Generalized maximum-overlap orbitals for multi-reference-state theories

Abstract

An attempt to generalize the maximum overlap or Brueckner orbitals, which are defined in the single-reference-state formulations of the many-electron theory, to the case of multi-referencestate approaches is made. The generalization is obtained by considering the orbitals that yield the maximum proximity of the subspace M spanned by the set of d exact wavefunctions considered in the MR method with the model space M 0 spanned by ddeterminants providing approximations to these wavefunctions. The new orbitals are referred to as maximum-proximity orbitals (MPOs). The general problem of defining the distance between pairs of finite dimensional subspaces of the Hilbert space is shortly reviewed. To better understand the impact of the distance of the M 0 and M spaces on MR-type approaches, model studies have been undertaken for the MBS H4 system, which offers the possibility of a simple parametrization of arbitrary symmetry-adapted orbital sets. Proximity indices of 13 standard quantum-chemical orbital sets are compared for various degrees of quasi-degeneracy of the states considered. It is demonstrated that the MPOs minimize the impact of singly-excited determinants on the structure of the wavefunctions. The MPOs are applied in calculations based on MR-CC approaches of valence-universal and state-universal types. Results superior to those for HF orbitals are obtained. The improvement is especially evident outside the strong quasi-degeneracy region.