Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis

We develop a combined coupled-cluster (CC) or equation-of-motion coupled-cl uster (EOM-CC) theory and Rayleigh-Schrodinger perturbation theory on the b asis of a perturbation expansion of the similarity-transformed Hamiltonian (H) over bar =exp(-T)H exp(T). This theory generates a series of perturbati ve corrections to any of the complete CC or EOM-CC models and hence a hiera rchy of the methods designated by CC(m)PT(n) or EOM-CC(m)PT(n). These metho ds systematically approach full configuration interaction (FCI) as the pert urbation order (n) increases and/or as the cluster and linear excitation op erators become closer to complete (m increases), while maintaining the orbi tal-invariance property and size extensivity of CC at any perturbation orde r, but not the size intensivity of EOM-CC. We implement the entire hierarch y of CC(m)PT(n) and EOM-CC(m)PT(n) into a determinantal program capable of computing their energies and wave functions for any given pair of m and n. With this program, we perform CC(m)PT(n) and EOM-CC(m)PT(n) calculations of the ground-state energies and vertical excitation energies of selected sma ll molecules for all possible values of m and 0 less than or equal ton less than or equal to5. When the Hartree-Fock determinant is dominant in the FC I wave function, the second-order correction to CCSD [CC(2)PT(2)] reduces t he differences in the ground-state energy between CCSD and FCI by more than a factor of 10, and thereby significantly outperforms CCSD(T) or even CCSD T. The third-order correction to CCSD [CC(2)PT(3)] further diminishes the e nergy difference between CC(2)PT(2) and FCI and its performance parallels t hat of some CCSD(TQ) models. CC(m)PT(n) for the ground state with some mult ideterminantal character and EOM-CC(m)PT(n) for the excitation energies, ho wever, appear to be rather slowly convergent with respect to n. (C) 2001 Am erican Institute of Physics.