Variational formulation of perturbative explicitly-correlated coupled-cluster methods.
We present a variational formulation of the recently-proposed CCSD(2)(R12) method [Valeev, Phys. Chem. Chem. Phys., 2008, 10, 106]. The centerpiece of this approach is the CCSD(2)(R12) Lagrangian obtained via Löwdin partitioning of the coupled-cluster singles and doubles (CCSD) Hamiltonian. Extremization of the Lagrangian yields the second-order basis set incompleteness correction for the CCSD energy. We also developed a simpler Hylleraas-type functional that only depends on one set of geminal amplitudes by applying screening approximations. This functional is used to develop a diagonal orbital-invariant version of the method in which the geminal amplitudes are fixed at the values determined by the first-order cusp conditions. Extension of the variational method to include perturbatively the effect of connected triples produces the method that approximates the complete basis-set limit of the standard CCSD plus perturbative triples [CCSD(T)] method. For a set of 20 small closed-shell molecules, the method recovered at least 94.5/97.3% of the CBS CCSD(T) correlation energy with the aug-cc-pVDZ/aug-cc-pVTZ orbital basis set. For 12 isogyric reactions involving these molecules, combining the aug-cc-pVTZ correlation energies with the aug-cc-pVQZ Hartree-Fock energies produces the electronic reaction energies with a mean absolute deviation of 1.4 kJ mol(-1) from the experimental values. The method has the same number of optimized parameters as the corresponding CCSD(T) model, does not require any modification of the coupled-cluster computer program, and only needs a small triple-zeta basis to match the precision of the considerably more expensive standard quintuple-zeta CCSD(T) computation.
Torheyden
Martin
M
Department of Chemistry, 107 Davidson Hall, Virginia Tech, Blacksburg, VA 24061, USA.
Valeev
Edward F
EF
D000465:Algorithms; D000473:Alkanes / Q000737:chemistry*; D002248:Carbon Monoxide / Q000737:chemistry; D003486:Cyanides / Q000737:chemistry; D004583:Electrons; D004735:Energy Transfer; D005459:Fluorides / Q000737:chemistry; D005461:Fluorine / Q000737:chemistry*; D006859:Hydrogen / Q000737:chemistry*; D009584:Nitrogen / Q000737:chemistry*; D011789:Quantum Theory; D013816:Thermodynamics
D000473:Alkanes; D003486:Cyanides; D005461:Fluorine; D002248:Carbon Monoxide; D006859:Hydrogen; D009584:Nitrogen; D005459:Fluorides