High order nonadiabatic perturbation theory on different adiabatic bases

Abstract

A new partitioning of the nonadiabatic terms of a Hamiltonian consisting of a “slow” and a “fast” subsystem is introduced for high order numerical calculations of perturbation series. The Hamiltonian H(ν,λ) depends on two parameters, λ and ν. While the momentum dependent part of the perturbation is taken to be a linear function of the perturbation parameter λ, the other nonadiabatic terms are either assumed to be independent of λ, or depend quadratically on it. Especially the diagonal correction is partitioned into a constant and a quadratic function of λ. This partitioning will be controlled by the parameter ν. In zeroth order, the Hamiltonian will therefore be either the Born–Oppenheimer Hamiltonian, when ν=1, or the Born–Huang Hamiltonian, when ν=0. For other values of ν, more general adiabatic bases result. The new partitioning, in combination with the Hutson and Howard approach, forms a new method for the calculation of nonadiabatic perturbation series which is tested on a set of four model Hamiltonians. These have been studied already by Špirko et al. in a similar context. It is shown that the new method, as compared to traditional approaches, strongly enhances the rate of convergence and the accuracy of summability of the perturbation series, especially in the case of nearly avoided intersections or of near degeneracies.