Diagrammatic many-body perturbation theory for general model spaces

Previous formulations, due to Brandow (1977) and subsequent authors, are limited to complete model spaces, including all possible occupations of open-shell orbitals. This definition of the model space may be troublesome for systems with several open shells, such as most molecular excited states, leading to intruder states and slowing or even destroying the convergence of the perturbation series. The formalism presented here applies to any model space, whether complete or incomplete, degenerate, quasi-degenerate or non-degenerate. Certain types of unlinked diagrams may appear for incomplete, quasi-degenerate model spaces. The orbitals are partitioned into two classes (holes and particles) for the purpose of diagram summation instead of Brandow's three (core, valence and particles), with the partitioning for a particular element of the effective interaction matrix determined by the ket state of that element.