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

We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-cluster wave function 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 substitutions 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. © 2000 American Institute of Physics. @S0021-9606~00!30130-1#