Second order perturbation corrections to singles and doubles coupled-cluster methods: General theory and applications to the valence optimized doubles model

S. R. Gwaltney, C. D. Sherrill, M. Head-Gordon, and A. I. Krylov
J. Chem. Phys. 113, 3548 – 3560 (2000)

We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-cluster wavefunction is used to define a similarity-transformed Hamiltonian, which is partitioned into a zeroth-order part that the reference problem solves exactly plus a first-order perturbation. Standard perturbation theory through second order provides the leading correction. Applied to the valence optimized doubles (VOD) approximation to the full-valence complete active space self-consistent field method, the second-order correction, which we call (2), captures dynamical correlation effects through external single, double, and semi-internal triple and quadruple substitutions. A factorization approximation reduces the cost of the quadruple substitutes to only sixth order in the size of the molecule. A series of numerical tests are presented showing that VOD(2) is stable and well-behaved provided that the VOD reference is also stable. The second-order correction is also general to standard unwindowed coupled-cluster energies such as the coupled-cluster singles and doubles (CCSD) method itself, and the equations presented here fully define the corresponding CCSD(2) energy.

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