Second-order many-body perturbation theory with non-canonical and non-orthogonal orbitals

Using non-orthogonal virtual and non-canonical (localized) occupied orbital s, a second-order many-body perturbation theory is formulated. The equation s of interest are derived from the first-order Bloch equation by using an a pproach based on a bi-orthogonal basis and operators expressed in second-qu antization. A wide variety of partitions of the Hamiltonian are permitted, since any one-body, non-diagonal, zeroth-order Hamiltonian H-0 may be used. A matrix formulation is also presented. (C) 2000 Published by Elsevier Sci ence B.V.