趋于线性标度的增长法:基于局域定域分子轨道的双电子积分（英文）
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摘要
基于哈特里-福克的增长法与量子快速多极展开方法相结合对大体系的计算可以达到线性标度。然而,只要把双电子积分从原子轨道转换到定域轨道,然后直接从定域分子轨道构建福克矩阵是更加简单的方法。增长法采用截断的手段剔除那些不需要转换的积分从而每一步增长法的计算量几乎不变,这些手段包括采用舒瓦茨不等式、分子轨道系数的筛选、以及利用杂化轨道等可进一步减少双电子转换的数目。对水分子链体系的测试证明线性标度是可以达到的。这个新方法表明如果一个相互作用区域不超过120个定域分子轨道,它就比从原子轨道构建福克矩阵的方法更有效率。
Elongation Hartree-Fock( ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However,it is a simpler method to form the Fock matrix directly from localized molecular orbitals,which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step,almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality,molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.
Elongation Hartree-Fock( ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However,it is a simpler method to form the Fock matrix directly from localized molecular orbitals,which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step,almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality,molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.
引文
[1]SCHMIDT M W,BALDRIDGE K K,BOATZ J A,et al.General atomic and molecular electronic structure system[J].Journal of Compututation Chemistry,1993,14:1347-1363.
[2]GORDON M S,SCHMIDT M W.Theory and applications of computational chemistry[M]∥DYKSTRA C E,et al,eds.The first forty years.Amsterdam,2005:1167-1189.
[3]WHITE C A,HEAD-GORDON M J.Derivation and efficient implementation of the fast multipole method[J].The Journal of Chemical Physics,1994,101:6593-6605.
[4]WHITE C A,JOHNSON B G,GILL P M W,et al.The continuous fast multipole method[J].Chemical Physics Letters,1994,230:8-16.
[5]CHALLACOMBE M,SCHWEGLER E,ALMLF J.Recurrence relations for calculation of the Certesian multipole tensor[J].Chemical Physivs Letters,1995,241:67-72.
[6]WHITE C A,JOHNSON B G,GILL P M W,et al.Linear scaling density functional calculations via the continuous fast multipole method[J].Chemical Physics Letters,1996,253:268-278.
[7]NEESE F.Some thoughts on the scope of linear scaling self-consistent field electronic structure methods[M]∥ZALE NY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:221-261.
[8]KITAURA K,IKEO E,ASADA T,et al.Fragment molecular orbital method:an approximate computational method for large molecules[J].Chemical Physics Letters,1999,313:701-706.
[9]FEDOROV D G,KITAURA K.The importance of threebody terms in the fragment molecular orbital method[J].The Journal of Chemical Physics,2004,120:6832-6840.
[10]FEDOROV D G,KITAURA K.The three-body fragment molecular orbital method for accurate calculations of large systems[J].Chemical Physics Letters,2006,433:182-187.
[11]FEDOROV D G,KITAURA K.Modern methods for theoretical physical chemistry of biopolymers[M]∥STARIKOV E B,et al,eds.Amsterdam,2006:39-52.
[12]FEDOROV D G,KITAURA K.The fragment molecular orbital method,practical applications to large molecular systems[M]∥FEDOROV D G,et al,eds.Boca Raton,2009.
[13]NAGATA T,FEDOROV D G,KITAURA K.Mathematical formulation of the fragment molecular orbital method[M]∥ZALE NY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:17-64.
[14]YAND W,LEE T S.A density-matrix devide-and-conquer approach for electronic structure[J].The Journal of Chemical Physics,1995,103:5674-5678.
[15]AKAMA T,KOBAYASHI M,NAKAI H.Implementation of divide-and-conquer method including Hartree-Fock exchange interacion[J].Journal of Computational Chemistry,2007,28:2003-2012.
[16]KOBAYASHI M,NAKAI H.Divide-and-conquer approaches to quantum chemistry:Theory and implementation[M]∥ZALE NY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:97-127.
[17]IMAMURA A,AOKI Y,MAEKAWA K.A theoretical synthesis of polymers by using uniform localization of molecular orbitals:Proposal of an elongation method[J].The Journal of Chemical Physics,1991,95:5419-5431.
[18]GU F L,AOKI Y,KORCHOWIEC K,et al.A new localization scheme for the elongation method[J].The Journal of Chemical Physics,2004,121:10385-10391.
[19]KORCHOWIEC J,LEWANDOWSKI J,MAKOWSKIM,et al.Elongation cutoff technique armed with quantum fast multipole method for linear[J].Journal of Computational Chemistry,2009,30:2515-2525.
[20]GU F L,AOKI Y.Chemical modelling:Applications and theory[M].Cambridge:Springborg M,2010:163-191.
[21]GU F L,KIRTMAN B,AOKI Y.Elongation method:towards linear scaling for electronic structure of random polymers and other quasilinear materials[M]∥ZALENY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:175-198.
[22]LI S,LI W,FANG T.An efficient fragment-based approach for predicting the ground-state energies and structure of large molecules[J].Journal of American Chemical Society,2005,127:7215-7226.
[23]LI W,NI Zh,LI Sh.Cluster-in-molecule local correlation method for post-Hartree-Fock calculations of large systems[J].Molecular Physics,2016,114:1447-1460.
[24]LI Z,LI H,SUO B,et al.Localization of molecular orbitals:From fragments to molecule[J].Accounts of Chemical Research,2014,47:2758-2767.
[25]HUANG Ch,LIU W J,XIAO Y L,et al.i Vl:An iterative vector interaction method for large eigenvalue problems[J].Journal of Computational Chemistry,2017,38:2481-2499.
[26]AOKI Y,IMAMURA A.Local density of states of aperiodic polymers using the localized orbitals from an ab initio elongation method[J].The Journal of Chemical Physics,1992,97:8432-8440.
[27]GU F L,IMAMURA A,AOKI Y.Atoms,molecules and clusters in electric fields:Theoretical approaches to the calculation of electric polarizabilities[M].London,2006:97-177.
[28]AOKI Y,GU F L.An elongation method for large systems toward bio-systems[J].Physical Chemistry Chemical Physics,2012,14:7640-7668.
[29]ORIMOTO Y,GU F L,IMAMURA A,et al.Efficient and accurate calculations on the electronic structure of B-type poly(d G)·polt(d C)DNA by elongation method:First step toward the understanding of the biological properties of aperiodic DNA[J].The Journal of Chemical Physics,2007,126:215104-1-7.
[30]LIU K,YAN Y,GU F L,et al.A modified localization scheme for the three-dimensional elongation method applied to large systems[J].Chemical Physics Letters,2013,565:143-147.
[31]HEHRE W J,STEWART R F,POPLE J A.Self-consistent molecular-orbital methods.i.use of gaussian expansions of slater-type atomic orbitals[J].The Journal of Chemical Physics,1969,51:2657-2664.
[32]HEHRE W J,DITCHFIELD R,POPLE J A.Self-consistent molecular orbital methods.XII.Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules[J].The Journal of Chemical Physics,1972,56:2257-2261.
[33]SCHTZ M,HETZER G,WERNER H J.Lower-order scaling local electron correlation methods.I.Linear scaling local MP2[J].The Journal of Chemical Physics,1999,111:5691-5705.
[34]HETZER G,SCHTZ M,STOLL H,et al.Lower-order scaling local correlation methods.II.Splitting the Coulomb operator in Linear scaling local second-order Mller-Plesset perturbation theory[J].The Journal of Chemical Physics,2000,113:9443-9455.
[35]BOYS S F.Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another[J].Reviews of Modern Physics,1960,32:296-299.
[36]PIPEK J,MEZEY P G.A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions[J].The Journal of Chemical Physics,1989,90:4916-4926.
[37]EDMISTON C,RUEDENBERG K.Localized atomic and molecular orbitals.II[J].The Journal of Chemical Physics,1965,43(S):97-116.
[2]GORDON M S,SCHMIDT M W.Theory and applications of computational chemistry[M]∥DYKSTRA C E,et al,eds.The first forty years.Amsterdam,2005:1167-1189.
[3]WHITE C A,HEAD-GORDON M J.Derivation and efficient implementation of the fast multipole method[J].The Journal of Chemical Physics,1994,101:6593-6605.
[4]WHITE C A,JOHNSON B G,GILL P M W,et al.The continuous fast multipole method[J].Chemical Physics Letters,1994,230:8-16.
[5]CHALLACOMBE M,SCHWEGLER E,ALMLF J.Recurrence relations for calculation of the Certesian multipole tensor[J].Chemical Physivs Letters,1995,241:67-72.
[6]WHITE C A,JOHNSON B G,GILL P M W,et al.Linear scaling density functional calculations via the continuous fast multipole method[J].Chemical Physics Letters,1996,253:268-278.
[7]NEESE F.Some thoughts on the scope of linear scaling self-consistent field electronic structure methods[M]∥ZALE NY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:221-261.
[8]KITAURA K,IKEO E,ASADA T,et al.Fragment molecular orbital method:an approximate computational method for large molecules[J].Chemical Physics Letters,1999,313:701-706.
[9]FEDOROV D G,KITAURA K.The importance of threebody terms in the fragment molecular orbital method[J].The Journal of Chemical Physics,2004,120:6832-6840.
[10]FEDOROV D G,KITAURA K.The three-body fragment molecular orbital method for accurate calculations of large systems[J].Chemical Physics Letters,2006,433:182-187.
[11]FEDOROV D G,KITAURA K.Modern methods for theoretical physical chemistry of biopolymers[M]∥STARIKOV E B,et al,eds.Amsterdam,2006:39-52.
[12]FEDOROV D G,KITAURA K.The fragment molecular orbital method,practical applications to large molecular systems[M]∥FEDOROV D G,et al,eds.Boca Raton,2009.
[13]NAGATA T,FEDOROV D G,KITAURA K.Mathematical formulation of the fragment molecular orbital method[M]∥ZALE NY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:17-64.
[14]YAND W,LEE T S.A density-matrix devide-and-conquer approach for electronic structure[J].The Journal of Chemical Physics,1995,103:5674-5678.
[15]AKAMA T,KOBAYASHI M,NAKAI H.Implementation of divide-and-conquer method including Hartree-Fock exchange interacion[J].Journal of Computational Chemistry,2007,28:2003-2012.
[16]KOBAYASHI M,NAKAI H.Divide-and-conquer approaches to quantum chemistry:Theory and implementation[M]∥ZALE NY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:97-127.
[17]IMAMURA A,AOKI Y,MAEKAWA K.A theoretical synthesis of polymers by using uniform localization of molecular orbitals:Proposal of an elongation method[J].The Journal of Chemical Physics,1991,95:5419-5431.
[18]GU F L,AOKI Y,KORCHOWIEC K,et al.A new localization scheme for the elongation method[J].The Journal of Chemical Physics,2004,121:10385-10391.
[19]KORCHOWIEC J,LEWANDOWSKI J,MAKOWSKIM,et al.Elongation cutoff technique armed with quantum fast multipole method for linear[J].Journal of Computational Chemistry,2009,30:2515-2525.
[20]GU F L,AOKI Y.Chemical modelling:Applications and theory[M].Cambridge:Springborg M,2010:163-191.
[21]GU F L,KIRTMAN B,AOKI Y.Elongation method:towards linear scaling for electronic structure of random polymers and other quasilinear materials[M]∥ZALENY R,et al,eds.Linear-scaling techniques in computational chemistry and physics.Springer,2011:175-198.
[22]LI S,LI W,FANG T.An efficient fragment-based approach for predicting the ground-state energies and structure of large molecules[J].Journal of American Chemical Society,2005,127:7215-7226.
[23]LI W,NI Zh,LI Sh.Cluster-in-molecule local correlation method for post-Hartree-Fock calculations of large systems[J].Molecular Physics,2016,114:1447-1460.
[24]LI Z,LI H,SUO B,et al.Localization of molecular orbitals:From fragments to molecule[J].Accounts of Chemical Research,2014,47:2758-2767.
[25]HUANG Ch,LIU W J,XIAO Y L,et al.i Vl:An iterative vector interaction method for large eigenvalue problems[J].Journal of Computational Chemistry,2017,38:2481-2499.
[26]AOKI Y,IMAMURA A.Local density of states of aperiodic polymers using the localized orbitals from an ab initio elongation method[J].The Journal of Chemical Physics,1992,97:8432-8440.
[27]GU F L,IMAMURA A,AOKI Y.Atoms,molecules and clusters in electric fields:Theoretical approaches to the calculation of electric polarizabilities[M].London,2006:97-177.
[28]AOKI Y,GU F L.An elongation method for large systems toward bio-systems[J].Physical Chemistry Chemical Physics,2012,14:7640-7668.
[29]ORIMOTO Y,GU F L,IMAMURA A,et al.Efficient and accurate calculations on the electronic structure of B-type poly(d G)·polt(d C)DNA by elongation method:First step toward the understanding of the biological properties of aperiodic DNA[J].The Journal of Chemical Physics,2007,126:215104-1-7.
[30]LIU K,YAN Y,GU F L,et al.A modified localization scheme for the three-dimensional elongation method applied to large systems[J].Chemical Physics Letters,2013,565:143-147.
[31]HEHRE W J,STEWART R F,POPLE J A.Self-consistent molecular-orbital methods.i.use of gaussian expansions of slater-type atomic orbitals[J].The Journal of Chemical Physics,1969,51:2657-2664.
[32]HEHRE W J,DITCHFIELD R,POPLE J A.Self-consistent molecular orbital methods.XII.Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules[J].The Journal of Chemical Physics,1972,56:2257-2261.
[33]SCHTZ M,HETZER G,WERNER H J.Lower-order scaling local electron correlation methods.I.Linear scaling local MP2[J].The Journal of Chemical Physics,1999,111:5691-5705.
[34]HETZER G,SCHTZ M,STOLL H,et al.Lower-order scaling local correlation methods.II.Splitting the Coulomb operator in Linear scaling local second-order Mller-Plesset perturbation theory[J].The Journal of Chemical Physics,2000,113:9443-9455.
[35]BOYS S F.Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another[J].Reviews of Modern Physics,1960,32:296-299.
[36]PIPEK J,MEZEY P G.A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions[J].The Journal of Chemical Physics,1989,90:4916-4926.
[37]EDMISTON C,RUEDENBERG K.Localized atomic and molecular orbitals.II[J].The Journal of Chemical Physics,1965,43(S):97-116.