1 FMO RHF MP2 MP2 RI MP2 RHF RHF 2

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2 1 FMO RHF MP2 MP2 RI MP2 RHF RHF 2

3 RHF RI MP RHF FMO RHF MP2 MP2 3

4 3 PAICS Teoretical study of the prion protein based on the fragment molecular orbital method, T. Ishikawa, T. Ishikura, and K. Kuwata, J. Comput. Chem., 30 (2009) PAICS Fragment interaction analysis based on local MP2, T. Ishiskawa, Y. Mochizuki, S. Amarai, T. Nakano, H. Tokiwa, S. Tanaka, and K. Tanaka, Theor. Chem. Acc., 118 (2007) An application of fragment interaction analysis based on local MP2, T. Ishikawa, Y. Mochizuki, S. Amari, T. Nakano, S. Tanaka, and K. Tanaka, Chem. Phys. Lett., 463 (2008) Teoretical study of the prion protein based on the fragment molecular orbital method, T. Ishikawa, T. Ishikura, and K. Kuwata, J. Comput. Chem., 30 (2009) Fragment molecular orbital calculation using the RI MP2 method, T. Ishikawa and K. Kuwata, Chem. Phys. Lett., 474 (2009) Acceleration of monomer self-consistent charge process in fragment molecular orbital method, T. Ishikawa and K. Kuwata, C.B.I.J., 10 (2010) Partial energy gradient based on the fragment molecular orbital method: application to geometry optimization, T. Ishikawa, N. Yamamoto, and K. Kuwata, Chem. Phys. Lett., 500 (2010)

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6 1 1.1 paics.zip Makefile paics Makefile make.inc make.inc Makefile make.sh bash clean.sh bash main.c PAICS paics.run.sh MPICH paics.run.lsf.sh LSF man / PDF PAICS development.pdf compile and execute.pdf input.pdf theory.pdf variable.pdf function.pdf PAICS 2

7 src / include / parallel control / memoryl control / paics / input / output / fmt / oneint / oneint grad / eri / eri grad / esp / projection / fragment / monomer scc / monomer / dimer es / dimer / rhf / cmp2 / ri cmp2 / localize / lmp2 / pol / geom opt / abmd / PAICS 1 1 SCC ES RHF MP2 RI MP2 MP2 basis / user.dat sto3g.dat 631g.dat 631gdp.dat cc-pvdz.dat STO-3G 6-31G 6-31G** cc-pvdz 3

8 cc-pvtz.dat cc-pvqz.dat cc-pvdzso.dat cc-pvtzso.dat cc-pvdzri.dat cc-pvtzri.dat cc-pvqzri.dat cc-pvtz cc-pvqz cc-pvdz segmented opt cc-pvtz segmented opt RI cc-pvdz RI cc-pvtz RI cc-pvqz sample / h2o-4-ccpvdz.inp h2o-4-ccpvdz.np1.out fmo-h2o-4-ccpvdz.inp fmo-h2o-4-ccpvdz.np1.out c12h26-ccpvdz.inp c12h26-ccpvdz.np1.out fmo-c12h26-ccpvdz.inp fmo-c12h26-ccpvdz.np1.out gly5-ccpvdz.inp gly5-ccpvdz.np1.out fmo-gly5-ccpvdz.inp fmo-gly5-ccpvdz.np1.out fmo-prion-ccpvdz.inp fmo-prion-ccpvdz.np8.out fmo-prion-gn8-ccpvdz.inp fmo-prion-gn8-ccpvdz.np8.out H 2 O 4 FMO H 2 O 4 FMO C 12 H 26 FMO C 12 H 26 FMO GLY 5 FMO GLY 5 FMO FMO GN8 FMO 1.2 PAICS MPI MPI LAPACK 4

9 make.inc make.inc ROOT DIR PAICS CC MPI C LIB LAPACK PAICS INCDIR PAICS_INCDIR = ${ROOT_DIR}/src/include CFLAGS CFLAGS = -c -O3 -I{PAICS_INCDIR} LFLAGS 2. make.sh make.sh main.exe make.sh make.sh % chmod 755 make.sh 5

10 2 2.1 PAICS CPU PAICS PaicsView 2.2 JOB PAICS ROOT PAICS main.exe MPI MPI 0 CPU PAICS PAICS WARNING 6

11 1: PAICS < mpirun paics.run.sh > #!/bin/bash export PAICS_ROOT=/home/ishi/program/paics INP=$1 NCPU=$2 DIR= pwd mpirun -np $NCPU $PAICS_ROOT/main.exe $DIR/$INP % paics.run.sh [ ] [ CPU ] >& [ ] & < lsf paics.run.lsf.sh > #!/bin/bash export PAICS_ROOT=/home/ishi/paics/paics 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 >& $DIR/$OUT_FILE" % paics.run.lsf.sh [ ] [ ] [ CPU ] 7

12 CPU h2o-4-ccpvdz.inp FMO RHF RI MP2 Core 2 Quad Q GByte fmo-h2o-4-ccpvdz.inp FMO RHF RI MP2 Core 2 Quad Q GByte c12h26-ccpvdz.inp FMO RHF RI MP2 Core 2 Quad Q GByte fmo-c12h26-ccpvdz.inp FMO RHF RI MP2 Core 2 Quad Q GByte gly5-ccpvdz.inp FMO RHF RI MP2 Core 2 Quad Q GByte fmo-gly5-ccpvdz.inp FMO RHF RI MP2 Core 2 Quad Q GByte 1 8

13 fmo-prion-ccpvdz.inp FMO RHF RI MP2 XeonE GByte fmo-prion-gn8-ccpvdz.inp FMO RHF RI MP2 XeonE GByte PAICS FMO FMO 1 FMO FMO FMO SCC ES FMO1 1 FMO2 2 FMO 1 FMO SCC 1 2 PAICS SCC SCC 9

14 SCC PAICS SCC 10 6 FMO 10

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16 1 1.1 [ ] mpi_np = 4 mpi_np mpi np [ int ] CPU CPU 8 2 2CPU 4 CPU 1 SCC CPU MPI FMO 1 CPU 1 1CPU 2 mpi np scc [ int ] SCC CPU mpi np mpi np CPU PAICS SCC CPU 1 mpi np 1 2

17 mpi np mon [ int ] CPU mpi np mpi np CPU mpi np 1 mpi np dim [ int ] CPU mpi np mpi np CPU mpi np 1 print rank [ int ] CPU mem mbyte [ int ] CPU MByte 128 1CPU 128Mbyte OS 1.4 PAICS lprint [ int ] PAICS coord unit [ int ] 3

18 0 : bohr 1 : 0 bohr w result file [ char ] 1020 SCC w log file [ int ] [ w result file ] [ mpi rank ]. log 0 : 1 : 0 w scc [ int ] SCC [ w result file ]. scc 0 : 1 : 0 r result file [ char ] 1020 r scc [ int ] SCC SCC [ r result file ]. scc 0 : 1 : 4

19 0 atom atom nucleus basis nucleus charge basis atom basis nucleus atom fragment [ int ] 1 FMO 1 FMO frag atom fragment fragment 1 frag def frag frag atom frag atom basis def 5

20 ex point charge ex_point_charge [ ] 1 [ ] [ x ] [ y ] [ z ] 2 [ ] [ x ] [ y ] [ z ]... position position [ ] 1 [ x ] [ y ] [ z ] 2 [ x ] [ y ] [ z ] eri tv [ double ] K ab 1.0E 12 eri cauchy tv [ double ] 1.0E 10 eri use gen [ int ] 4 0 : 1 : 6

21 0 eri 3cen use gen [ int ] 3 0 : 1 : FMO scc maxit [ int ] SCC 999 scc tv 1 [ double ] SCC 1 1.0E 6 scc tv 1 scc tv 2 scc tv 2 [ double ] SCC 1 FMO1 1.0E 6 scc tv 1 scc tv 2 ldimer [ double ] ES ES 2.0 lptc [ double ] 2.0 7

22 laoc [ double ] projection tv [ double ] projection 1.0E+6 cp corr [ int ] IFIE counter-poise BSSE 1 : CP 0 : CP 0 RHF MP2 RI MP2 BSSE BSSE CP BSSE 1 BSSE IFIE scc no dyn [ int ] SCC 1 : 0 : 0 SCC mpi np scc mpi np 1 pro loc tv [ double ] projection 1.0E 8 PAICS 8

23 SCC RHF pro loc maxit [ int ] projection 999 pro h basis [ char * ] projection CH 4 STO-3G 001 frag calc pair [ int ] [ list... ] FMO IFIE frag_calc_pair [ ] [ 1 ] [ 2 ]... [ ] 1 : ifrag jfrag 2 : ifrag jfrag1-jfrag2 3 : ifrag ALL ---> ifrag jfrag ---> ifrag jfrag1 jfrag2 ---> ifrag 1.7 RHF rhf chk [ int ] RHF 1 : RHF 0 : RHF 9

24 1 rhf chk no int buff RHF 1 : 0 : 0 1 rhf lprint 1 [ int ] RHF -1-1 rhf lprint 2 [ int ] RHF -1-1 rhf maxit [ int ] SCF 999 rhf ndiis [ int ] DIIS FOCK 4 rhf diis tv [ double ] DIIS DIIS 1.0 rhf orth [ int ] 0 : 1 : 0 rhf init mo [ int ] 10

25 0 : HCORE 1 : 1 FMO SCC 1 2 RHF SCC RHF RHF rhf orth tv [ double ] 1.0E 6 rhf eng tv [ double ] 1.0E MP2 MP2 cmp2 chk [ int ] MP2 0 : 1 : 0 MP2 RI MP2 cmp2 lprint 1 [ int ] MP cmp2 lprint 2 [ int ] MP cmp2 th iajs [ double ] MP E 8 cmp2 th iars [ double ] MP E 8 11

26 cmp2 th pqrs [ double ] MP E RI MP2 ri cmp2 chk [ int ] RI MP2 0 : 1 : 0 RI MP2 cc pvdz cc pvtz cc pvdzri cc pvtzri cc-pvdzri cc-pvdz cc-pvdzso 6-31G 6-31G** cc-pvtzri cc-pvtz ri cmp2 lprint 1 [ int ] RI MP ri cmp2 lprint 2 [ int ] RI LMP MP2 lmp2 chk [ int ] MP2 0 : 1 : 0 PAICS LMP2 FILM lmp2 lprint 1 [ int ] LMP

27 lmp2 lprint 2 [ int ] LMP lmp2 lprint loc 1 [ int ] LMP lmp2 lprint loc 2 [ int ] LMP lmp2 loc [ int ] 0 : Pipek-Mezey 1 : Boys 2 : 0 lmp2 max itr [ int ] 30 lmp2 th 1 [ double ] lmp2 th 1 dim [ double ] lmp2 th 2 [ double ] lmp2 th 2 dim [ double ] lmp2 th 3 [ double ]

28 lmp2 th 4 [ double ] 1.0E 12 14

29 2 PAICS atom ATOM [ ] [ ] [ ] [ ] [ ] [ X ] [ Y ] [ Z ] [ ] [ ] [ ] [ X ] [ Y ] [ Z ].. 0 : d 6 f 10 g 15 1 : d 5 f 7 g 9 coord unit 0 bohr 1 Å 0 coord unit bohr G** ATOM G**_ G**_ G**_ G**_ G**_ G**_ G**_ G**_ G**_ G**_ G**_ G**_

30 3 FRAGMENT FRAG ATOM FRAG ATOM FRAGMENT [ ] FRAG_ATOM [ ] [ ] [ ] [ [ ]... ] [ [ ]... ] FRAG_ATOM [ ] [ ] [ ] [ [ ]... ] [ [ ]... ] FRAG_ATOM... C 12 H 26 1 FRAGMENT 3 FRAG_ATOM FRAG_ATOM FRAG_ATOM fragment1 fragment fragment1 14 fragment2 26 fragment3 16

31 1: C 12 H C 8 C 14 C 20 C 26 C 32 C C 5 C 11 C 17 C 23 C 29 C 35 fragment 1 fragment 2 fragment 3 17

32 4 PAICS 1 STO-3G STO-3G *** basis / sto3g.dat G 6-31G *** basis / 631g.dat G** 6-31G** *** basis / 631gdp.dat cc-pvdz cc-pvdz *** basis / cc-pvdz.dat cc-pvtz cc-pvtz *** basis / cc-pvtz.dat cc-pvqz cc-pvqz *** basis / cc-pvqz.dat cc-pvdzso cc-pvdzso *** basis / cc-pvdzso.dat cc-pvtzso cc-pvtzso *** basis / cc-pvtzso.dat cc-pvdzri cc-pvdzri *** basis / cc-pvdzri.dat cc-pvtzri cc-pvtzri *** basis / cc-pvtzri.dat 1 36 BASIS DEF BASIS_DEF [ ] [ ] [ ] [ ] [ ] [ ] [ ].. [ ] [ ] [ ] [ ] [ ].. [ ] [ ].. 2 cc-pvdz user def.dat PAICS uset def.dat 18

33 2: cc-pvdz BASIS_DEF cc-pvdz_

34 1 FMO RHF 2 FMO RHF 3 FMO MP2 4 FMO RI MP2 5 FMO LMP2 1

35 1 FMO RHF 1.1 FMO RHF Fock Fock X X = I X = IJ f X =f X + K X { u (K) + v (K)} + P X (1.1) u (K) = A K Z A R A r 1 (1.2) v (K) = dr 2 ρ K (r 2 ) r 1 r 2 (1.3) ˆP X = B k θ X k θ X k (1.4) u (K) K v (K) K P X f X Fock f X = h X + 2 J X K X (1.5) h X = A X Z A R A r 1 (1.6) J X K X X µ, ν H core X µν = µ h X ν (1.7) 2

36 u X(K) µν = µ u K ν (1.8) v X(K) µν = µ v K ν (1.9) P X µν = µ P ν (1.10) G X µν = µ 2J X K X ν (1.11) V X(K) = u X(K) + v X(K) (1.12) V X = K X V X(K) (1.13) H core X = H core X + V X + P X (1.14) F X = H core X + G X (1.15) f X Fock ψ i X = µ C X µi φ µ (1.16) D X µν = 2 i C X µi C X νi (1.17) 3

37 PAICS E HF X = 1 2 T r { D X( H core X + F X ) } (1.18) E HF E HF X = E HF X T r { D X V X} (1.19) FMO1 RHF FMO2 RHF E HF fmo1 = I E HF I (1.20) E HF fmo2 = I<J E HF IJ ( N 2 ) I E HF I (1.21) E HF fmo2 E HF fmo2 = I E HF I + I>J ( ) E HF IJ E HF I E HF J (1.22) E HF E HF fmo2 = E HF I + ( ) E HF IJ E HF I E HF J I I>J + { T r D I V I} + ( { T r D IJ V IJ} { T r D I V I} { ) T r D J V J} I I>J (1.23) 4

38 E HF fmo2 = I E HF I + I>J ( + I>J ( ) E HF IJ E HF I E HF J T r { D IJ V IJ} T r { D I(J) V IJ} T r { D J(I) V IJ} ) (1.24) D I(J) IJ µ I ν I D I(J) µν = D I µν D I(J) µν = 0 D IJ D IJ = D IJ D I(J) D J(I) (1.25) 1.24 E HF fmo2 = I E HF I + I>J ( ) E HF IJ E HF I E HF J + { T r D IJ V IJ} (1.26) I>J E HF IJ ( ) { E HF IJ = E HF IJ E HF I E HF J + T r D IJ V IJ} (1.27) FMO2 RHF E HF fmo2 = I E HF I + I>J E HF IJ (1.28) 1 FMO1 RHF E HF fmo2 = E HF fmo1 + I>J E HF IJ (1.29) E HF IJ FMO1 RHF 2 inter fragment interaction energy IFIE pair interaction energy PIE 1 2 5

39 1.2 V X u X v X V X = K X u X(K) + K X v X(K) (1.30) u X(K) K X u X(K) µν = µ K X A K Z A R A r 1 ν (1.31) v X(K) esp-aoc 3. esp-ptc v X(K) K X v X(K) = K 4 v 4 X(K 4) + K 3 v 3 X(K 3) + K p v p X(K p) (1.32) 4 X(K 1.32 v 4) 4 4 K 4 ρ K4 (r) K 4 v 4X(K4) µν = K 4 µ dr 2 ρ K4 (r 2 ) r 1 r 2 ν (1.33) 6

40 ρ K4 (r) SCC D s X ρ K4 (r) = K D 4λσ s φ K4 λ(r)φ K4 σ(r) (1.34) λσ K 4 K 4 v 4X(K4) µν = K 4 K D 4λσ s ( µν λσ ) (1.35) λσ K 4 3 X(K 1.32 v 3 ) 3 3 K 3 ρ K 3 (r) k 3 v 3X(K3) µν = K 3 µ dr 2 ρ K 3 (r 2 ) r 1 r 2 ν (1.36) ρ K3 (r) SCC D s X ρ K3 (r) = ( ) K D 3λσ s S σλ φ λ φ λ (1.37) λ K 3 σ K 3 K 3 v 3X(K3) µν = K 3 ( ) D K 3 s S λλ λ K 3 ( µν λλ ) (1.38) 7

41 PAICS 6 d K 3 v 3X(K3) µν = K 3 λ K 3 ( D K 3 S ) λλ 1 ( µν λλ ) (1.39) λ λ X(K 1.32 v p ) p SCC B p cb K p v px(kp) µν = K p µ B K p p cb R B r 1 ν (1.40) ES ES RHF E HF IJ E HF IJ = E HF I + E HF J + ZA ρ I (r 1 ) R A r 1 dr 1 + A J A I ZA ρ J (r 1 ) R A r 1 dr 1 + ρ I (r 1 )ρ J (r 2 ) dr 1 dr 2 (1.41) r 1 r 2 E HF IJ = E HF I + E HF J + D I µνu I(J) µν + D J µνu J(I) µν + D I µν D J λσ( µν λσ ) (1.42) µν I µν J µν I λσ J 8

42 ES T r { D IJ V IJ} = T r { D IJ V IJ} T r { D I(J) V IJ} T r { D J(I) V IJ} = 0 (1.43) 1.27 E HF IJ E HF IJ =E HF IJ E HF I E HF J (1.44) E HF IJ = µν I D I µνu I(J) µν + µν J D J µνu J(I) µν + µν I λσ J D I µν D J λσ( µν λσ ) (1.45) Ē HF X = 1 { 2 T r D X( H X core + F X ) } + z A z B R A R B (A<B) X + z A z C R A R C + za ρ K (r) dr (1.46) R A r K X A X C K K X A X 2 X 3 X 4 X Z u X = (A<B) X z A z B (1.47) R A R B Z u X K = A X C K z A z C R A R C (1.48) 9

43 Z e X K = A X za ρ K (r) dr (1.49) R A r 1.46 Ē HF X = E HF X + Z X u + Z X K u + K X K X Z e X K (1.50) FMO1 RHF Ē HF fmo1 = I E HF I + I Z u I (1.51) FMO1 RHF 1 2 FMO1 RHF FMO2 RHF Ē HF fmo2 = Ē HF IJ (N 2) I<J I Ē HF I (1.52) Ē HF fmo2 = E HF IJ (N 2) I<J I { E HF I + Z I u + } I J Z u (1.53) I<J I FMO2 RHF FMO2 RHF Ē HF fmo2 = ĒHF fmo1 + ( ) E HF I J IJ + Z u (1.54) I<J 2 2 IFIE ĒHF IJ = E HF IJ + Z u I J (1.55) IFIE 1 2 IFIE 10

44 fock f X =f X + K X { u K + v K} + P X + v e X (1.56) v X e (r) V e X µν = µ v e ν (1.57) E HF X E HF X 1.56 fock E HF X X E HF X E HF X = E HF X T r { D X V e X } (1.58) 1.20 FMO1 RHF E HF fmo1 = I E HF I + I T r { D I V e I } (1.59) 1 2 FMO2 RHF 1.26 E HF X E HF fmo2 = E HF I + ( ) E HF IJ E HF I E HF J + T r { D IJ V IJ} I I>J I>J + { } T r D I I V e + ( { } { } { } ) T r D IJ IJ V e T r D I I V e T r D J J V e I I>J (1.60) V e T r { D I V e I } = T r { D I(J) V e IJ } (1.61) 11

45 T r { D J V e J } = T r { D J(I) V e IJ } (1.62) E HF fmo2 = I E HF I + I>J ( ) E HF IJ E HF I E HF J + T r { D IJ V IJ} I>J + { } T r D I I V e + T r { D } IJ IJ V e I I>J (1.63) E HF fmo2 = E HF fmo1 + { (E HF IJ E HF I E HF ) J I>J +T r ( D IJ V IJ) + T r ( D IJ V e IJ ) } (1.64) 2 2 IFIE E HF IJ = ( E HF IJ E HF I E HF ) J +T r ( D IJ V IJ) + T r ( D IJ V e IJ ) (1.65) E HF X E HF X V X e 1.27 FMO1 RHF FMO2 RHF IFIE 1.65 ES

46 Z I ext (1.66) I Z X ext X F 1 F 2 F 1 I J F 2 K L FMO1 RHF 1.20 E HF fmo1 = I E HF I + K E HF K (1.67) FMO2 RHF 1.28 E HF fmo2 = I E HF I + E HF IJ + I>J I + K K E HF IK E HF K + K>L E HF KL (1.68) F FMO2 RHF F 1 F 2 5 F 1 F 2 F 1 F 2 1/10 IFIE 13

47 F 1 3 F 1 F 2 F 1 E HF fmo2(f 1 ) = I E HF I + I>J E HF IJ + I E HF IK (1.69) K 1.7 BSSE FMO CP IFIE BSSE HF J I : E vac I (IJ) HF I J : E vac J (IJ) HF I : E vac I HF J : E vac J 4 BSSE E HF BSSE IJ = ( E vac HF I (IJ) E vac HF I ) + ( E vac HF J (IJ) E vac HF J ) (1.70) CP IFIE E HF CP IJ = E HF IJ E HF BSSE IJ (1.71) SCC 14

48 + charge center SCC - charge center SCC 1 rhf ( E ) E HF I + Z u I + Z I ext (1.72) 2 rhf ( E ) 1 1 E HF I + Z u I (1.73) FMO1 RHF 1 total FMO1 RHF { E HF I + Z I u + Z I ext} (1.74) I FMO1 RHF 2 internal FMO1 RHF 1 FMO1 RHF 1 { } E HF I I + Z u (1.75) I 15

49 FMO1 RHF 3 external FMO1 RHF 1 FMO1 RHF 2 FMO1 RHF 3 FMO1 RHF 1 { T r ( D I I V ) e + Z I ext} (1.76) I RHF IFIE 1 rhf IFIE E HF IJ + Z u I J (1.77) RHF IFIE 2 rhf ( cp ) RHF IFIE 1 BSSE E HF IJ + Z u I J E HF BSSE IJ (1.78) FMO2 RHF 1 total FMO2 RHF { E HF I + Z I u + T r ( D I I V ) e + Z I ext} + I { (E HF IJ E HF I E HF J) I>J } +T r ( D IJ V IJ ) + Z I J u + T r ( D IJ V IJ e ) (1.79) FMO2 RHF 2 internal FMO2 RHF 1 FMO2 RHF 1 { } E HF I I + Z u + I { (E HF IJ E HF I E HF J) I>J +T r ( D IJ V IJ ) + Z u I J } (1.80) 16

50 FMO2 RHF 3 external FMO2 RHF 1 FMO2 RHF 2 FMO2 RHF 3 FMO2 RHF 1 { T r ( D I I V ) e + Z I ext} + T r ( D IJ V IJ e ) (1.81) I I>J 17

51 1: FMO RHF rhf mon energy d rhf mon trdv rhf mon trdv e rhf mon energy vac cp E HF I } T r {D I V I T r {D } I I V e HF E vac I rhf dim ifie rhf dim trdv e rhf dim ifie cp E HF IJ T r { D } IJ IJ V e E HF BSSE IJ 18

52 2: FMO RHF frag nuclear repulsion frag nuclear ext Z u I Z I ext scc d mat scc mulliken ba scc mulliken bo * nbo 2 X (a) D s (a) p sb ( nbo D X s S) λλ (a) (b) rhf mon nmo rhf mon moe rhf mon moe vac cp rhf mon c mat rhf mon c mat vac cp * nbo (c) * nbo * nbo 2 * nbo 2 (c) (a) SCC (b) nbo (c) BSSE 19

53 2 FMO RHF 2.1 ρ X (r) ψ X i (r) ρ X (r) = occ. i X n i ψ X i (r) ψ X i (r) (2.1) n i RHF ρ X (r) = ( ) n i CX µi CX νi φ µ (r) φ ν (r) (2.2) µν X i ρ X (r) = µν X D X µν φ µ (r) φ ν (r) (2.3) FMO ρ fmo1 (r) = I ρ I (r) (2.4) ρ fmo2 (r) = I>J ρ IJ (r) (N 2) I ρ I (r) (2.5) ρ fmo2 (r) ρ fmo2 (r) = ρ fmo1 (r) + { } ρ IJ (r) ρ I (r) ρ J (r) I>J (2.6) ρ IJ (r) = ρ IJ (r) ρ I (r) ρ J (r) = D IJ µν φ µ (r) φ ν (r) (2.7) µν IJ 20

54 ρ fmo2 (r) = ρ fmo1 (r) + I>J ρ IJ (r) (2.8) Mulliken N elec N elec = ρ (r) dr (2.9) S N elec (fmo1) = I ( D S) I µµ µ I (2.10) N elec (fmo2) = N elec (fmo1) + I>J µ IJ ( ) D IJ S µµ (2.11) N elec = N elec (fmo1) = N elec (fmo2) (2.12) A N A fmo1 = I ( D S) I µµ µ A (2.13) { N A fmo2 = N A fmo1 + I>J µ A ( ) } D IJ S µµ (2.14) N I A N IJ A 21

55 N I A = ( ) D I S µµ µ A (2.15) N A IJ = µ A ( ) D IJ S µµ (2.16) N A fmo1 = I N A I (2.17) N A fmo2 = N A fmo1 + I>J N A IJ (2.18) ρ(r) r m φ(r m ) = ρ(r) r m r dr (2.19) FMO φ fmo1 (r m ) = I µν I D I µν µ 1 r m r ν (2.20) φ fmo2 (r m) = φ fmo1 (r m) + I>J µν IJ D IJ µν µ 1 r m r ν (2.21) u X (r m ) u X (r m ) µν = µ 1 r m r ν (2.22) 22

56 φ fmo1 (r m ) = I ) T r( D I u I (r m ) (2.23) φ fmo2 (r m ) = φ fmo1 (r m ) + ( ) T r D IJ u IJ (r m ) I>J (2.24) 2.4 FMO E fmo1 (r m ) = φ fmo1 = r m I T r { D I( ) } u I (r m ) r m (2.25) E fmo2 (r m ) = φ fmo2 = E fmo1 (r m ) { T r D ( IJ ) } u IJ (r m ) r m r m I>J (2.26) g m I = T r { g IJ m = T r { ( D I ) } u I (r m ) r m D ( IJ ) } u IJ (r m ) r m (2.27) (2.28) E fmo1 (r m ) = I g m I (2.29) E fmo2 (r m ) = E fmo1 (r m ) I>J g m IJ (2.30) ES g IJ m u X (r m ) r m u X (r m ) µν = r m µ 1 r m r ν = µ ( r m 1 r m r ) ν (2.31) µ ν r m 23

57 2.5 Mulliken population 1 rhf pop. Mulliken population 2 rhf charge Mulliken population 1 density 1 esp ( elec. ) 2 esp ( nuc. ) * 3 esp ( sum ) ( ele ) 2 ( nuc ) * 3 ( sum )

58 3: FMO RHF rhf mon m pop ba I N A I rhf mon pos dns I ρi (r) rhf mon pos esp ( ) I T r D I u I (r m ) rhf mon pos efi x rhf mon pos efi y rhf mon pos efi z I g m I x I g m I y I g m I z rhf dim m pop ba I>J N A IJ rhf dim pos dns I>J ρij (r) rhf dim pos esp ) I>J ( T r D IJ u IJ (r m ) rhf dim pos efi x rhf dim pos efi y rhf dim pos efi z I>J g m IJ x I>J g m IJ y I>J g m IJ z 25

59 3 FMO MP2 3.1 FMO1 MP2 FMO2 MP2 MP2 E MP 2 I MP2 E MP 2 IJ E MP 2 fmo1 = I E MP 2 I (3.1) E MP 2 fmo2 = I>J E MP 2 IJ (N 2) I E MP 2 I (3.2) E MP 2 I = E HF I + E corr(mp 2) I (3.3) E MP 2 IJ = E HF IJ + E corr(mp 2) IJ (3.4) E corr(mp 2) I E corr(mp 2) IJ MP E MP 2 fmo1 = E HF fmo1 + I E corr(mp 2) I (3.5) E MP 2 fmo2 = E HF fmo2 + ( I>J E corr(mp 2) IJ (N 2) I E corr(mp 2) I ) (3.6) 3.6 ( E MP 2 fmo2 = E HF fmo2 + E corr(mp 2) I + E corr(mp 2) IJ I>J I ) (3.7) 26

60 E corr(mp 2) IJ = E corr(mp 2) IJ E corr(mp 2) I E corr(mp 2) J (3.8) E corr(mp 2) fmo1 = I E corr(mp 2) I (3.9) E corr(mp 2) fmo2 = I E corr(mp 2) I + I>J E corr(mp 2) IJ (3.10) FMO1 MP2 FMO2 MP2 E MP 2 fmo1 = E HF fmo1 + E corr(mp 2) fmo1 (3.11) E MP 2 fmo2 = E HF fmo2 + E corr(mp 2) fmo2 (3.12) IFIE HF IFIE MP2 E MP 2 IJ = E HF IJ + E corr(mp 2) IJ (3.13) spin-compornent-scaled MP2 SCS MP BSSE MP2 HF BSSE CP corr I (IJ) J I : E vac corr J (IJ) I J : E vac corr I I : E vac corr J J : E vac 27

61 MP2 BSSE E corr BSSE IJ = ( E vac corr I (IJ) E vac corr I ) + ( E vac corr J (IJ) E vac corr J ) (3.14) CP MP2 IFIE E MP 2 CP IJ = E HF CP IJ + ( E corr IJ E corr BSSE IJ ) (3.15) corr corr 4 E vac I E vac J MP2 corr corr E vac I (IJ) E vac J (IJ) MP2 HF MP MP2 1 cmp2 ( normal ) MP2 MP2 2 cmp2 ( grimme ) Grimme SCS MP2 MP2 3 cmp2 ( jung ) Jung SCS MP2 MP2 4 cmp2 ( hill ) Hill SCS MP2 28

62 FMO1 MP2 1 corr. MP2 FMO1 RHF FMO1 MP2 2 Grimm s scs Grimme SCS MP2 FMO1 RHF FMO1 MP2 3 Jung s scs Jung SCS MP2 FMO1 RHF FMO1 MP2 4 Hill s scs Hill SCS MP2 FMO1 RHF MP2 IFIE 1 normal ( not scs ) IFIE MP2 RI MP2 CP BSSE MP2 IFIE 2 Grimme s scs IFIE MP2 Grimme SCS MP2 CP BSSE MP2 IFIE 3 Jung s scs IFIE MP2 Jung SCS MP2 CP BSSE MP2 IFIE 4 Hill s scs IFIE RI MP2 Jung SCS MP2 CP BSSE 29

63 FMO2 MP2 1 corr. MP2 FMO2 RHF FMO2 MP2 Grimm s scs Grimme SCS MP2 FMO2 RHF FMO2 MP2 : Jung s scs Jung SCS MP2 FMO2 RHF FMO2 MP2 Hill s scs Hill SCS MP2 FMO2 RHF 30

64 4: FMO MP2 SCS MP2 s t cmp2 mon energy s cmp2 mon energy t cmp2 mon energy vac cp s cmp2 mon energy vac cp t E corr(mp 2) I E corr(mp 2) I corr E vac I corr E vac I cmp2 dim ifie s cmp2 dim ifie t cmp2 dim ifie cp s cmp2 dim ifie cp t E corr(mp 2) IJ E corr(mp 2) IJ E corr BSSE IJ E corr BSSE IJ cmp2 fmo 1 s 1 E corr(mp 2) fmo1 cmp2 fmo 1 t 1 E corr(mp 2) fmo1 cmp2 fmo 2 s 1 E corr(mp 2) fmo2 cmp2 fmo 2 t 1 E corr(mp 2) fmo2 31

65 4 FMO RI MP2 4.1 FMO MP2 RI MP BSSE FMO MP RI MP2 1 ri cmp2 ( normal ) RI MP2 RI MP2 2 ri cmp2 ( grimme ) Grimme SCS RI MP2 RI MP2 3 ri cmp2 ( jung ) Jung SCS RI MP2 RI MP2 4 ri cmp2 ( hill ) Hill SCS RI MP2 FMO1 RI MP2 1 corr. RI MP2 FMO1 RHF 32

66 FMO1 RI MP2 2 Grimm s scs Grimme SCS RI MP2 FMO1 RHF FMO1 RI MP2 3 Jung s scs Jung SCS RI MP2 FMO1 RHF FMO1 RI MP2 4 Hill s scs Hill SCS RI MP2 FMO1 RHF MP2 RI IFIE normal ( not scs ) IFIE RI MP2 RI MP2 CP BSSE MP2 RI IFIE Grimme s scs IFIE RI MP2 Grimme SCS RI MP2 CP BSSE MP2 RI IFIE Jung s scs IFIE RI MP2 Jung SCS RI MP2 CP BSSE MP2 RI IFIE Hill s scs IFIE RI MP2 Jung SCS RI MP2 CP BSSE FMO2 RI MP2 corr. RI MP2 FMO2 RHF 33

67 FMO2 RI MP2 Grimm s scs Grimme SCS RI MP2 FMO2 RHF FMO2 RI MP2 : Jung s scs Jung SCS RI MP2 FMO2 RHF FMO2 RI MP2 Hill s scs Hill SCS RI MP2 FMO2 RHF 34

68 5: FMO RI MP2 SCS RI MP2 s t ri cmp2 mon energy s ri cmp2 mon energy t ri cmp2 mon energy vac cp s ri cmp2 mon energy vac cp t E corr(mp 2) I E corr(mp 2) I corr E vac I corr E vac I ri cmp2 dim ifie s ri cmp2 dim ifie t ri cmp2 dim ifie cp s ri cmp2 dim ifie cp t E corr(mp 2) IJ E corr(mp 2) IJ E corr BSSE IJ E corr BSSE IJ ri cmp2 fmo 1 s 1 E corr(mp 2) fmo1 ri cmp2 fmo 1 t 1 E corr(mp 2) fmo1 ri cmp2 fmo 2 s 1 E corr(mp 2) fmo2 ri cmp2 fmo 2 t 1 E corr(mp 2) fmo2 35

69 5 FMO LMP2 5.1 FMO1 LMP2 FMO2 LMP2 FMO MP2 LMP2 FMO1 LMP2 FMO2 LMP2 LMP2 E LMP 2 I LMP2 E LMP 2 IJ E LMP 2 fmo1 = I E LMP 2 I (5.1) E LMP 2 fmo2 = I>J E LMP 2 IJ (N 2) I E LMP 2 I (5.2) E LMP 2 I = E HF I + E corr(lmp 2) I (5.3) E LMP 2 IJ = E HF IJ + E corr(lmp 2) IJ (5.4) E corr(lmp 2) I E corr(lmp 2) IJ MP E LMP 2 fmo1 = E HF fmo1 + I E corr(lmp 2) I (5.5) E LMP 2 fmo2 = E HF fmo2 + ( I>J E corr(lmp 2) IJ (N 2) I E corr(lmp 2) I ) (5.6) 5.6 ( E LMP 2 fmo2 = E HF fmo2 + E corr(lmp 2) I + ) corr(lmp 2) E sub IJ I I>J (5.7) 36

70 E sub corr(lmp 2) IJ = E corr(lmp 2) IJ E corr(lmp 2) I E corr(lmp 2) J (5.8) E corr(lmp 2) fmo1 = I E corr(lmp 2) I (5.9) E sub corr(lmp 2) fmo2 = I E corr(mp 2) I + I>J E sub corr(lmp 2) IJ (5.10) FMO1 LMP2 FMO2 LMP2 E LMP 2 fmo1 = E HF fmo1 + E corr(lmp 2) fmo1 (5.11) E LMP 2 fmo2 = E HF fmo2 + E sub corr(lmp 2) fmo2 (5.12) IFIE HF IFIE E LMP 2 IJ = E HF IJ + E sum corr(lmp 2) IJ (5.13) corr(lmp 2) E sum IJ LMP2 E sum corr(lmp 2) IJ = i I ɛ ij (5.14) j J ɛ ij LMP2 IFIE E sum corr(lmp 2) fmo2 = I E corr(mp 2) I + I>J E sum corr(lmp 2) IJ (5.15) corr(lmp 2) 5.12 E sub fmo2 2 2 FMO2 LMP2 6 37

71 5.2 BSSE MP2 BSSE 5.3 LMP2 lmp2 LMP2 FMO1-LMP2 corr. LMP2 FMO1 RHF LMP2 IFIE lmp2 IFIE LMP2 FMO2-LMP2 1 corr. ( sub. ) LMP2 FMO2 RHF E sub corr(lmp 2) fmo2 (5.16) FMO2-LMP2 2 corr. ( sum. ) LMP2 FMO2 RHF E sum corr(lmp 2) fmo2 (5.17) 38

72 6: FMO LMP2 lmp2 mon energy E corr(lmp 2) I lmp2 dim ifie sub lmp2 dim ifie sum corr(lmp 2) E sub IJ corr(lmp 2) E sum IJ lmp2 fmo 1 1 E corr(lmp 2) fmo1 lmp2 fmo 2 sub 1 E sub corr(lmp 2) fmo2 lmp2 fmo 2 sum 1 E sum corr(lmp 2) fmo2 39

73 FMO 17 SCC 18 ES 19 RHF 20 MP2 21 RI MP2 22 MP2 1

74 1 PARA MPI MAX PROC 1024 MEM MAX VAL 1024 memory alloc allocate ANG L6 MAX 12 ang l6max ANG L5 MAX 4 ang l5max ANG L6 XYZ MAX 91 angl l6xyz max CONST MAX IATOM BDEF MAX 128 bdef max BDEF MAX SH 40 bdef max sh BDEF MAX NC 30 bdef max nc BDEF MAX L 4 bdef max l PRJ MAX FRAG ORB 16 PRJ MAX NBA 4 2

75 PRJ MAX NBO 64 FRAG MAX LINK 8 3

76 2 int para mpi nproc MPI MPI COMM WORLD initialize mpi MPI_Comm_size(MPI_COMM_WORLD,&para_mpi_nproc); int para mpi my rank MPI COMM WORLD initialize mpi MPI_Comm_rank(MPI_COMM_WORLD,&para_mpi_my_rank); int para mpi print rank MPI COMM WORLD initialize mpi 0 MPI Comm para mpi single comm initialize mpi my_key=para_mpi_my_rank/1; MPI_Comm_split(MPI_COMM_WORLD,my_key,para_mpi_my_rank,&para_mpi_single_comm); char para mpi proc name [ PARA MPI MAX PROC ] [ 128 ] 127 PARA MPI MAX PROC initialize mpi MPI_Get_processor_name(&para_mpi_proc_name[para_mpi_my_rank][0],&itmp); for(i=0;i<para_mpi_nproc;i++){ MPI_Bcast(&para_mpi_proc_name[i][0],128,MPI_CHAR,i,MPI_COMM_WORLD); } int para mpi np scc SCC CPU CPU para mpi nproc 4

77 int para mpi np mon CPU CPU para mpi nproc int para mpi np dim CPU CPU para mpi nproc 5

78 3 double * mem core ( [ mem size ] ) initialize memory mem_core = ( double * ) malloc ( mem_size * 8 ) ; long int mem size double initialize memory 32bit long int * 8 / 1024 / 1024 / 1024 = GByte 1CPU 16GByte 64bit int mem mbyte MByte mem size mem_size = mem_mbyte * ( 1024 * 1024 / 8 ) ; mem mbyte initialize memory int mem nval mem core MEM MAX VAL char max val name [ MEM MAX VAL ] [ 40 ] mem core 39 mem core MEM MAX VAL long int mem val size [ MEM MAX VAL ] mem core double EM MAX VAL 6

79 4 int cntrl run type read input list 01 0 : 1 : 2 : 0 int cntrl lprint pcs PAICS 0 : 1 : 2 : int cntrl lprint inp int cntrl lprint prj int cntrl lprint scc SCC 0 : 1 : 2 : SCC 3 : RHF 7

80 int cntrl lprint mon 0 : 1 : 2 : 3 : int cntrl lprint des int cntrl lprint dim int cntrl coord unit 0 : bohr 1 : angstrom read input list 01 0 bohr int cntrl w log file log 0 : 1 : 0 int cntrl r scc SCC 0 : 1 : 8

81 0 int cntrl w scc SCC 0 : 1 : 0 cntrl w result file.scc char * cntrl w result file [ 1024 ] char cntrl r result file [ 1024 ] char cntrl w log file name [ 1024 ] log cntrl w result file cntrl w result file [mpi-rnak].log char cntrl w scc file name [ 1024 ] SCC cntrl r result file cntrl w result file.scc char cntrl r scc file name [ 1024 ] SCC cntrl r result file cntrl r result file.scc double cntrl scc time1 SCC double cntrl mon time1 double cntrl dim time1 9

82 double cntrl des time1 ES double cntrl total time1 double cntrl total time2 10

83 5 int ang l6max = ANG L6 MAX 1 4 ANG L6 MAX int ang l6xyz max = ANG L6 XYZ MAX 1 ANG L6 XYZ MAX int * ang l6n [ ang l6max+1 ] 1 1 int * ang l6sum [ ang l6max+1 ] 1 1 l int l1 = ang_l6sum [l] - ang_l6n [l] int l2 = ang_l6sum [l] for ( i=l1 ; i<l2 ; i++ ) {... } int * ang l6xyz [ ang l6max+1 ] [ ang l6xyz max ] [ 3 ] 1 x y z l i x : ang_l6xyz [ ( ang_l6xyz_max * 3 ) * l + 3 * i + 0 ] y : ang_l6xyz [ ( ang_l6xyz_max * 3 ) * l + 3 * i + 1 ] z : ang_l6xyz [ ( ang_l6xyz_max * 3 ) * l + 3 * i + 2 ] int * ang l6xyz idx [ ang l6max+1 ] [ ang l6max+1 ] [ ang l6max+1 ] 1 x y z ang l6xyz xyz 11

84 int p01=(ang_l6max+1)*(ang_l6max+1); int p02=(ang_l6max+1); ang_l6xyz_idx [ p01 * 0 + p02 * ] 0 ang_l6xyz_idx [ p01 * 1 + p02 * ] 1 ang_l6xyz_idx [ p01 * 2 + p02 * ] 4 int ang l5max = ANG L5 MAX ANG L5 MAX int * ang l5n [ ang l5max+1 ] 1 2 int * ang l5sum [ ang l5max+1 ]

85 1: ang l6n ang l6sum ang l6n ang l6sum

86 2: sys l5n sys l5sum ang l5n ang l5sum

87 6 double const bohr = double const vdw radius [ CONST MAX IATOM ] CONST MAX IATOM int const atomic nfzc [ CONST MAX IATOM ] CONST MAX IATOM char const atomic label [ CONST MAX IATOM ] [ 4 ] CONST MAX IATOM 15

88 7 int fmt mmax = 17 4 m m 4 g 1 int fmt mt = 20 4 m +3 int fmt nt = m double fmt dt = E-4 double * fmt table double fmt tf [ 18 ] 4 4 m 16

89 8 double eri tv 1.0E 12 read input list 01 eri tv double eri cauchy tv 1.0E 10 read input list 01 eri cauchy tv double eri grad tv 1.0E 12 read input list 01 eri grad tv double eri use gen 0 : 1 : 0 read input list 01 eri use gen double eri 3cen use gen 3 0 : 1 : 0 read input list 01 eri use gen double eri grad use gen 17

90 0 : 1 : 0 read input list 01 eri use gen 18

91 9 int bdef max = BDEF MAX BDEF MAX int bdef max sh = BDEF MAX SH cc-pvdz 6 sssppd BDEF MAX SH int bdef max nc = BDEF MAX NC cc-pvdz G 6 BDEF MAX NC int bdef max l = BDEF MAX L BDEF MAX L int bdef n char * bdef name ( [ bdef max * 21 ] ) 20 read basis define read basis define file int * bdef nsh ( [ bdef max ] ) read basis define read basis define file int * bdef nbo ( [ bdef max ] ) nbo read basis define read basis define file cc-pvdz int * bdef sh nc ( [ bdef max * bdef max sh ] ) read basis define read basis define file i j 19

92 bdef_sh_nc [ bdef_max_sh * i + j ] int * bdef sh l ( [ bdef max * bdef max sh ] ) read basis define read basis define file i j bdef_sh_l [ bdef_max_sh * i + j ] double * bdef sh expon ( [ bdef max * bdef max sh * bdef max nc ] ) read basis define read basis define file i j k bdef_sh_expon [ bdef_max_sh * bdef_max_nc * i + bdef_max_nc * j + k ] double * bdef sh coeff ( [ bdef max * bdef max sh * bdef max nc ] ) read basis define read basis define file i j k bdef_sh_coeff [ bdef_max_sh * bdef_max_nc * i + bdef_max_nc * j + k ] 20

93 10 int basis spher 0 : 1 : read basis int basis n read basis int basis nbo total nbo basis define assign int basis max nc basis define assign int basis max l basis define assign int basis aux RI 1 0 RI 0 int * basis type ( [ basis n ] ) read basis basis define assign PAICS iba bdef_nsh [ basis_type [ iba ] ] bdef_nbo [ basis_type [ iba ] ] 21

94 int * basis type ini ( [ basis n ] ) read basis basis define assign PAICS RHF int * basis type aux ( [ basis n ] ) RI char * basis name ( [ basis n * 21 ] ) 20 read basis char * basis name ini ( [ basis n * 21 ] ) 20 char * basis name aux ( [ basis n * 21 ] ) RI 20 int * basis nucleus ( [ basis n ] ) -1 double * basis x ( [ basis n ] ) x read basis basis x orig double * basis y ( [ basis n ] ) y read basis basis y orig double * basis z ( [ basis n ] ) z read basis basis z orig 22

95 double * basis x orig ( [ basis n ] ) x read basis double * basis y orig ( [ basis n ] ) y read basis double * basis z orig ( [ basis n ] ) z read basis int * basis aux to basis ( [ basis n ] ) RI char * basis label [ 2 ] [ 5 ] [ 15 ] [ 6 ] 3 23

96 3: basis label [ ] [ i ] [ j ] [ k ] i j k basis label [ 0 ] [ ] [ ] [ ] i j k basis label [ 1 ] [ ] [ ] [ ] s s px px py py pz pz d d d d d d d d d d d f f f f f f f f f f f f f f f f f g g g g g g g g g g g g g g g g g g g g g g g g

97 11 int nucleus n double * nucleus u ( [ nucleus n ] ) double * nucleus x ( [ nucleus n ] ) x nucleus x orig double * nucleus y ( [ nucleus n ] ) y nucleus y orig double * nucleus z ( [ nucleus n ] ) z nucleus z orig double * nucleus x orig ( [ nucleus n ] ) x double * nucleus y orig ( [ nucleus n ] ) y double * nucleus z orig ( [ nucleus n ] ) z double * nucleus vx ( [ nucleus n ] ) x double * nucleus vy ( [ nucleus n ] ) 25

98 y double * nucleus vz ( [ nucleus n ] ) z double * nucleus vx orig ( [ nucleus n ] ) x double * nucleus vy orig ( [ nucleus n ] ) y double * nucleus vz orig ( [ nucleus n ] ) z int * nucleus atomic ( [ nucleus n ] ) MCP nucleus u char * nucleus opt fix ( [ nucleus n ] ) 0 : 1 : 0 char * nucleus abmd fix ( [ nucleus n ] ) nucleus opt fix double * nucleus u grad xyz ( [ nucleus n * 3 ] ) calc nuclear repulsion grad 26

99 12 int ext point charge n double * ext point charge x ( [ ext point charge n ] ) x double * ext point charge y ( [ ext point charge n ] ) y double * ext point charge z ( [ ext point charge n ] ) z double * ext point charge q ( [ ext point charge n ] ) 27

100 13 int pos n double * pos x ( [ pos n ] ) x double * pos y ( [ pos n ] ) y double * pos z ( [ pos n ] ) z 28

101 14 int * frag list esp 4 n ( [ frag n ] ) 4 int * frag list esp 3 n ( [ frag n ] ) 3 int * frag list dscf n ( [ frag n ] ) SCF int * frag list esp 4 idx ( [ frag n ] ) frag list exp 4 int * frag list esp 3 idx ( [ frag n ] ) frag list exp 3 int * frag list dscf idx ( [ frag n ] ) frag list dscf int * frag list esp 4 ( [ ] ) 4 int * frag list esp 3 ( [ ] ) 3 int * frag list dscf ( [ ] ) SCF int frag n 29

102 int frag n orig int * frag nelec ( [ frag n ] ) read fragment int * frag nelec orig ( [ frag n ] ) read fragment int frag nelec all initialize fragment int * frag nfzc ( [ frag n ] ) initialize fragment int * frag npch ( [ frag n ] ) initialize fragment int frag nnu1 all frag nch1 charge n initialize fragment int frag nnu1 max frag nch1 initialize fragment int * frag nnu1 ( [ frag n ] ) nch1 30

103 int * frag nnu1 orig ( [ frag n ] ) nch1 read fragment int * frag nnu1 in ( [ frag n ] ) read fragment frag_nch1 = frag_nnu1_in + PAICS int * frag nnu1 in orig ( [ frag n ] ) read fragment int * frag nnu1 idx ( [ frag n ] ) 1 read fragment int * frag nnu1 idx orig ( [ frag n ] ) 1 read fragment int * frag nucleus ( [ frag nch1 all ] ) nucleus ifrag ich frag_charge [ frag_nch1_idx [ ifrag ] + ich ] 31

104 int * frag nucleus orig ( [ frag nch1 all ] ) double * frag nucleus u ( [ frag nch1 all ] ) read fragment ifrag ich frag_charge_u [ frag_nch1_idx [ ifrag ] + ich ] int frag nba1 all frag nba1 basis n read fragment int frag nba1 max int * frag nba1 ( [ frag n ] ) read fragment int * frag nba1 orig ( [ frag n ] ) read fragment int * frag nba1 in ( [ frag n ] ) read fragment frag_nba1 = frag_nba1_in + 32

105 int * frag nba1 in orig ( [ frag n ] ) read fragment int * frag nba1 idx ( [ frag n ] ) 1 read fragment int * frag nba1 idx orig ( [ frag n ] ) 1 read fragment int * frag basis ( [ frag nba1 all ] ) read fragment ifrag iba frag_basis [ frag_nba1_idx [ ifrag ] + iba ] int * frag basis orig ( [ frag nba1 all ] ) read fragment int * frag basis add frag ifrag iba mon_basis_add_frag [ mon_basis_add_frag_idx [ ifrag ] + iba ] int * frag basis add frag idx ( [ frag n ] ) mon basis add frag int frag nsh1 all 33

106 int frag nsh1 max int * frag nsh1 ( [ frag n ] ) int * frag nsh1 idx ( [ frag n ] ) 1 int * frag nsh1 xyz idx ( [ frag n ] ) x,y,z 1 int * frag shell ( [ frag nsh1 all * 3 ] ) PAICS ao ao ifrag ish 0 frag_shell [ frag_nsh1_idx [ ifrag ] + 3 * ish + 0 ] 1 frag_shell [ frag_nsh1_idx [ ifrag ] + 3 * ish + 1 ] 2 frag_shell [ frag_nsh1_idx [ ifrag ] + 3 * ish + 2 ] int * frag shell xyz ( [ frag nsh1 all * 3 ] ) ifrag ish frag_shell [ frag_nsh1_xyz_idx [ ifrag ] + 3 * ish + 0 ] frag_shell [ frag_nsh1_xyz_idx [ ifrag ] + 3 * ish + 1 ] frag_shell [ frag_nsh1_xyz_idx [ ifrag ] + 3 * ish + 2 ] ( x ) ( y ) ( z ) int frag nbo1 all nbo1 34

107 int frag nbo1 max nbo1 int * frag nbo1 ( [ frag n ] ) nbo int * frag nbo1 idx ( [ frag n ] ) bo 1 int frag nbot all nbot int frag nbot max nbot int * frag nbot ( [ frag n ] ) nbo int * frag nbot idx ( [ frag n ] ) bo 1 int * frag nbot idx ( [ frag n ] ) bo 1 ifrag frag_nbot_idx [ ifrag ] int frag nbo2 all nbo2 int frag nbo2 max nbo2 int * frag nbo2 ( [ frag n ] ) bo 35

108 frag_nbo2[ifrag] = frag_nbo1[ifrag] * frag_nbo1[ifrag] int * frag nbo2 idx ( [ frag n ] ) bo 1 int frag pro n all projection orbital frag pro n make projection operator int * frag pro n ( [ frag n ] ) projection orbital make projection operator int * frag pro idx ( [ frag n ] ) projection orbital make projection operator int * frag pro ( [ frag pro n all ] ) projection orbital make projection operator ifrag ipro frag_pro [ frag_pro_idx [ ifrag ] + ipro ] int frag link n all frag link n make projection operator int * frag link n ( [ frag n ] ) make projection operator int * frag link idx ( [ frag n ] ) make projection operator int * frag link 1 ( [ frag pro link n all ] ) make projection operator 36

109 int * frag link 2 ( [ frag pro link n all ] ) make projection operator int * frag calc order ( [ frag n ] ) make frag calc order int * frag calc fprop ( [ frag n ] ) 0 : 1 : int * frag ovl diag ( [ frag nbo1 all ] ) double * frag muclear repulsion ( [ frag n ] ) double * frag muclear ext ( [ frag n ] ) int frag pair calc n int frag pair calc n orig int frag pair calc n es ES make frag pair calc order n ES MP2 37

110 int frag pair calc n scf SCF make frag pair calc order n SCF MP2 int frag pair calc 1 idx frag pair calc 1 frag pair calc 2 int frag pair calc 1 idx orig frag pair calc 1 orig frag pair calc 2 orig int * frag pair calc 1 ( [ frag pair calc n ] ) read fragment int * frag pair calc 2 ( [ frag pair calc n ] ) read fragment int * frag pair calc 1 orig ( [ frag pair calc n ] ) int * frag pair calc 2 orig ( [ frag pair calc n ] ) int * frag pair calc order ( [ frag pair calc n scf * 2 ] ) SCF make frag pair calc order SCF int frag calc total chk 1 0 frag calc pair 1 1 fragment initalize 38

111 15 int prj lpring int prj loc tv int prj loc tv RHF DIIS int prj loc maxit int prj total n 1 1 C C 5 int prj total nba 1 1 frag pro total n int prj total nbo nbo int * prj nba ( [ prj total n ] ) int * prj basis idx ( [ prj total n ] ) int * prj basis ( [ prj total nba ] ) ipro iba 39

112 prj_basis [ prj_basis_idx [ ipro ] + iba ] ifrag ipro iba prj_basis[prj_basis_idx[frag_pro[frag_pro_idx[ifrag]+ipro]]+iba] int * prj nbo ( [ prj total n ] ) bo int * prj c idx ( [ prj total n ] ) int * prj c ( [ prj total nbo ] ) ipro ibo bo prj_c [ prj_c_idx [ ipro ] + ibo ] int * prj ifrag ( [ prj total n ] ) int * prj jfrag ( [ prj total n ] ) int * prj h basis name [ 21 ] 4 STO 3G FMO STO-3G int * pro h basis type 40

113 16 FMO int fmo scc maxit SCC 99 read input list 01 scc maxit int fmo scc no dyn SCC 0 : 1 : 0 int fmo cp corr IFIE CP 0 read input list 01 textsfcp corr 0 : 1 : double fmo scc tv SCC 1 1.0E 6 read input list 01 scc tv double fmo scc tv total SCC 1 FMO1 1.0E 6 read input list 01 scc tv total double fmo ldimer [ ] * [ fmo_ldimer ] ES 2.0 read input list 01 ldimer 41

114 double fmo laoc [ ] * [ fmo_laoc ] read input list laoc double fmo lptc [ ] * [ fmo_lptc ] 2.0 read input list 01 lptc double fmo projecion tv 1.0E+6 read input list 01 projection tv FMO 42

115 17 SCC int * scc chk read frag ( [ frag n ] ) 0 : 1 : 1 SCC int * scc d mat ( [ frag nbot all ] ) SCC ifrag i j i j scc_d_mat [ frag_nbot_idx[irag] + (i+1)*i/2 + j ] int * scc mulliken ba ( [ frag nba1 all ] ) SCC Mulliken int * scc mulliken bo ( [ frag nbo1 all ] ) SCC bo Mulliken int * scc e charge center ( [ frag n ] [ 3 ] ) int * scc u charge center ( [ frag n ] [ 3 ] ) 43

116 double scc time scf SCC SCF double scc time eps SCC double scc time eps 4 SCC 4 double scc time eps 3 SCC 3 double scc time eps m SCC double scc time eps u SCC double scc time eps ext SCC 44

117 18 ES double esa time e ES double esa time u ES double esa time grad e ES double esa time frag u ES 45

118 19 RHF int rhf chk RHF 0 : 1 : FMO RHF 1 int rhf chk grad RHF 0 0 : 1 : int rhf chk no int buff 0 : 1 : RHF 4 4 int rhf chk mon worb RHF 0 : 1 : cntrl w result file int rhf lprint 1 RHF

119 3 : -1 4 : Mulliken int rhf lprint 2 RHF : 2 : BSSE double rhf eng tv RHF double rhf orth type RHF 0 : 1 : double rhf orth tv RHF int rhf init mo type RHF 0 : H-CORE 1 : int rhf maxit RHF int rhf maxit mkinit RHF rhf init mo type 1 int rhf ndiis RHF DIIS 47

120 int rhf diis tv RHF DIIS int rhf diis tv ini RHF DIIS double rhf diff fock tv RHF differential fock char rhf mon conv chk all RHF monomer calculation RHF 1 0 : RHF 1 : RHF char * rhf mon conv chk ( [ frag n ] ) RHF 0 : 1 : int * rhf mon nmo ( [ frag n ] ) nmo nbo > nmo doube * rhf mon moe ( [ frag nbo1 all ] ) ifrag imo rhf_mon_moe[frag_nbo1_idx[ifrag]+imo] doube * rhf mon c mat ( [ frag nbo2 all ] ) ifrag imo ibo 48

121 rhf_mon_c_mat[frag_nbo2_idx[ifrag]+frag_nbo1[ifrag]*imo+ibo] double * rhf mon energy d ( [ frag n ] ) RHF E rhf initialize allocte rhf monomer double * rhf mon trdv ( [ frag n ] ) rhf initialize allocte rhf monomer double * rhf mon trdv e ( [ frag n ] ) rhf initialize allocte rhf monomer double * rhf mon m pop ba frag ( [ frag nba1 all ] ) RHF double * rhf mon moe vac cp ( [ frag nbo1 all ] ) RHF BSSE CP double * rhf mon c mat vac cp ( [ frag nbo2 all ] ) RHF BSSE CP double * rhf mon energy vac cp ( [ frag n ] ) RHF BSSE CP double * rhf mon m pop ba ( [ basis n ] ) FMO1 RHF Mulliken population double * rhf mon pos dns ( [ pos n ] ) FMO1 RHF double * rhf mon pos esp ( [ pos n ] ) FMO1 RHF 49

122 double * rhf mon pos efi x ( [ pos n ] ) FMO1 RHF double * rhf mon pos efi y ( [ pos n ] ) FMO1 RHF double * rhf mon pos efi z ( [ pos n ] ) FMO1 RHF char rhf dim conv chk all RHF dimer calculation RHF : RHF 1 : RHF char * rhf dim conv chk ( [ ( frag n -1 ) * frag n / 2 ] ) RHF calculation dimer es calculation dimer 0 : 1 : ifrag jfrag ifrag jfrag rhf_dim_conv_chk [ ( frag_0[ifrag] - 1 ) * frag_0[ifrag] / 2 + frag_0[jfrag] ] double * rhf dim ifie ( [ ( frag n - 1 ) * frag n / 2 ] ) IFIE dimer initialize dimer rhf ifrag jfrag IFIE ifrag jfrag rhf_dim_ifie [ ( frag[ifrag] - 1 ) * frag[ifrag] / 2 + frag[jfrag] ] 50

123 double * rhf dim trdv ( [ ( frag n - 1 ) * frag n / 2 ] ) RHF dimer initialize dimer rhf ifrag jfrag ifrag jfrag rhf_dim_trdv [ ( frag[ifrag] - 1 ) * frag[ifrag] / 2 + frag[jfrag] ] double * rhf dim trdv i ( [ ( frag n - 1 ) * frag n / 2 ] ) RHF dimer initialize dimer rhf ifrag jfrag ifrag jfrag rhf_dim_trdv_i [ ( frag[ifrag] - 1 ) * frag[ifrag] / 2 + frag[jfrag] ] double * rhf dim trdv j ( [ ( frag 0 n - 1 ) * frag 0 n / 2 ] ) RHF dimer initialize dimer rhf ifrag jfrag ifrag jfrag rhf_dim_trdv_j [ ( frag[ifrag] - 1 ) * frag[ifrag] / 2 + frag[jfrag] ] double * rhf dim trdv e ( [ ( frag n - 1 ) * frag n / 2 ] ) RHF dimer initialize dimer rhf double * rhf dim trdv e i ( [ ( frag n - 1 ) * frag n / 2 ] ) RHF dimer initialize dimer rhf double * rhf dim trdv e j ( [ ( frag n - 1 ) * frag n / 2 ] ) RHF dimer initialize dimer rhf double * rhf dim ifie cp ( [ ( frag 0 n - 1 ) * frag 0 n / 2 ] ) IFIE BSSE double * rhf dim m pop ba ( [ basis n ] ) FMO2-RHF 51

124 double * rhf dim pos dns ( [ pos n ] ) FMO2 RHF double * rhf dim pos esp ( [ pos n ] ) FMO2 RHF double * rhf dim pos efi x ( [ pos n ] ) FMO2 RHF double * rhf dim pos efi y ( [ pos n ] ) FMO2 RHF double * rhf dim pos efi z ( [ pos n ] ) FMO2 RHF double rhf fmo 1 FMO1 RHF rhf_fmo_1 = rhf_fmo_1_int + rhf_fmo_1_ext double rhf fmo 1 int FMO1 RHF double rhf fmo 1 ext FMO1 RHF double rhf fmo 2 FMO2 RHF rhf_fmo_2 = rhf_fmo_2_int + rhf_fmo_2_ext double rhf fmo 2 int FMO2 RHF double rhf fmo 2 ext FMO2 RHF 52

125 double rhf mon time RHF double rhf mon time esp RHF double rhf mon time esp 4 RHF 4 double rhf mon time esp 3 RHF 3 double rhf mon time esp m RHF double rhf mon time esp u RHF double rhf mon time esp ext RHF double rhf mon time scf RHF SCF double rhf mon time grad RHF double rhf dim time RHF double rhf dim time esp RHF 53

126 double rhf dim time esp 4 RHF 4 double rhf dim time esp 3 RHF 3 double rhf dim time esp m RHF double rhf dim time esp u RHF double rhf dim time scf RHF SCF double rhf dim time grad RHF 54

127 20 MP2 int cmp2 chk Canonical MP2 int cmp2 lprint 1 MP2 int cmp2 lprint 2 MP2 double cmp2 th iajs MP2 1 double cmp2 th iars MP2 1 double cmp2 th pqrs MP2 1 double cmp2 grimme ps = Grimme SCS-MP2 double cmp2 grimme pt = Grimme SCS-MP2 double cmp2 jung ps = Jung SCS-MP2 double cmp2 jung pt = Jung SCS-MP2 double cmp2 hill ps =

128 Hill SCS-MP2 double cmp2 hill pt = Hill SCS-MP2 double * cmp2 mon energy s ( [ frag n ] ) MP2 double * cmp2 mon energy t ( [ frag n ] ) MP2 double * cmp2 mon energy vac cp s ( [ frag n ] ) MP2 BSSE double * cmp2 mon energy vac cp t ( [ frag n ] ) MP2 BSSE double * cmp2 dim ifie s ( [ ( frag n - 1 ) * frag n / 2 ] ) MP2 IFIE dimer es calculation cmp2 dimer double * cmp2 dim ifie t ( [ ( frag n - 1 ) * frag n / 2 ] ) MP2 IFIE dimer es calculation cmp2 dimer double * cmp2 dim ifie cp s ( [ ( frag n - 1 ) * frag n / 2 ] ) MP2 IFIE BSSE double * cmp2 dim ifie cp t ( [ ( frag n - 1 ) * frag n / 2 ] ) MP2 IFIE BSSE double cmp2 fmo 1 s 56

129 FMO1 MP2 double cmp2 fmo 1 t FMO1 MP2 double cmp2 fmo 2 s FMO2 MP2 double cmp2 fmo 2 t FMO2 MP2 double cmp2 mon time MP2 double cmp2 dim time MP2 57

130 21 RI MP2 int ri cmp2 chk RI MP2 int ri cmp2 lprint 1 RI MP2 int ri cmp2 lprint 2 RI MP2 double * ri cmp2 mon energy s ( [ frag n ] ) RI MP2 double * ri cmp2 mon energy t ( [ frag n ] ) RI MP2 double * ri cmp2 mon energy vac cp s ( [ frag n ] ) RI MP2 BSSE double * ri cmp2 mon energy vac cp t ( [ frag n ] ) RI MP2 BSSE double * ri cmp2 dim ifie s ( [ ( frag n - 1 ) * frag n / 2 ] ) RI MP2 IFIE ri cmp2 dimer double * ri cmp2 dim ifie t ( [ ( frag n - 1 ) * frag n / 2 ] ) RI MP2 IFIE ri cmp2 dimer double * ri cmp2 dim ifie cp s ( [ ( frag n - 1 ) * frag n / 2 ] ) RI MP2 IFIE BSSE 58

131 double * ri cmp2 dim ifie cp t ( [ ( frag n - 1 ) * frag n / 2 ] ) RI MP2 IFIE BSSE double ri cmp2 fmo 1 s FMO1 RI MP2 double ri cmp2 fmo 1 t FMO1 RI MP2 double ri cmp2 fmo 2 s FMO2 RI MP2 double ri cmp2 fmo 2 t FMO1 RI MP2 double ri cmp2 mon time RI MP2 double ri cmp2 dim time RI MP2 59

132 22 MP2 int lmp2 chk LMP2 int lmp2 ch worb LMP2 int lmp2 lprint 1 LMP2-1 int lmp2 lprint 2 LMP2-1 int lmp2 lprint loc 1 LMP2-1 int lmp2 lprint loc 2 LMP2-1 int lmp2 loc LMP2 0 : population localization 1 : moment localization 2 : not locallizatin int lmp2 max itr LMP2 double lmp2 th 1 LMP2 double lmp2 th 1 dim LMP2 60

133 double lmp2 th 2 LMP2 double lmp2 th 2 dim LMP2 double lmp2 th 3 LMP2 double lmp2 th 4 LMP2 double lmp2 th l1 LMP2 double lmp2 th l2 LMP2 double * lmp2 mon energy ( [ frag n ] ) LMP2 double * lmp2 dim ifie sum ( [ ( frag n - 1 ) * frag n / 2 ] ) LMP2 IFIE double * lmp2 dim ifie sub ( [ ( frag n - 1 ) * frag n / 2 ] ) LMP2 IFIE double lmp2 fmo 1 LMP2 FMO-1 double lmp2 fmo 2 sum LMP2 FMO-2 double lmp2 fmo 2 sub LMP2 FMO-2 double lmp2 mon time LMP2 61

134 double lmp2 dim time LMP2 62

135 1 2 main PAICS SCC ES RHF MP2 22 RI MP2 23 MP2 1

136 1 List 2.1 void main 3.1 void initialize mpi 3.2 void finalize mpi 4.1 void initialize memory 4.2 void finalize memory 4.3 double * memory alloc 4.4 int memory dealloc 4.5 long int get remain memory 4.6 double * memory get pointer 4.7 void memory shift left 4.8 int memory check val name 4.9 void memory print 4.10 int memory get nval 4.11 void memory get val name 4.12 int memory get val size 5.1 void paics main 5.2 void print paics title 5.3 void print paics tiltle log file 5.4 void initialize paics 5.5 void paicd finalize 5.6 void initialize angular parameter 5.7 void initialize basis label 5.8 void initialize atomic label 5.9 double calc nuclear repulsion double calc nuclear repulsion void nuclear grad 5.12 void calc nuclear repulsion grad double calc nuclear repulsion grad double calc nuclear repulsion grad double calc nuclear repulsion grad void calc nuclear esp 5.17 void calc nuclear efi 2

137 5.18 double inter fragment distance nucleus 5.19 double inter fragment distance basis 5.20 void make diagonal matrix 5.21 void make inverse matrix 5.22 void make sqrt matrix 5.23 void make inverse sqrt matrix 5.24 void make d matrix 5.25 void make d matrix energy weight 5.26 void make mulliken population 5.27 void make electronic charge center 5.28 void unite density matrix 5.29 void unite c matrix 5.30 int get nkab 5.31 void make kab 5.32 void transformation spherical void transformation spherical 2 mom 5.34 void transformation spherical void transformation spherical void make cauchy 5.37 void get basis xyz value 5.38 void get orbital xyz value 5.39 void paics int to char 5.40 int paics check char exist 5.41 int paics get range char 5.42 int paics dgemm 5.43 int paics daxpy 5.44 int paics daxpy 5.45 int get frag pair nuclear repulsion 5.46 void * basis nucleus assign 5.47 void basis ini assign 5.48 void basis define assign 5.49 void basis normalize 6.1 void read input 6.2 void read input list void read input list void check input validity void check input validity 02 3

138 6.6 int check open file r 6.7 int check open file w 6.8 void read atom 6.9 void read basis 6.10 void read nucleus 6.11 void read fragment 6.12 void read ext point charge 6.13 void read position 6.14 void read basis define 6.15 void read basis define file 6.16 void read monomer scc result 7.1 void print input information 7.2 void print input information rhf 7.3 void print input information cmp2 7.4 void print input information ri cmp2 7.5 void print input information lmp2 7.6 void print nucleus coordinate 7.7 void print basis set coordinate 7.8 void print basis set definition 7.9 void print ext point charge coordinate 7.10 void print fragment definition 7.11 void print memory information 7.12 void print frag information 7.13 void print frag pair information 7.14 void print monomer scc result 7.15 void print monomer calculation result 7.16 void print dimer es result 7.17 void print dimer calculation result 7.18 void print dimer ifie result 7.19 void print molecular orbital 7.20 void print monomer mulliken population 7.21 void write monomer scc result 7.22 void write grid rhf monomer orbital 7.23 void write grid orbital 8.1 void initialize fmt 8.2 void fmt 4