Perturbative treatment of the similarity transformed Hamiltonian in equation-of-motion coupled-cluster approximations

A series of size-consistent approximations to the equation-of-motion coupled cluster method in the singles and doubles approximation (EOM-CCSD) are developed by subjecting the similarity transformed Hamiltonian H̄=exp(−T)H exp(T) to a perturbation expansion. Attention is directed to N and N−1 electron final state realizations of the method defined by truncation of H̄ at second order. Explicit spin–orbital equations for the energy and its first derivative are documented for both approaches [EOMEE-CCSD(2) and EOMIP-CCSD(2), respectively], and have been implemented in a large-scale quantum chemistry program. Vertical ionization potentials calculated by EOMIP-CCSD(2) are shown to be equivalent to those of an approach presented recently by Nooijen and Snijders [J. Chem. Phys. 102, 1681 (1995)]. Applications of both EOMIP-CCSD(2) and EOMEE-CCSD(2) provide results for final state properties that compare favorably with those obtained in full EOM-CCSD calculations. Analysis of the computational aspects of the approximate and full EOM-CCSD methods shows that the cost of EOMIP-CCSD(2) energy and gradient calculations scales in proportion to the fifth power of the basis set size, a significant savings over the sixth power dependence of EOMIP-CCSD. This feature is of great practical importance, as it shows that this N−1 electron final state approach has a large domain of applicability and is therefore likely to become a valuable tool for application calculations. On the other hand, the same cannot be said for EOMEE-CCSD(2) since its asymptotic computational dependence and storage requirements are the same as the full EOMEE-CCSD method.