Quasidegenerate variational perturbation theory and the calculation of first-order properties from variational perturbation theory wave functions

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Abstract
In previous work on the treatment of correlation in molecular systems we have applied a multireference version of second‐order Hylleraas variational perturbation theory. The choice made for the partitioning of H treated the interactions between the correlating functions to infinite order and gave the corrections to the wave function to first order. The method was shown to be accurate in many cases, but became less so when near degeneracies occurred between the reference energy and other eigenvalues of H 0. In this article we introduce an effective Hamiltonian method that is analogous to variational perturbation theory, but which is significantly more accurate when near degeneracies are important. This quasidegenerate variational perturbation theory (QDVPT) is an explicitly multireference procedure and treats the entire reference space as a quasidegenerate space. A novel method for solving the QDVPT equations is introduced that avoids explicit construction of the effective Hamiltonian. As a result, the work involved in application of QDVPT is on the roder of that required for variational perturbation theory. We also present an approximate method for calculating first‐order atomic and molecular properties based on Hylleraas variational perturbation theory, multireference linearized coupled cluster, and QDVPT wave functions. The properties are calculated as derivatives of the energy with respect to the field strength. Construction of a one‐electron density matrix based on the energy derivative expression allows rapid evaluation of one‐electron properties. Results are presented and compared to full and truncated CI results. Good agreement is found in the cases examined.