Brueckner orbitals for multi-reference state theories

Various ways of generalizing the concept of maximum overlap or Brueckner or bitals (BOs), which are defined in single-reference (SR) state formulations of many-electron theory, to the case of multi-reference (MR) state approac hes are proposed. These generalizations can be classified into two categori es. The first one consists of orbitals that yield the maximum proximity of the model space. M-0, spanned by d-determinants constructed from the orbita ls considered and the target space, M, spanned by the set of d exact wavefu nctions of interest in the MR approach. Due to the fact that there are many proximity criteria, the first category includes various maximum proximity orbitals (MPOs). The second category includes the set of orbitals (MR-BOs) which satisfy the generalized Brueckner condition (the requirement is that in the cunfiguration-interaction expansion of the exact wavefunctions in th e intermediate normalization there are no singly-excited configurations). i nteresting relationships between various MPG-type sets, as well as between MPO and MR-BOs sets, have been disclosed. it has been shown that there exis ts such a proximity measure of M and M-0 that the orbitals maximizing it si multaneously satisfy the generalized Brueckner condition. These orbitals se em to provide the most satisfactory MR generalization of the BOs. To illust rate the detailed structure of the various orbital sets considered and to t est the sensitivity of various proximity measures results of calculations f or the H4 model are presented and discussed.