Multireference second-order Brillouin–Wigner perturbation theory§

Abstract

The multireference, state-specific, second-order, Brillouin–Wigner perturbation theory (MR-BWPT2) is presented. A posteriori corrections are made which, in the case of a single reference function, recover the well-known formula of second-order many-body perturbation theory, i.e. Møller–Plesset ‘MP2’ theory, and in the multireference case suppress terms which scale non-linearly with the number of electrons in the system. Prototype calculations are reported for the (H2)4 model in which the degree of quasi-degeneracy can be varied by changing a single geometric parameter. The calculated total energies obtained by a second-order Brillouin–Wigner treatment are compared with those supported by CAS-MP2 (complete active space self-consistent field followed by second-order Møller–Plesset-like treatment of dynamic correlation effects), by MR-BWCC (multireference Brillouin–Wigner coupled cluster expansion), and by full configuration interaction. MR-BWPT2 provides a theoretical apparatus comparable to the widely used MP2 theory, but which can be applied to quantum chemical problems requiring a multireference formalism.