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Uncorrected Proof 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. 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ComD5F98 K=H< 5 HF58=H=CB5@ CPU, 5 GPGPU 75F8 CB H<9 DFC79Gsor. *I7< 5B 5HH9ADH CB H<9 EI5BHIA 7<9A=GHFM GC:HK5F9 DCGG9GG9G ACF9 DFC79GG=B; 7CF9G 5B8 CJ9F5@@ <5G AI7< <=;<9F H<9CF9H- #*DalHCB G<CK98 [10] H<5H =H =G GH=@@ G9J9F5@ H=A9G G@CK9F CB H<9 "%# =75@ D95? :@C5H=B; DC=BH CD9F5H=CBG D9F G97CB8 (FLOPS). &B H<9 CH<9F H<5B 5 8I5@ /9CB CPU system. +<9 8=::=7I@HM K5G ACGH@M 5HHF=6IH98 HC <5B8 H<9 BH9@ MIC H97<BC@C;M =G 5 F989G=;B C: H<9 DF9J=CIG ;9B9F- H<9 =B9::=7=9BH IG9 C: VPUs, K<=7< 5F9 H<9 SIMD (Sin;@9 =BGHFI7tion, 5H=CB C: Celeron 5B8 '9BH=IA 7CF9G 5B8 7CB89BG9G H<9G9 7CF9G CBHC AI@H=D@9 data) DFC79GG=B; IB=HG =B H<9 '<= DFC79GGCF [1,2,11]. For 9::97- CB9 DFC79Gsor. 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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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