Benchmark Studies for Explicitly Correlated Perturbation- and Coupled Cluster Theories. javascript:filterformular(´3´)

Abstract The recently developed explicitly correlated MP2-F12 and CCSD(T)-F12x (x = a,b) methods are reviewed. The explicit correlation treatment leads to a dramatic improvement of the basis set convergence. Extensive benchmarks for reaction energies, atomization energies, electron affinities, ionization potentials, equilibrium structures, vibrational frequencies, and intermolecular interaction energies are presented which show that for many molecular properties the intrinsic accuracy of the CCSD(T) method is already reached with double-zeta (VDZ-F12) basis sets, while triple-zeta (VTZ-F12) basis sets yield results that are very close to the complete basis set limit. The steep scaling of the MP2-F12 method with molecular size can be reduced by local approximations. This has made it possible to carry out MP2-F12 calculations for molecules with up to 100 atoms. The errors caused bjavascript:filterformular(´3´)y the local domain approximation are largely removed by the explicitly correlated terms, which account for the neglected configurations in an approximate way. Extensions to LCCSD(T)-F12 are discussed and preliminary results for LCCSD-F12 are presented.

[1]  Hans-Joachim Werner,et al.  Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar. , 2008, The Journal of chemical physics.

[2]  D. Tew,et al.  A diagonal orbital-invariant explicitly-correlated coupled-cluster method , 2008 .

[3]  Seiichiro Ten-no,et al.  Initiation of explicitly correlated Slater-type geminal theory , 2004 .

[4]  Kirk A. Peterson,et al.  Optimized complementary auxiliary basis sets for explicitly correlated methods: aug-cc-pVnZ orbital basis sets , 2009 .

[5]  D. Tew,et al.  New correlation factors for explicitly correlated electronic wave functions. , 2005, The Journal of chemical physics.

[6]  Seiichiro Ten-no,et al.  Explicitly correlated second order perturbation theory: introduction of a rational generator and numerical quadratures. , 2004, The Journal of chemical physics.

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

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

[9]  Hans-Joachim Werner,et al.  Coupled cluster theory for high spin, open shell reference wave functions , 1993 .

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

[11]  Christof Hättig,et al.  Quintuple-ζ quality coupled-cluster correlation energies with triple-ζ basis sets , 2007 .

[12]  P. Botschwina,et al.  High-level Ab-initio Calculations for Astrochemically Relevant Polyynes (HC2nH), their Isomers (C2nH2) and their Anions (C2nH−) , 2009 .

[13]  W. Klopper,et al.  Coupled-cluster theory with simplified linear-r(12) corrections: the CCSD(R12) model. , 2005, The Journal of chemical physics.

[14]  So Hirata,et al.  Higher-order explicitly correlated coupled-cluster methods. , 2009, The Journal of chemical physics.

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

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

[17]  R. T. Pack,et al.  Cusp Conditions for Molecular Wavefunctions , 1966 .

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

[19]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[20]  Hans-Joachim Werner,et al.  Local explicitly correlated coupled-cluster methods: efficient removal of the basis set incompleteness and domain errors. , 2009, The Journal of chemical physics.

[21]  Hans-Joachim Werner,et al.  Eliminating the domain error in local explicitly correlated second-order Møller-Plesset perturbation theory. , 2008, The Journal of chemical physics.

[22]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

[23]  J. Noga,et al.  Second order explicitly correlated R12 theory revisited: a second quantization framework for treatment of the operators' partitionings. , 2007, The Journal of chemical physics.

[24]  S. F. Boys.  Localized Orbitals and Localized Adjustment Functions , 1966 .

[25]  W. Klopper,et al.  Inclusion of the (T) triples correction into the linear‐r12 corrected coupled‐cluster model CCSD(R12) , 2006 .

[26]  D. Tew,et al.  A comparison of linear and nonlinear correlation factors for basis set limit Møller-Plesset second order binding energies and structures of He2, Be2, and Ne2. , 2006, The Journal of chemical physics.

[27]  Guntram Rauhut,et al.  Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory. , 2009, The Journal of chemical physics.

[28]  Werner Kutzelnigg,et al.  r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l , 1985 .

[29]  Juana Vázquez,et al.  HEAT: High accuracy extrapolated ab initio thermochemistry. , 2004, The Journal of chemical physics.

[30]  Edward F. Valeev,et al.  Analysis of the errors in explicitly correlated electronic structure theory. , 2005, Physical chemistry chemical physics : PCCP.

[31]  B. Ruscic,et al.  W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions. , 2006, The Journal of chemical physics.

[32]  A. Köhn.  Explicitly correlated connected triple excitations in coupled-cluster theory. , 2009, The Journal of chemical physics.

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

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

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

[36]  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.

[37]  D. Tew,et al.  Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence. , 2008, The Journal of chemical physics.

[38]  J. Noga,et al.  Coupled cluster theory that takes care of the correlation cusp by inclusion of linear terms in the interelectronic coordinates , 1994 .

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

[40]  Wim Klopper,et al.  CC-R12, a correlation cusp corrected coupled-cluster method with a pilot application to the Be2 potential curve , 1992 .

[41]  J. Noga,et al.  Explicitly correlated R12 coupled cluster calculations for open shell systems , 2000 .

[42]  So Hirata,et al.  Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations. , 2008, The Journal of chemical physics.

[43]  Jirí Cerný,et al.  Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. , 2006, Physical chemistry chemical physics : PCCP.

[44]  Edward F. Valeev.  Improving on the resolution of the identity in linear R12 ab initio theories , 2004 .

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

[46]  J. Noga,et al.  Explicitly correlated coupled cluster F12 theory with single and double excitations. , 2008, The Journal of chemical physics.

[47]  Hans-Joachim Werner,et al.  Accurate calculations of intermolecular interaction energies using explicitly correlated coupled cluster wave functions and a dispersion-weighted MP2 method. , 2009, The journal of physical chemistry. A.

[48]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited , 2001 .

[49]  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..

[50]  Edward F. Valeev,et al.  Equations of explicitly-correlated coupled-cluster methods. , 2008, Physical chemistry chemical physics : PCCP.

[51]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

[52]  Hans-Joachim Werner,et al.  Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions. , 2008, Physical chemistry chemical physics : PCCP.

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

[54]  Edward F. Valeev.  Combining explicitly correlated R12 and Gaussian geminal electronic structure theories. , 2006, The Journal of chemical physics.

[55]  Kirk A Peterson,et al.  Optimized auxiliary basis sets for explicitly correlated methods. , 2008, The Journal of chemical physics.

[56]  Paul G. Mezey,et al.  A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions , 1989 .

[57]  Frederick R. Manby,et al.  R12 methods in explicitly correlated molecular electronic structure theory , 2006 .

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

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