A nondiagonal quasidegenerate fourth-order perturbation theory

A canonical quasidegenerate Rayleigh-Schrödinger perturbation theory, correct through fourth order in the energy, is explored for a block-diagonal unperturbed Hamiltonian. The theory is developed completely within a Lie Algebra in Hilbert space. Explicit equations forn-particle transition elements in terms of solutions of simultaneous linear equations are presented. A two-dimensional anisotropic anharmonic oscillator is used to provide numerical results. The perturbation theory is shown to be stable under small separation of model and complement spaces. An iterative variant of the fourth order perturbation theory is introduced; the iterative variant is related to the non-iterative one in much the same way as nondegenerate coupled cluster theories are related to nondegenerate perturbation theory. The quasidegenerate coupled cluster theory appears to be stable in the presence of multiple intruder states.