Excitation energies with multireference many-body perturbation theory

Abstract

Excitation energy calculations with multireference many-body perturbation theory (MRMBPT) are theoretically and numerically studied. An extension of the Hose–Kaldor (HK) scheme is presented, which removes disconnected terms and, hence, the size-extensivity error for higher-order MRMBPT approximations. The excitation problem requires the use of an incomplete model space for which connectivity of the effective Hamiltonian Heff, is incompatible with intermediate normalization. In our formulation a proper choice of the model space as an introduction of a ‘‘quasiintermediate’’ normalization leads to the connected structure of Heff. This guarantees size extensivity of the method which generally could not be achieved with the earlier Hose–Kaldor (HK) framework based upon intermediate normalization. Special attention is paid to the case when the Hartree–Fock (HF) approximation is used in the zeroth-order step. In this specific case the HK formalism applied to a subspace of the model space spanned by singly excited determinants gives the same result through third order which means that in the HF case disconnected contributions to Heff disappear and size extensivity is preserved to that order. MRMBPT(3) results for N2 and CO are presented to offer illustrative comparisons with the recently proposed EOM-CCSD and Fock space MRCCSD results.