A NONDIAGONAL QUASI-DEGENERATE 4TH-ORDER PERTURBATION-THEORY

A canonical quasidegenerate Rayleigh-Schrodinger perturbation theory, correct through fourth order in the energy, is explored for a block-di agonal unperturbed Hamiltonian. The theory is developed completely wit hin a Lie Algebra in Hilbert space. Explicit equations for n-particle transition elements in terms of solutions of simultaneous linear equat ions are presented. A two-dimensional anisotropic anharmonic oscillato r is used to provide numerical results. The perturbation theory is sho wn to be stable under small separation of model and complement spaces. An iterative variant of the fourth-order perturbation theory is intro duced; the iterative variant is related to the non-iterative one in mu ch the same way as nondegenerate coupled cluster theories are related to nondegenerate perturbation theory. The quasidegenerate coupled clus ter theory appears to be stable in the presence of multiple intruder s tates.