Acceleration of fragment molecular orbital calculations with Cholesky decomposition approach

Abstract A novel method, Cholesky decomposition with adaptive metric (CDAM), is applied to the two-electron integral calculations in the fragment molecular orbital (FMO) method. We thus accelerate the Hartree–Fock and the second-order Moller–Plesset perturbation (MP2) energy calculations substantially. Especially, the MP2 part for fragment dimers, which is computationally expensive, is accelerated by a factor of about 10. The CDAM approximations would enable FMO-MP2 calculations to easily process multiple structure samples even including dynamics of large molecular systems and lead to next-generation high-performance computations where statistical samplings or free energy estimates would be important.

[1]  Roland Lindh,et al.  Unbiased auxiliary basis sets for accurate two-electron integral approximations. , 2007, The Journal of chemical physics.

[2]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[3]  Masami Uebayasi,et al.  Pair interaction molecular orbital method: an approximate computational method for molecular interactions , 1999 .

[4]  K. Kitaura,et al.  Fragment molecular orbital method: an approximate computational method for large molecules , 1999 .

[5]  Roland Lindh,et al.  Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. , 2009, The Journal of chemical physics.

[6]  T. Nakano,et al.  Fragment interaction analysis based on local MP2 , 2007 .

[7]  Kaori Fukuzawa,et al.  Large scale FMO-MP2 calculations on a massively parallel-vector computer , 2008 .

[8]  Francesco Aquilante,et al.  Quartic scaling evaluation of canonical scaled opposite spin second-order Møller Plesset correlation energy using Cholesky decompositions , 2007 .

[9]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[10]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[11]  Marco Häser,et al.  Auxiliary basis sets to approximate Coulomb potentials , 1995 .

[12]  Francesco Aquilante,et al.  Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co(III)(diiminato)(NPh). , 2008, Journal of chemical theory and computation.

[13]  FRANCESCO AQUILANTE,et al.  MOLCAS 7: The Next Generation , 2010, J. Comput. Chem..

[14]  J. Simons,et al.  Application of cholesky-like matrix decomposition methods to the evaluation of atomic orbital integrals and integral derivatives , 1989 .

[15]  Kazuo Kitaura,et al.  Extending the power of quantum chemistry to large systems with the fragment molecular orbital method. , 2007, The journal of physical chemistry. A.

[16]  Takeshi Ishikawa,et al.  Fragment molecular orbital calculation using the RI-MP2 method , 2009 .

[17]  Marek Sierka,et al.  Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation , 2003 .

[18]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[19]  Henrik Koch,et al.  Method specific Cholesky decomposition: coulomb and exchange energies. , 2008, The Journal of chemical physics.

[20]  Seiichiro Ten-no,et al.  Multiconfiguration self‐consistent field procedure employing linear combination of atomic‐electron distributions , 1996 .

[21]  L. Cederbaum,et al.  On the Cholesky decomposition for electron propagator methods: General aspects and application on C(60). , 2009, The Journal of chemical physics.

[22]  Alistair P. Rendell,et al.  COUPLED-CLUSTER THEORY EMPLOYING APPROXIMATE INTEGRALS : AN APPROACH TO AVOID THE INPUT/OUTPUT AND STORAGE BOTTLENECKS , 1994 .

[23]  Yutaka Akiyama,et al.  Fragment molecular orbital method: application to polypeptides , 2000 .

[24]  Kaori Fukuzawa,et al.  Fragment molecular orbital method: use of approximate electrostatic potential , 2002 .

[25]  F. Weigend,et al.  RI-MP2: first derivatives and global consistency , 1997 .

[26]  I. Røeggen,et al.  On the Beebe-Linderberg two-electron integral approximation , 1986 .

[27]  Thomas Bondo Pedersen,et al.  Reduced scaling in electronic structure calculations using Cholesky decompositions , 2003 .

[28]  Rick A. Kendall,et al.  The impact of the resolution of the identity approximate integral method on modern ab initio algorithm development , 1997 .

[29]  Yuto Komeiji,et al.  Fragment molecular orbital method: analytical energy gradients , 2001 .

[30]  Kaori Fukuzawa,et al.  Possibility of mutation prediction of influenza hemagglutinin by combination of hemadsorption experiment and quantum chemical calculation for antibody binding. , 2009, The journal of physical chemistry. B.

[31]  Nicholas J. Higham,et al.  LAPACK-Style Codes for Pivoted Cholesky and QR Updating , 2006, PARA.

[32]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

[33]  Kazuo Kitaura,et al.  The importance of three-body terms in the fragment molecular orbital method. , 2004, The Journal of chemical physics.

[34]  Thomas Bondo Pedersen,et al.  Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions. , 2004, The Journal of chemical physics.

[35]  Emily A Carter,et al.  Cholesky decomposition within local multireference singles and doubles configuration interaction. , 2010, The Journal of chemical physics.

[36]  R. Lindh,et al.  Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals. , 2007, The Journal of chemical physics.

[37]  Florian Weigend,et al.  Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods. , 2009, The Journal of chemical physics.

[38]  Jonas Boström,et al.  Ab Initio Density Fitting: Accuracy Assessment of Auxiliary Basis Sets from Cholesky Decompositions. , 2009, Journal of chemical theory and computation.

[39]  John R. Sabin,et al.  On some approximations in applications of Xα theory , 1979 .

[40]  Jonas Boström,et al.  Calibration of Cholesky Auxiliary Basis Sets for Multiconfigurational Perturbation Theory Calculations of Excitation Energies. , 2010, Journal of chemical theory and computation.

[41]  Stephen Wilson,et al.  Universal basis sets and Cholesky decomposition of the two-electron integral matrix , 1990 .

[42]  Roland Lindh,et al.  Analytic derivatives for the Cholesky representation of the two-electron integrals. , 2008, The Journal of chemical physics.

[43]  Roland Lindh,et al.  Density fitting with auxiliary basis sets from Cholesky decompositions , 2009 .

[44]  D. Bernholdt,et al.  Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers , 1996 .

[45]  Michio Katouda,et al.  Efficient parallel algorithm of second‐order Møller–Plesset perturbation theory with resolution‐of‐identity approximation (RI‐MP2) , 2009 .

[46]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[47]  Roland Lindh,et al.  Accurate ab initio density fitting for multiconfigurational self-consistent field methods. , 2008, The Journal of chemical physics.

[48]  Robert J. Harrison,et al.  An implementation of RI–SCF on parallel computers , 1997 .