Optimized partitioning in perturbation theory: Comparison to related approaches

Abstract

A generalized Epstein–Nesbet type perturbation theory is introduced by a unique, “optimal” determination of level shift parameters. As a result, a new partitioning emerges in which third order energies are identically zero, most fifth order terms also vanish, and low (2nd, 4th) order corrections are quite accurate. Moreover, the results are invariant to unitary transformations within the zero order excited states. Applying the new partitioning to many-body perturbation theory, the perturbed energies exhibit appealing features: (i) they become orbital invariant if all level shifts are optimized in an excitation subspace; and (ii) meet the size-consistency requirement if no artificial truncations in the excitation space is used. As to the numerical results, low order corrections do better than those of Mo/ller–Plesset partitioning. At the second order, if the single determinantal Hartree–Fock reference state is used, the CEPA-0 (=LCCD) energies are recovered. Higher order corrections provide a systematic way of improving this scheme, numerical studies showing favorable convergence properties. The theory is tested on the anharmonic linear oscillator and on the electron correlation energies of some selected small molecules.