An efficient local coupled cluster method for accurate thermochemistry of large systems.

An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo̸ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.

[1]  Hans-Joachim Werner,et al.  Local perturbative triples correction (T) with linear cost scaling , 2000 .

[2]  Hans-Joachim Werner,et al.  An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit. , 2011, The Journal of chemical physics.

[3]  Wei Li,et al.  Local correlation calculations using standard and renormalized coupled-cluster approaches. , 2009, The Journal of chemical physics.

[4]  M. Schütz,et al.  Intermolecular interactions in photodamaged DNA from density functional theory symmetry-adapted perturbation theory. , 2011, Chemphyschem : a European journal of chemical physics and physical chemistry.

[5]  Frederick R. Manby,et al.  Linear scaling local coupled cluster theory with density fitting. Part I: 4-external integrals , 2003 .

[6]  Martin Head-Gordon,et al.  Noniterative local second order Mo/ller–Plesset theory: Convergence with local correlation space , 1998 .

[7]  Christof Hättig,et al.  CC2 excitation energy calculations on large molecules using the resolution of the identity approximation , 2000 .

[8]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[9]  Frederick R Manby,et al.  General orbital invariant MP2-F12 theory. , 2007, The Journal of chemical physics.

[10]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[11]  Frederick R. Manby,et al.  Density fitting in second-order linear-r12 Møller–Plesset perturbation theory , 2003 .

[12]  Hans-Joachim Werner,et al.  Local treatment of electron correlation in coupled cluster theory , 1996 .

[13]  Peter Pulay,et al.  Orbital-invariant formulation and second-order gradient evaluation in Møller-Plesset perturbation theory , 1986 .

[14]  T Daniel Crawford,et al.  Potential energy surface discontinuities in local correlation methods. , 2004, The Journal of chemical physics.

[15]  Guntram Rauhut,et al.  Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory , 1998 .

[16]  Peter Pulay,et al.  Local configuration interaction: An efficient approach for larger molecules , 1985 .

[17]  Hans-Joachim Werner,et al.  Explicitly correlated RMP2 for high-spin open-shell reference states. , 2008, The Journal of chemical physics.

[18]  L. Maschio,et al.  Fitting of local densities in periodic systems , 2008 .

[19]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[20]  Martin Head-Gordon,et al.  Non-iterative local second order Møller–Plesset theory , 1998 .

[21]  Hans-Joachim Werner,et al.  Calculation of smooth potential energy surfaces using local electron correlation methods. , 2006, The Journal of chemical physics.

[22]  J. Simon,et al.  A role for sunlight in skin cancer: UV-induced p53 mutations in squamous cell carcinoma. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Walter Thiel,et al.  Toward accurate barriers for enzymatic reactions: QM/MM case study on p-hydroxybenzoate hydroxylase. , 2008, The Journal of chemical physics.

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

[25]  Florian Weigend,et al.  A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency , 2002 .

[26]  Frederick R. Manby,et al.  Fast Hartree–Fock theory using local density fitting approximations , 2004 .

[27]  Georg Hetzer,et al.  Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory , 2000 .

[28]  Peter Pulay,et al.  The local correlation treatment. II. Implementation and tests , 1988 .

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

[30]  Hans-Joachim Werner,et al.  Correlation regions within a localized molecular orbital approach. , 2008, The Journal of chemical physics.

[31]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[32]  Hans-Joachim Werner,et al.  Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) , 2001 .

[33]  Tatiana Korona,et al.  Local CC2 electronic excitation energies for large molecules with density fitting. , 2006, The Journal of chemical physics.

[34]  Aziz Sancar,et al.  Structure and function of DNA photolyase and cryptochrome blue-light photoreceptors. , 2003, Chemical reviews.

[35]  F. Weinhold,et al.  Natural population analysis , 1985 .

[36]  B. I. Dunlap,et al.  Robust variational fitting: Gáspár's variational exchange can accurately be treated analytically , 2000 .

[37]  Guntram Rauhut,et al.  Local Treatment of Electron Correlation in Molecular Clusters: Structures and Stabilities of (H2O)n, n = 2−4 , 1998 .

[38]  Martin Schütz,et al.  A multistate local coupled cluster CC2 response method based on the Laplace transform. , 2009, The Journal of chemical physics.

[39]  Frank Weinhold,et al.  Natural localized molecular orbitals , 1985 .

[40]  Stinne Høst,et al.  Local orbitals by minimizing powers of the orbital variance. , 2011, The Journal of chemical physics.

[41]  R. Bartlett,et al.  Natural linear-scaled coupled-cluster theory with local transferable triple excitations: applications to peptides. , 2008, The journal of physical chemistry. A.

[42]  Martin Schütz,et al.  Low-order scaling local electron correlation methods. V. Connected triples beyond (T): Linear scaling local CCSDT-1b , 2002 .

[43]  Tatiana Korona,et al.  Transition strengths and first-order properties of excited states from local coupled cluster CC2 response theory with density fitting. , 2007, The Journal of chemical physics.

[44]  John A. Parkhill,et al.  Penalty functions for combining coupled-cluster and perturbation amplitudes in local correlation methods with optimized orbitals , 2008 .

[45]  Ricardo A. Mata,et al.  Local correlation methods with a natural localized molecular orbital basis , 2007 .

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

[47]  Brett I. Dunlap,et al.  Robust and variational fitting , 2000 .

[48]  Hans-Joachim Werner,et al.  A simple and efficient CCSD(T)-F12 approximation. , 2007, The Journal of chemical physics.

[49]  Roland Lindh,et al.  Linear scaling multireference singles and doubles configuration interaction. , 2008, The Journal of chemical physics.

[50]  Hans-Joachim Werner,et al.  Simplified CCSD(T)-F12 methods: theory and benchmarks. , 2009, The Journal of chemical physics.

[51]  Frederick R Manby,et al.  Analytical energy gradients for local second-order Møller-Plesset perturbation theory using density fitting approximations. , 2004, The Journal of chemical physics.

[52]  B. Dunlap,et al.  Robust and variational fitting: Removing the four-center integrals from center stage in quantum chemistry , 2000 .

[53]  A. Dutoi,et al.  Accurate local approximations to the triples correlation energy: formulation, implementation and tests of 5th-order scaling models , 2005 .

[54]  Peter Pulay,et al.  Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method , 1987 .

[55]  Local and long-range correlation in extended systems , 1986 .

[56]  G. Rauhut,et al.  The vibrational spectra of furoxan and dichlorofuroxan: A comparative theoretical study using density functional theory and local electron correlation methods , 2003 .

[57]  Dimitrios G Liakos,et al.  Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis. , 2009, The Journal of chemical physics.

[58]  Daniel Kats,et al.  Local CC2 response method for triplet states based on Laplace transform: excitation energies and first-order properties. , 2010, The Journal of chemical physics.

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

[60]  F. Manby.  Accurate condensed-phase quantum chemistry , 2010 .

[61]  Frederick R Manby,et al.  Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor. , 2006, The Journal of chemical physics.

[62]  Guntram Rauhut,et al.  Impact of local and density fitting approximations on harmonic vibrational frequencies. , 2006, The journal of physical chemistry. A.

[63]  Frederick R. Manby,et al.  Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms , 2007 .

[64]  F. Manby,et al.  Explicitly correlated second-order perturbation theory using density fitting and local approximations. , 2006, The Journal of chemical physics.

[65]  Martin Head-Gordon,et al.  A local correlation model that yields intrinsically smooth potential-energy surfaces. , 2005, The Journal of chemical physics.

[66]  F. Manby,et al.  An explicitly correlated second order Møller-Plesset theory using a frozen Gaussian geminal. , 2004, The Journal of chemical physics.

[67]  Hans-Joachim Werner,et al.  A comparison of the efficiency and accuracy of the quadratic configuration interaction (QCISD), coupled cluster (CCSD), and Brueckner coupled cluster (BCCD) methods , 1992 .

[68]  Martin Head-Gordon,et al.  A Resolution-Of-The-Identity Implementation of the Local Triatomics-In-Molecules Model for Second-Order Møller-Plesset Perturbation Theory with Application to Alanine Tetrapeptide Conformational Energies. , 2005, Journal of chemical theory and computation.

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

[70]  Peter Pulay,et al.  Comparison of the boys and Pipek–Mezey localizations in the local correlation approach and automatic virtual basis selection , 1993, J. Comput. Chem..

[71]  Frederick R Manby,et al.  Local explicitly correlated second-order perturbation theory for the accurate treatment of large molecules. , 2009, The Journal of chemical physics.

[72]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[73]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[74]  Frederick R Manby,et al.  Tensor factorizations of local second-order Møller-Plesset theory. , 2010, The Journal of chemical physics.

[75]  Amir Karton,et al.  Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267] , 2005, physics/0509216.

[76]  H. Werner,et al.  Chapter 4 On the Selection of Domains and Orbital Pairs in Local Correlation Treatments , 2006 .

[77]  Georg Hetzer,et al.  Multipole approximation of distant pair energies in local MP2 calculations , 1998 .

[78]  Cesare Pisani,et al.  Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications , 2008, J. Comput. Chem..

[79]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

[80]  Philippe Y. Ayala,et al.  Linear scaling coupled cluster and perturbation theories in the atomic orbital basis , 1999 .

[81]  Michael Dolg,et al.  Fully Automated Incremental Evaluation of MP2 and CCSD(T) Energies: Application to Water Clusters. , 2009, Journal of chemical theory and computation.

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

[83]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[84]  Peter Pulay,et al.  An efficient reformulation of the closed‐shell self‐consistent electron pair theory , 1984 .

[85]  Martin Schütz,et al.  A new, fast, semi-direct implementation of linear scaling local coupled cluster theory , 2002 .

[86]  Walter Thiel,et al.  Reductive half-reaction of aldehyde oxidoreductase toward acetaldehyde: Ab initio and free energy quantum mechanical/molecular mechanical calculations. , 2010, The Journal of chemical physics.

[87]  H. Werner,et al.  The effect of local approximations in coupled-cluster wave functions on dipole moments and static dipole polarisabilitiesDedicated to Prof. W. Meyer on the occasion of his 65th birthday. , 2004 .

[88]  Peter Pulay,et al.  Efficient elimination of basis set superposition errors by the local correlation method: Accurate ab initio studies of the water dimer , 1993 .

[89]  Branislav Jansík,et al.  Linear scaling coupled cluster method with correlation energy based error control. , 2010, The Journal of chemical physics.

[90]  Martin Schütz,et al.  Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T) , 2000 .

[91]  Martin Schütz,et al.  Molpro: a general‐purpose quantum chemistry program package , 2012 .

[92]  Joseph G. Hoffman,et al.  Quantum Theory of Atoms, Molecules and the Solid State: A Tribute to John C. Slater , 1967 .

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