1E01  ᰴ਎ઍ FMO ᴺߩߚ߼ߩ⋧㑐⸘▚ࡊࡠࠣ࡜ࡓߩ㐿⊒㧔┙ᢎᄢ࡮ℂ 1㧘JST-CREST2㧘᧲ᄢ࡮↢↥⎇ 3㧘࿖┙ⴡ⎇ 4㧘NEC ࠰ࡈ࠻ 5㧘ߺߕ߶ᖱႎ✚⎇ 6㧘␹ᚭᄢ㒮࡮Ꮏ 7㧕٤ᦸ᦬␭ᔒ 1, 2, 3㧘ਛ㊁㆐਽ 2,3, 4㧘ጊਅൎ⟤ 5㧘ᴒጊ૫↢ 3㧘⑔Ỉ⮍ 6㧘↰ਛᚑౖ 2, 7‫ޣ‬ᐨ‫࠻ࡦࡔࠣ࡜ࡈ ޤ‬ಽሶ゠㆏(FMO)ᴺߪ‫ޔ‬Ꮒᄢಽሶ♽ߩߚ߼ߩ㊂ሶൻቇ⸘▚ࡈ࡟࡯ࡓࡢ࡯ࠢߣ
ߒߡ 10 ᐕ⒟೨ߦർᶆࠄߦࠃࠅవߕၮᧄߩ HF ㄭૃߢឭ᩺ߐࠇߚ[1,2]‫ߩߘޕ‬ᓟ‫ޔ‬ฦ⒳ߩ⋧㑐࡮ബ⿠⁁ᘒ⸘▚߇ਗ೉ಣℂߢ೑↪಴᧪ࠆࠃ߁ߦߥߞߡ߅ࠅ‫↢ޔ‬ൻቇ⊛ߦ㊀ⷐߥታ࠲ࡦࡄࠢ⾰ߩ⸃ᨆ੐଀
߽ᄙᢙႎ๔ߐࠇߡ޿ࠆ[3,4]‫ޕ‬ታ↪ᕈߩ⋡቟ߣߥࠆ⸘▚ㅦᐲߣߒߡߪ‫ ߇ߜߚ⑳ޔ‬100㧑⥄ਥ㐿⊒ߒߡ޿ࠆ FMO ࡊࡠࠣ࡜ࡓ ABINIT-MPX ߩ႐ว‫ޔ‬922 ᱷၮߩࠗࡦࡈ࡞ࠛࡦࠩ HA ᛫ේ-᛫૕ࠪࠬ࠹
ࡓߩ 1 ᭴ㅧߩ FMO-MP2/6-31G*࡚ࠫࡉ[5]߇ 128 ࠦࠕߩ Xeon(2.66 GHz)ࠢ࡜ࠬ࠲࡯ߢߪ 2.2 ᣣߢቢੌ಴᧪ࠆ࡟ࡌ࡞ߦ޽ࠆ‫ ߚ߹ޕ‬6-31G ၮᐩߢߩ࠲ࠗࡒࡦࠣߛ߇‫ޔ‬ᣥ࿾⃿ࠪࡒࡘ࡟࡯࠲ 4096 ࡊࡠ࠮࠶ࠨࠍ↪޿ߡหኻ⽎ࠍ 53.4 ಽߢಣℂ಴᧪ࠆ⿥ਗ೉ታⴕᕈ(ℂ⺰ᕈ⢻Ყ 11.5%)߽⏕⹺ߒߡ޿ࠆ[6]‫ޕ‬ߒ߆ߒ‫ំߪߢ⾰ࠢࡄࡦ࠲ޔ‬േ᭴ㅧߩ⛔⸘⊛ߥ⠨ᘦߪᧄ⾰⊛ߢ޽ࠅ‫ޔ‬᳓๺ߩ⥄↱ࠛࡀ࡞ࠡ࡯ߩ▚ቯߥߤ߽ᗧ⼂ߔࠇ߫‫ޔ‬ᄙᢙߩࠨࡦࡊ࡞ࠍࠃࠅ㜞ㅦߦಣℂߔࠆᔅⷐ߇޽ࠆߎߣߪ᣿⊕ߢ‫ޔ‬DF/RI/CDߥߤߩ࿃ሶಽ⸃♽ߩⓍಽㄭૃ[7-10]ߩዉ౉ߪਇนㆱߢ޽ࠆ‫ઁޕ‬ᣇ‫⋧ޔ‬㑐ᴺ߽㔚ሶኻ㑆ߩ⋧੕૞↪ࠍ♖⏕ߦขㄟ߼ࠆࠢ࡜ࠬ࠲࡯ዷ㐿[11]ߦઍ⴫ߐࠇࠆ㜞ᰴℂ⺰ߣߒߚࠅ‫ޔ‬ᔕ↪ኻ⽎♽ࠍᐢߍࠆߚ߼ߦ㐿Ზෳᾖ߿ᄙ㈩⟎ෳᾖ߳ߩ᜛ᒛ[12]߽࿑ߞߡ޿߆ߥߊߡߪߥࠄߥ޿‫ࠍ⚛ⷐߩࠄࠇߎޔߪߜߚ⑳ޕ‬ゲߣߔࠆ̌ᰴ਎ઍߩ FMO ⸘▚̍ߩౕ⃻ൻߦะߌߡߩḰ஻ࠍᆎ߼ߡ޿ࠆ‫ⷐߩߎޕ‬ᣦߢߪ‫ޔ‬㑐ㅪߔࠆ࠻ࡇ࠶ࠢࠍ⚫੺ߒߚ޿‫ޕ‬‫ޣ‬CD ߩዉ౉‫ߎߎ ޤ‬ᢙᐕ‫ޔ‬MOLCAS ߩࠣ࡞࡯ࡊߪ CD ߩ⎇ⓥ㐿⊒ࠍⓍᭂ⊛ߦዷ㐿ߒߡ߅ࠅ‫ᦨޔ‬ᣂߩ MOLCAS7 ߢߩ৻⇟ߩࠕࡇ࡯࡞ࡐࠗࡦ࠻ߣ߽ߥߞߡ޿ࠆ[10,13]‫ޕ‬CD ߩࡔ࡝࠶࠻ߪ‫⵬ޔ‬ഥ㑐ᢙࠍ․೎ߦዉ౉ߒߥߊߡᷣ߻ߎߣ‫ߚ߹ޔ‬ᱜ⏕ߥ୯߳ߩ♖ᐲ೙ᓮ߇⋥ᚥߢ޽ࠆߎߣ‫ߚ߹ޔ‬ᓸಽ⸘▚߳ߩኻᔕ߽ኈᤃߢ޽ࠆߎߣߥߤ߇᜼ߍࠄࠇ‫ ߪߜߚ⑳ޔ‬CDAM(Cholesky Decomposition withAdaptive Metric)ߣߒߡ ABINIT-MPX ߳ߩዉ౉ࠍㅴ߼ߡ޿ࠆ[14,15]‫ޕ‬ታⵝߢߪ‫ޔ‬AO Ⓧ߆ࠄߩ
Cholesky ၮᐩߩ࠮࠶࠻ࠕ࠶ࡊ‫⸘ࡦࡠ࡯ࠢޔ‬㊂ߦ㑐ߔࠆᡆૃ 3 ਛᔃⓍಽߩ↢ᚑ‫ ࠆࠁࠊ޿ޔ‬B ⴕ೉ߩ BLAS ࠍ↪޿ߚṶ▚߇ⷐᚲߣߥߞߡ޿ࠆ‫ޕ‬ㅢᏱߩ MP2 ⸘▚ߢߪ(pq,rs)→(ia,jb)ߩⓍಽᄌ឵߇ࠦ
ࠬ࠻ࠍ᳿ߔࠆߚ߼‫߽ߩ߽ߩߜߚ⑳ޔ‬฽߼‫ޟ‬ᅤ૗ߦⓍಽᄌ឵ࠍ㜞ല₸ߦⴕ߁߆‫ࡦࠫࡦࠛ߇ޠ‬㐿⊒ߩਥ⺖㗴ߢ޽ࠆ߇‫ޔ‬CD ߿ RI ߢߪ BpqI→Bia I ߣᄌ឵(I ߪ Cholesky ၮᐩߩᷝሼ)ߔࠆṶ▚╬ࠍ DGEMM
ಣℂ[16]಴᧪ࠆߚ߼ߦࠪࡦࡊ࡞ߦ㜞ㅦൻน⢻ߢ޽ࠆ‫ޕ‬CDAM ߢ AO Ⓧ✚ᢙߦኻߔࠆ I ߩᱷሽ₸ߪ೙ᓮ㑣୯ 10-3 ߩ႐วߪ㜞‫ޘ‬ᢙ%ߢ‫ޔ‬ㅢᏱߩ MP2 ⸘▚ߦኻߔࠆടㅦߪ 8-10 ୚ߣߥࠆ(RI ߢ߽ห᭽ߢ޽ࠆ[17])‫৻ޕ‬ᣇ‫ޔ‬HF ߦߟ޿ߡߪࠢ࡯ࡠࡦ㗄ߣ੤឵㗄ߢಣℂ߇⇣ߥࠆ߇‫ޔ‬SCF ෻ᓳ⸘▚ߣߒߡߪ⋧ኻ⊛ߦߪ MP2 ࠃࠅ߽ࠦࠬ࠻߇ᄢ߈ߊߥߞߡߒ߹ߞߡ߅ࠅ‫ޔ‬෼᧤ᕈࠍᡷༀߔࠆᎿᄦࠍ੹ᓟ࿑ߞߡ޿߆ߥߊߡߪ޿ߌߥ޿‫ޕ‬MP2 ࠛࡀ࡞ࠡ࡯ᓸಽ[18]߽ FMO ᧦ઙߢታⵝᷣߺ[19]ߛ߇‫ޔ‬዁᧪⊛ߦߪ CDAM ߦࠃߞߡ‫ޔ‬ᓸಽ⸘▚߹ߢߩ࠻࡯࠲࡞ߢ 10 ୚ߩടㅦࠍ⏕଻ߒߚ޿ߣ⠨߃ߡ޿ࠆ‫ޕ‬CDAMߦߟ޿ߡࠃࠅ⹦ߒߊߪ‫⺰⸛ᧄޔ‬ળ 1P128 ߩⷐᣦߣࡐࠬ࠲࡯⊒⴫ࠍߏෳᾖ޿ߚߛ߈ߚ޿‫ޕ‬‫ޣ‬㜞ᰴ MP ߣ CC ߩታⵝ‫ ޤ‬GAMESS ࡌ࡯ࠬߩ FMO 㜞ᰴ⋧㑐⸘▚ߪᣢߦ CCSD(T)࡟ࡌ࡞[11,20]
ߢታ⃻ߐࠇߡ޿ࠆ[21]‫ ߩߢ߹ࠇߎߪߜߚ⑳ޔߒ߆ߒޕ‬ABINIT-MPX ߳ߩ⒳‫▚⸘ߩޘ‬ᴺߩታⵝߣห
᭽‫ߩ࠼࡯ࠦޔ‬᜛ᒛᕈߣ⿥ਗ೉/BLAS ታⴕ[6]߳ߩㆡ↪ᕈࠍ㊀ⷞߔࠆⷰὐ߆ࠄࡈ࡞ࠬࠢ࡜࠶࠴ߩ㐿⊒ࠍⴕߞߡ޿ࠆ‫ߪߢࠣࡦࡇࠗ࠲࠻ࡠࡊޕ‬ᣢߦ‫ޔ‬CCSD(T)ࠍߪߓ߼ QCISD(T)[22]߿ MP4(SDTQ)[23]޽ࠆ޿ߪ CEPA[24]߹ߢࠍ‫ޔ‬Scuseria ࠄߩࠬࡇࡦㆡวဳߩቯᑼൻ[25]ࠍၮߦߒߡᷣ߹ߖߡ޿ࠆ߇‫ޔ‬ਗ೉ൻߒߚᧄታⵝߣߒߡߪవߕ 2 㔚ሶബ⿠㒢ቯߩ CCD ࠛࡦࠫࡦࠍ㐿⊒ߒߚ‫ࠅࠃޔࠎࠈߜ߽ޕ‬ㄭૃ⊛ߥ CEPA-1(D)߿ MP4(DQ)߽⸘▚಴᧪ࠆ‫ޕ‬2 㔚ሶᝄ᏷ࡌࠢ࠻࡞ߩ෻ᓳᦨㆡൻਛ‫(ޔ‬ac,bd)Ⓧಽߩಣℂߪ Fock ᭽ᛛᴺ(EEO)[26]ߦࠃߞߡ AO Ⓧಽ߆ࠄ⋥ߦⴕ߁‫ߩઁޔߚ߹ޕ‬ಽሶⓍಽߦ㑐ߔࠆ࠹ࡦ࠰࡞ဳ❗⚂⸘▚ߪ(߶߷)ోߡ DGEMM ൻߒߡ޽ࠆ‫ޕ‬ਅ⴫ߪ‫ޔ‬Xeon(3.4 GHz)ߦࠃࠆ 6-31G**ၮ
ᐩࠍ૶ߞߚ Gly8 ߩ FMO ⸘▚ߩ MPI ਗ೉ታⴕߢߩ࠲ࠗࡒࡦࠣ࠺࡯࠲(ᤨ㑆ߪ⑽)ߢ޽ࠆ㧦AO ߩ✚ᢙߪ 625‫ޕ‬㪤㪧㪉㪤㪧㪋㩿㪛㪨㪀㪚㪜㪧㪘㪄㪈㩿㪛㪀㪚㪚㪛㪋㩷㪺㫆㫉㪼㫊 㪏㪎㪍㪅㪇㪋㪏㪇㪋㪅㪋㪈㪐㪋㪌㪏㪅㪉㪉㪉㪊㪇㪉㪅㪍㪏㩷㪺㫆㫉㪼㫊 㪋㪍㪍㪅㪈㩷㩿㫏㪈㪅㪏㪏㪀 㪉㪋㪐㪈㪅㪋㩷㩿㫏㪈 㪅㪐㪊㪀 㪈㪇㪈㪎㪍㪅㪇㩷㩿㫏㪈㪅㪐㪈㪀 㪈㪈㪌㪏㪏㪅㪌㩷㩿㫏㪈㪅㪐㪉㪀MP2 ߦᲧߴࠆߣ MP4(DQ)ߩࠦࠬ࠻ߪ 6 ୚‫ޔ‬CEPA-1(D)ߢߪ 22 ୚‫ޔ‬CCD ߢߪ 25 ୚ߣߥߞߡ߅ࠅ‫ޔ‬CCD ߦߟ޿ߡߪᒻᑼ⊛ߥ N ଐሽᕈᲧߢ޽ࠆ‫ޟ‬㕖෻ᓳ N5 ኻ ෻ᓳ N 6‫ߣߞߕ߽ࠅࠃޠ‬ૐࠦࠬ࠻ߢᷣࠎߢ޿ࠆߩߪ FMO ࠬࠠ࡯ࡓߩᕲᕺߢ޽ࠆ‫ޕ‬Gly 㑆ߩ⋧੕૞↪ࠛࡀ࡞ࠡ࡯⸃ᨆߢߪ‫ޔ‬MP2 ࡟ࡌ࡞ߦᲧߴߡ㜞ᰴ⋧㑐ࠍ⠨ᘦߒߚ႐วߦߪ⋧㑐⵬ᱜߩㆊᄢ⹏ଔ߇ᤚᱜߐࠇࠆ߇‫◲ޔ‬ଢߥ SCS-MP2
ୃᱜ[27]ߢ߽ᅢ߹ߒ޿⚿ᨐ߇ᓧࠄࠇࠆߎߣࠍઃ⸥ߒߡ߅ߊ‫ⷐᧄޕ‬ᣦၫ╩ᤨὐߢߪ‫ޔ‬1 㔚ሶബ⿠ߩㇱಽ ߣ DIIS ᄖᝌ [28] ࠍ ㅊ ട ߢ ᧄ ታ ⵝߔ ࠆ ૞ ᬺ ࠍ ᆎ ߼ ߡ ߅ ࠅ ‫ ߪ ߦ ⑺ ߩ ߎ ޔ‬FMO-CCSD ߿
FMO-MP4(SDQ)߇ ABINIT-MPX ߢ೑↪಴᧪ࠆࠃ߁ߦߥࠆ‫ޕ‬ਗ೉ൻߦߟ޿ߡߪ MPI ߣ OpenMPߩᷙᚑ૶↪߽⹜ߺ‫ޔ‬ᄙࠦࠕ࡮ᄢࡔࡕ࡝࡮SSD ࠬࠢ࡜࠶࠴ߥߤߩ⸘▚ᯏⅣႺߩะ਄ࠍ೨ឭߣߒߟߟ‫ޔ‬㕖෻ᓳ N7 ࠦࠬ࠻ߩ(T)⵬ᱜߩᧄታⵝߦߟ޿ߡ߽ㆃṛߥߊⴕߞߡ޿߈ߚ޿‫ઁޕ‬ᣇ‫ޔ‬Cu+2 ߿ NO ߥߤࠍ฽߻㐿Ზ♽ߩ⸘▚ኻ⽎[12]ߦߟ޿ߡ߽ GAMESS ߩ UHF/ROHF ታⵝ[29]ߦ⠌ߞߡ SCF ࠛࡦࠫࡦߩ⁛⥄㐿⊒ࠍㅴ߼ߡ߅ࠅ‫ޔ‬዁᧪⊛ߦߪ㐽Ზ♽ߣห᭽ߦ MP2 ߆ࠄ CCSD(T)߹ߢࠍࠞࡃ࡯಴᧪ࠇ
߫ߣ⠨߃ߡ޿ࠆ‫ޔߚ߹ޕ‬CYP ╬ࠍᛒ߁ߦߪ CASSCF ߣ MRPT ߩታⵝ߽੹ᓟߩ㊀ⷐ⺖㗴ߢ޽ࠆ‫ޕ‬‫⻢ޣ‬ㄉ‫⎇ᧄ ޤ‬ⓥߪ‫ޔ‬JST-CREST ࡊࡠࠫࠚࠢ࠻‫࠻ࡦࡔࠣ࡜ࡈޟ‬ಽሶ゠㆏ᴺߦࠃࠆ↢૕ಽሶ⸘▚ࠪࠬ࠹ࡓߩ㐿⊒‫․࡮⾌⎇⑼ޔޠ‬ቯ㗔ၞ‫ޟ‬ታ࿷♽ߩಽሶℂ⺰‫┙ޔޠ‬ᢎᄢቇ‫᧪ᧂޟ‬ಽሶ⎇ⓥ‫ࠚࠫࡠࡊޠ‬ࠢ࠻߆ࠄߩᡰេࠍฃߌߡ޿ࠆ‫ޔߚ߹ޕ‬FMO ࠦࡒࡘ࠾࠹ࠖߩਛߢߏᢎ␜࡮ߏ⼏⺰޿ߚߛ޿ߡ޿ࠆർᶆవ↢ߣ Fedorov ඳ჻ߦ⻢ᗧࠍ⴫ࠊߒߚ޿‫ޕ‬‫ޣ‬ᢥ₂‫[ ޤ‬1] ർᶆࠄ, CPL 312 (1999) 319. [2] ർᶆࠄ, CPL 313 (1999) 701. [3] Fedorov ࠄ,
JPC A111 (2007) 6904. [4] Fedorov&ർᶆ ✬㓸, “The Fragment Molecular Orbital Method”,
CRC press (2009). [5] ┻᧻ࠄ, JPC B113 (2009) 4991. [6] ᦸ᦬ࠄ, CPL 457 (2008) 396. [7]Dunlap ࠄ, JCP 71 (1979) 3396. [8] Vahtras ࠄ, CPL 213 (1993) 514. [9] Beebe ࠄ, IJQC 12(1977) 683. [10] Pedersen ࠄ, TCA ශ೚ਛ. [11] Bartlett ࠄ, RMP 79 (2007) 291. [12] Fedorov ࠄ,
JCP 122 (2005) 054108. [13] Acuilante ࠄ, JCC ශ೚ਛ. [14] ᴒጊࠄ, ICQC2009/C98. [15] ᴒጊࠄ, CPL ᛩⓂḰ஻ਛ. [16] Hättig, NIC Series 31 (2006) 245. [17] ⍹Ꮉࠄ, CPL 472 (2009) 195.
[18] Frisch ࠄ, CPL 166 (1990) 275. [19] ᦸ᦬ࠄ, CPL ᛩⓂḰ஻ਛ. [20] Raghavachari ࠄ, CPL
157 (1989) 479. [21] Fedorov ࠄ, JCP 123 (2005) 134103. [22] Pople ࠄ, JCP 87 (1987) 5968.
[23] Pople ࠄ, IJQC-symp 22 (1988) 377. [24] Ahlrichs, CPC 17 (1979) 31. [25] Scuseria ࠄ, JCP
89 (1988) 7382. [26] Taylor, IJQC 31 (1987) 521. [27] Grimme, JCP 118 (2003) 9095. [28] Pulay,CPL 73 (1980) 393. [29] Schmidt ࠄ, JCC 14 (1993) 1347.