the monomer calculations and the fragments respectively monomer calculations are performed to order with large size Note that only the monomer calculations performed with the core whose mpi_rank is 0 are printed out For each monomer calculation the progress of the calculations are printed out by the following order e monomer rhf e monomer cmp2 monomer ri cmp2 e monomer Imp2 e monomer field property 3 10 FMO 1 result After the following keyword values evaluated using the monomer calculation results are printed out 3 10 FMO 1 RESULT 37 3 10 1 lt monomer rhf energy gt rhf E ext The monomer energy of each fragment including the nucleus potential and the interaction energy with the external potentia
66. re 4 3 3 and 4 3 7 the total electron number is written as N froi gt Drs 4 3 18 I pel RE NER Na P 5 D ADEF Sis 4 3 19 I gt J weld BE where NE SIN Nao 4 3 20 Thus we obtain the following expression for the electron population of atom A of the FMO1 and FMO2 N no A gt gt gt gt DF S 4 3 21 I pea Bie NF A Na A 5 DD ADEF Sis 4 3 22 I gt JuEA EE Here we introduce NEF and ANB F defined as the following equations NEF A gt DFFSr 4 3 23 EA 4 4 FMO MP2 65 AN A gt gt api S1 4 3 24 LEA HR Using these values the following expression is obtained Nimo ee 4 3 25 NFR 2 A NE A J ANF A 4 3 26 I gt J We should note that the second term of the FMO2 population is two body correction on the FMO1 population 4 4 FMO MP2 In this section the theory related to the FMO MP2 is explained making it be related to the output of the PAICS The formulation basically follows the previous publications reporting the theory and method of the FMO scheme 14 15 16 7 4 4 1 Energy The MP2 total energy of one body approximation FMO1 MP2 and two body approximation FMO MP2 is corr M P2 BME BEE st Be 4 4 1 corr M P2 Efo Efino2 on Ee Ms 4 4 2 Here nee and PA are defined with the MP2 correlation energy of monomer or dimer as peer MP2 corr M P2 pi LE ES J 4 4 3 poorr MP2 _ 3 per MP2 y Ape ME 4 4 4 I
67. rix defined as Diy Dis ale D5in gt 4 2 4 and using this matrix Eq 4 2 3 is written as B Np 2 Bree EPF SDENT 4 2 5 T I gt J Thus the FMO2 RHF gradient could be obtained as a derivative of this equation a a a Eha Np 2 GBF gt aa eit 2 Tr DGRVEF 4 2 6 I I gt J lt Derivative of E gt The derivative of the E a F is written as i j 2 Dw Vix Ph Ax Vie 4 2 7 Because derivative of EF is calculated as a normal RHF energy gradient we obtain the following equation sae tt x a Ho gabe 1 1 a t3 Dee Pr DF Pio 5q uy Ag pvrAoEL o o 2 SO Wie geri PF D Van 28 pvel pvel where the derivative of the projection operator is negracted and WHF is 1 wif gDx FxDx 4 2 9 As we shall see below the last term is canceled with the terms from the dimer parts of Eq 4 2 17 It should be noted that the derivative of the environmental electrostatic potential Vx is not needed for the derivative of E YF lt Derivative of BEF gt Because the derivative of the EEF is calculated as a normal RHF gradient its derivative is written as the following equation Dy Fw sabre pvEIJ 1 1 HF o t3 DD DIF w Dr r0 a PTF vaDIJ vo gg HY e pvrAoEL I o o 2 0 W aa wr S DEF w ga Viw 4 2 10 pvels pvel ds where the derivative of the projection operator is negracted In the case of BE 7 the derivative of the environmental electrostatic potential is neede
68. rr M P2 ESS AD a 4 4 15 I lt J pvEx where ADAME is defined as ADNa Des a Dees 4 4 16 4 4 6 Electrostatic potential Electrostatic potential of the FMO2 MP2 is corr MP A E a ah 4 4 17 where the MP2 correlation term is written as FAR MP2 p e D Dorr P2 u 1 tm TCAD P u J Em 4 4 18 I gt J 68 CHAPTER 4 THEORY 4 4 7 Electric field Electric field of the FMO2 MP2 is corr MP EMP2 tm EAE o tm Bers tm 4 4 19 where the correlation term is written as Bp Pen D Tr DF Sarl corr M P2 o 3 Tr AD ER urs rm 4 4 20 I gt J 4 4 8 Mulliken population Mulliken population of the FMO2 MP2 is N al A N iEo A Nemos P A 4 4 21 where the correlation term is written as a eee A y y DPS I pea 0 ADS 4 4 22 I gt J wEA 4 5 FMO RI MP2 In this section the theory related to the FMO RI MP2 is explained making it be related to the output of the PAICS The formulation basically follows the previous publications reporting the theory and method of the FMO scheme 19 20 21 4 5 1 Energy The RI MP2 total energy of one body approximation FMO1 RI MP2 and two body approxi mation FMO RI MP2 is oe corr RI M P2 ae S E Efko g B 4 5 1 D cea E SAN lea 4 5 2 Here A mall and a es are defined with the RI MP2 correlation energy of monomer of dimer as corr RI M P2 corr RI M P2 Ee Ss Er l 1 4 5 3 I corr RI M P2 corr RI M P2 corr
69. sult of calculation fmo h2co water12 inp FMO calculation of HCO in water fmo h2co water12 out result of calculation h2co water12 pc inp conventional calculation of HCO in water h2co water12 pc out result of calculation h2co water128 pc inp conventional calculation of HCO in water h2co water128 pc out result of calculation fmo h2co water128 inp conventional calculation of HzCO in water fmo h2co water128 out result of calculation fmo h2co water128 pc inp conventional calculation of H2CO in water fmo h2co water128 pc out result of calculation fmo prp gn8 inp FMO calculation of print protein and GN8 fmo prp gn8 out result of calculation 1 1 2 CHAPTER 1 COMPILE AND EXECUTE fmo hiv lpv inp FMO calculation of HIV1 protease and lorinavir fmo hiv lpv out result of calculation fmo dna inp FMO calculation of DNA fmo dna out result of calculation Compiler and library For compile of the PAICS MPI compiler and LAPACK libraries are needed 1 1 3 Compile 1 modification of make inc Appropriate modification for your computer system should be made in the make inc ROOT_DIR Absolute path of the root directory of the PAICS CC MPI compiler of C language LIB Libraries needed for the PAICS PAICS_INCDIR Directory containing the header files Usually this is set as PAICS_INCDIR ROOT_DIR src include CFLAGS Options of the compile Usually this is set as CFLAGS c 03 I PAICS_INCDIR LFLAGS Options of the li
70. t c Number of atoms added to the fragment d Sequential serial number of the atoms in the fragment e Sequential serial number of the atoms added to the fragment The atom added to the fragment is the atoms in the other fragment But to achieve appropriate fragmentation with cutting covalent bonds portion of the nucleus charge and basis function of the atoms in the neighboring fragment is added into the fragment when performing the monomer and dimer calculations Here such atoms are called atom added to the fragment Definition of the fragment is very complicated so an illustrative example is given In Figure 2 1 the fragmentation of C12H 6 is showed 2 2 KEYWORDS 21 Figure 2 1 An illustrative example of the fragmentation The numbers in the figure are the sequential serial numbers of the atoms This is C12H26 molecule the hydrogen atoms are omitted 26 C c Ee Cc YYY I na l c c yY yY 1 fragment 1 fragment 2 fragment 3 The definition of the fragmentation in Figure 2 1 is FRAGMENT 3 FRAG_ATOM O 13 1 1234567 89 10 11 12 13 14 FRAG_ATOM O 12 1 14 15 16 17 18 19 20 21 22 23 24 25 26 FRAG_ATOM O 13 0 26 27 28 29 30 31 32 33 34 35 36 37 38 Although 14th atom is not an atom in the fragment 1 an positive charge 1 0 e and basis function of this atom are included in the calculation of the fragment 1 to achieve an appropriate fragmentation Thus for the definition of the fragment 1 14
71. th atom is treated as the atom added to the fragment Similarly 26th atom is the atom added to the fragment for the fragment 2 For the fragment 3 the atom added to the fragment dose not exist 22 CHAPTER 2 INPUT 2 2 10 basis_def keyword Basis set is defined using basis_def keyword But in calculations using the basis functions ready defined in the PAICS this keyword is not needed The format of basis_def keyword is BASIS_DEF a b c da e g c d fe tf Lg c d where each column is a Name of definition b Number of shells c Angular momentum d Number of contraction e Sequential serial number of primitive gaussian f coefficient of primitive gaussian g exponential of primitive gaussian The name of definition is used in atom keyword to determine the basis function of each atom Because this definition is complicated an example of the cc pVDZ basis set of carbon atom is given in Figure 2 2 2 3 EXAMPLE 23 Figure 2 2 Definition of the cc pVDZ basis set of carbon atom BASIS_DEF cc pVDZ_006 6 0 8 1 0 0006920 6665 0000000 2 0 0053290 1000 0000000 3 0 0270770 228 0000000 4 0 1017180 64 7100000 5 0 2747400 21 0600000 6 0 4485640 7 4950000 T 0 2850740 2 7970000 8 0 0152040 0 5215000 0 8 1 0 0001460 6665 0000000 2 0 0011540 1000 0000000 3 0 0057250 228 0000000 4 0 0233120 64 7100000 5 0 0639550 21 0600000 6 0 14
72. us the FMO1 energy including the nucleus potential is written as ea leeta L SER Tr DEF ve 5y EZZ N ee 4 1 61 T 54 CHAPTER 4 THEORY The FMO2 energy is defined as raves ext Z HF ext Z HF ext Z Bere NO Ns 2 E 4 1 62 I lt J I Thus we can obtain the FMO2 RHF energy including the nucleus potential as o BEE oor 3 Tr D VF X Tr AD V5 fmo2 I gt J DEF DER Ter G6 I lt J I This is rewritten as PORA eee a gt D AnH Tr ADYE ve x E Z 4 1 64 I lt J where the second term is two body correction on the FMO1 RHF energy Thus we can consider that the second term of this equation is the IFIE explicitly including the nucleus potential i e Re AEPHF Tr ADEF vet E74 4 1 65 Ty IJ Vis T J 4 1 8 Restriction of dimer calculation First we divide the fragments into two groups F and F gt and the fragments in the F and F gt are identified using the indices of IJ and KL respectively Using these indices the FMO1 RHF energy in Eq 4 1 21 is written as Eno gt BPP S BR 4 1 66 I K On the other hands the FMO2 RHF energy in Eq 4 1 28 is written as Efko ge ee S Cone I gt J gt gt E R AER 4 1 67 K gt L Here we perform only the dimer calculations of the pair including the fragments in the F In this case because the fifth term of Eq 4 1 23 is not performed the FMO2 RHF energy can not be calculated But at the following condition the number of fr
73. ust be given in all calculations How to use this keyword is described in the following section basis_def Basis set is defined How to use this keyword is described in the following section ex_point_charge External point charges are defined After description of the number of point charges the values and coordinates are given ex_point_charge number of point charges 1 charge x y z 2 charge x y z See example input 2 3 5 position Positions are defined For these positions some field properties are calculated i e electron density electrostatic potential and electric field When this keyword is set these field properties are automatically calculated After description of the number of positions the coordinates are given position number of positions ESZI EYL pe 2CxJ pyb pa See example input 2 3 5 2 2 2 FMO method scc_maxit int Maximum iteration number of the monomer SCC calculation Default value is 199 scc_tv_l double One of the threshold values used for convergence check of the monomer SCC calculation When all the monomer energy changes become smaller than this value the iteration is judged to be converged Default value is 1 0E 6 Both the values of scc_tv_1 and scc_tv_2 must be fulfilled for the convergence 2 2 KEYWORDS 13 scc_tv _2 double One of the threshold values used for convergence check of the monomer SCC calculation When the total energy chan
74. y with the external potential see the sections 4 1 1 and 4 1 5 y e P Tr DEF vert sis EZ Efe I internal The value obtained by excluding the interaction energy with the external potential from the total Thus in the case that the external potential dose not exist this value is equivalent to the total see the sections 4 1 4 and 4 1 5 So EF Ef I external The contribution of the interaction energy with the external potential in the total Thus sum of the internal and external is equivalent to the total In the case that the external potential dose not exist this value is zero see the sections 4 1 1 and 4 1 5 rr Di ve 4 Efe I 3 10 6 lt cmp2 total energy fmo 1 gt normal MP2 correlatoin energy of the FMO1 Correlation energy and sum with the RHF energy are printed out see the sections 4 4 1 M P2 HF ext Z orr M P2 Emol E fmol F Emol Grimm s scs SCS MP2 correlatoin energy of the FMO1 scaled with Grimme s factor Correlation energy and sum with the RHF energy are printed out see the sections 4 4 1 and 4 4 3 Ben Ee eee Jung s scs MP2 correlatoin energy of the FMO1 scaled with factors developed by Jung Correlation energy and sum with the RHF energy are printed out see the sections 4 4 1 and 4 4 3 corr M P2 1 HF ext Z corr M P2 2 E fmol E fmol E fmol Hill s scs MP2 correlatoin energy of the FMO1 scale

Download Pdf Manuals

Related Search

Related Contents

Manual Lijadora orbital `delta` - 12v  Samsung GT-S5050 Instrukcja obsługi  Epson Equity 386SX Product Support Bulletin  CHROME REAR MASTER CYLINDER KIT - Harley  Tecumseh VSAG490ZXTXM Performance Data Sheet  Whirlpool ACP102PS2 User's Manual  

Copyright © All rights reserved. Failed to retrieve file