Chemical Physics Letters LLL (2018) xxx-xxx Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com )9G95F7< D5D9F An 9::=7=9BH =AD@9A9BH5H=CB C: G9A=-numerical 7CADIH5H=CB C: H<9 Hartree-Fock 9L7<5B;9 CB H<9 BH9@ '<= DFC79GGCF Fenglai #=I, !=B; "CB;⁎ Department of Chemistry and Center for Computational Science, Middle Tennessee State University, TN, 37130, United States ARTICLE INFO ABSTRACT Article history: ,B=EI9 H97<B=75@ 7<5@@9B;9G 5B8 H<9=F GC@IH=CBG :CF =AD@9A9BH=B; G9A=-numer=75@ Hartree-Fock 9L7<5B;9 CB )979=J98 30 !5BI5FM 2018 H<9 '<=@ 'FC79GGCF 5F9 8=Gcussed, 9GD97=5@@M 7CB79FB=B; H<9 G=B;@9- =BGHFI7H=CB-mulH=D@9-data HMD9 C: DFC79GG- Accepted 11 $5M 2018 =B; 5B8 GA5@@ 757<9 size. BenchA5F? 75@7I@5H=CBG CB 5 G9F=9G C: 6I7?M65@@ AC@97I@9G K=H< J5F=CIG Gauss=5B Available CB@=B9 LLL 65G=G G9HG CB 5 '<= DFC79GGCF 5B8 5 G=L-core CPU G<CK H<5H H<9 '<= DFC79GGCF DFCJ=89G 5G AI7< 5G 12 H=A9G C: GD998ID K=H< @5F;9 65G=G G9HG 7CAD5F98 K=H< H<9 7CBJ9BH=CB5@ four-cenH9F 9@97HFCB F9DI@G=CB =BH9;F5H=CB 5D- DFC57< D9F:CFA98 CB H<9 CPU. +<9 577IF57M C: H<9 G9A=-numer=75@ G7<9A9 =G 5@GC 9J5@I5H98 5B8 :CIB8 HC 69 7CAD5F56@9 HC H<5H C: H<9 F9GC@IH=CB-of-idenH=HM 5Dproach. Q 2018. 1. Introduction :CF CCSD(T) 75@7I@5H=CB [8], 5B8 H<9 =AD@9A9BH5H=CB 5@GC 57<=9J98 2–3 H=A9G speedup. &B H<9 CH<9F hand, )9=8 etc. [9] AC8=:=98 CP2K +<9 89BG=HM :IB7H=CB5@ H<9CFM (DFT) =G H<9 ACGH K=89@M 5DD@=98 'FC;F5A :CF H<9 KNC 5B8 A589 D9F:CFA5B79 7CAD5F=GCB K=H< 5 8I5@ EI5BHIA A97<5B=75@ A9H<C8G :CF 7<9A=75@ 5B8 A5H9F=5@ GHI8ies. &B9 /9CB CPU(16 cores) GMGH9A :CF 9B9F;M 75@7I@5tions, 5B8 :CIB8 H<5H K5M HC A5?9 DFT 7CADIH5H=CB ACF9 DFC8I7H=J9 =G HC H5?9 H<9 58- H<9 7C89 F5B 56CIH 5.43 H=A9G G@CK9F CB H<9 KNC H<5B CB H<9 J5BH5;9 C: B9K 7CADIH9F H97<BC@Cgies, GI7< 5G H<9 Gen9F5@-Purpose CPU-only system, 9J9B H<CI;< H<9 H<9CF9H=75@ FLOPS 7CIBH :CF H<9 Graph=7G 'FC79GG=B; ,B=HG (GPGPU) 5B8 H<9 BH9@ $5BM BH9;F5H98 8I5@ CPUs =G 56CIH 0.8 H9FaFLOPS J9FGIG 1 H9FaFLOPs :CF H<9 KNC Core (MIC) 5F7<=H97ture. +<9 GPGPU 9LH9B8G H<9 IG9 C: H<9 ;F5D<=7G DFC79Gsor. +<9 G97CB8 ;9B9F5H=CB C: '<= DFC79GGCF S"B=;<H #5B8=B;T DFC79GG=B; IB=H HC D9F:CFA ;9B9F5@ DIFDCG9 7CADIH5H=CB GI7< 5G G7=- (KNL) GIDDCFHG H<9 8=F97H 7CAD=@5H=CB 5B8 9L97IH=CB C: H<9 GC:HK5F9 9BH=:=7 75@7I@5tions. 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Coulomb 5B8 H<9 BIA9F=75@ =BH9;F5H=CB C: 9L7<5B;9-corF9@5H=CB :IB7- B 7CAD5F=GCB HC H<9 G=;B=:=75BH 89J9@CDA9BH 9::CFH A589 CB H=CB5@G [12–14]. .9 <5J9 F979BH@M DI6@=G<98 H<9 =AD@9A9BH5H=CB C: 5 GPGPU :FCA EI5BHIA 7<9A=GHFM GC:HK5F9 7CAAIB=HM [3–6], @9GG 89- G9A=-numer=75@ =BH9;F5H=CB G7<9A9 :CF 7CADIH=B; H<9 HF 9L7<5B;9 J9@CDA9BH 9::CFHG <5J9 699B F9DCFH98 :CF H<9 '<= DFC79GGCF =B 7CApu- 9B9F;M 5B8 A5HF=L K=H< G9@:-conG=GH9BH field(SCF) :CF 7CBJ9BH=CB5@ H5H=CB5@ EI5BHIA 7<9Aistry, D9F<5DG 6975IG9 =H 75A9 56CIH ACF9 F9- CPUs [15]. +<9 G7<9A9 =G G=A=@5F HC H<9 COS-X 5@;CF=H<A [16,17] 5B8 79BH@M H<5B H<9 GPGPU. #95B; 9H al. [7] GHI8=98 H<9 9::=7=9B7M C: A5- DG9I8C-specHF5@ G7<9A9 [18,19]. B H<=G KCF? K9 89G7F=69 H<9 =AD@9- HF=L CD9F5H=CBG CB H<9 :=FGH ;9B9F5H=CB C: H<9 '<= DFC79GGCF S"B=;<H A9BH5H=CB C: H<9 G7<9A9 CB H<9 MIC 5F7<=H97ture. .9 G<CK98 H<5H H<9 CorB9FT (KNC) 5B8 G<CK98 H<5H KNC 75B M=9@8 ID HC H<F99 H=A9G G9A=-numer=75@ G7<9A9 =G ACF9 9::=7=9BH :CF @5F;9 65G=G G9HG 5B8 @5F;9 GD998ID 7CAD5F98 K=H< H<9 <CGH CPU.UNCORRECTED Apra 9H 5@. 9AD@CM98 H<9 KNC AC@97I@9G 8I9 HC EI58F5H=7 G75@=B; K=H< PROOF F9GD97H H<9 65G=G G9H size. Fur- H<9Fmore, =H F9EI=F9G :9K9F H9ADCF5FM J5F=56@9G H<9F9:CF9 :=H 69HH9F H<9 '<= 'FC79GGCF H<5H <5G AI7< GA5@@9F 757<9 G=N9 H<5B 5 GH5B85F8 CPU. +<9 G9A=-numer=75@ HF 9L7<5B;9 =G 5@GC 5B 9GG9BH=5@ =B;F98=9BH :CF ⁎ Corresponding author. H<9 9A9F;=B; @C75@ <M6F=8 :IB7H=CB5@G [17,20–24]. Email address: [email protected] (J. Kong) https://doi.org/10.1016/j.cplett.2018.05.026 0009-2614/ Q 2018. 2 Chemical Physics Letters LLL (2018) xxx-xxx 2. The semi-numerical algorithm for HF exchange =BH9;F5@ 75@7I@5H=CB 5@GC =BJC@J9G 5 @CCD CJ9F H<9 7CBHF57H=CB :CF 957< D5=F C: Gauss=5B 65G=G :IB7tions. +<9 HCH5@ 7CGH C: ESP =BH9;F5@G H<9B +<9 G9A=-numer=75@ 5@;CF=H<A HC 75@7I@5H9 H<9 HF 9L7<5B;9 A5- 75B 69 5DDFCL=A5H9@M 9GH=A5H98 5G HF=L <5G 699B 8=G7IGG98 =B 89H5=@ =B CIF DF9J=CIG D5D9F [15]. .9 6F=9:@M (“6:T GH5B8G :CF S65G=G :IB7H=CBT). +<9F9:CF9 CIF =AD@9A9BH5H=CB 9:- GIAA5F=N9 =H here. :CFH 7CB79BHF5H9G CB HF5BG:9FF=B; H<9 ESP =BH9;F5@ 75@7I@5H=CB :FCA H<9 +<9 HF 9L7<5B;9 A5HF=L =G 89F=J98 H<FCI;< H<9 89F=J5H=J9 C: H<9 BCFA5@ CPU D@5H:CFA HC H<9 '<= DFC79Gsor. HF 9L7<5B;9 9B9F;M K=H< F9GD97H HC H<9 GD=B-reGC@J98 89BG=HM A5HF=L : 3. 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