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.