A simple and efficient CCSD(T)-F12 approximation.

A new explicitly correlated CCSD(T)-F12 approximation is presented and tested for 23 molecules and 15 chemical reactions. The F12 correction strongly improves the basis set convergence of correlation and reaction energies. Errors of the Hartree-Fock contributions are effectively removed by including MP2 single excitations into the auxiliary basis set. Using aug-cc-pVTZ basis sets the CCSD(T)-F12 calculations are more accurate and two orders of magnitude faster than standard CCSD(T)/aug-cc-pV5Z calculations.

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

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

[3]  Edward F. Valeev Computation of precise two-electron correlation energies with imprecise Hartree–Fock orbitals , 2006 .

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

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

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

[7]  E. Hylleraas,et al.  Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium , 1929 .

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

[9]  T. Helgaker,et al.  Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals , 2002 .

[10]  J. Noga,et al.  Alternative formulation of the matrix elements in MP2‐R12 theory , 2005 .

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

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

[13]  Wim Klopper,et al.  Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory , 1991 .

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

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

[16]  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.

[17]  T. Helgaker,et al.  Computation of two-electron Gaussian integrals for wave functions including the correlation factor r12exp(−γr122) , 2002 .

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

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

[20]  Trygve Helgaker,et al.  Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations , 2000 .

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

[22]  W. Kutzelnigg,et al.  MP2-R12 calculations on the relative stability of carbocations , 1990 .

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

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

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

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

[27]  W. Klopper A hybrid scheme for the resolution-of-the-identity approximation in second-order Møller-Plesset linear-r(12) perturbation theory. , 2004, The Journal of chemical physics.

[28]  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.

[29]  Wim Klopper,et al.  Explicitly correlated second-order Møller–Plesset methods with auxiliary basis sets , 2002 .

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

[31]  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.

[32]  W. Kutzelnigg,et al.  Møller-plesset calculations taking care of the correlation CUSP , 1987 .

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

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

[35]  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 .