Investigation of the global second-derivative non-adiabatic contributions: Rovibrational energies of [formula omitted], [formula omitted], and prospects for [formula omitted] (Part II)

Abstract

The influence of the non-adiabaticity on the rovibrational bound states of H2+, H2, and H3+ is investigated. For this purpose a full configuration interaction (FCI) treatment using Gaussian basis functions is applied to calculate the energies of the electronic states as well as all couplings between them caused by the nuclear motion. These ‘derivative couplings’ were evaluated up to second order by means of a perturbation treatment. While this has been possible already for H2+ and H2, nothing equivalent has been available for H3+. The present work is an extension of the investigation of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses needed for only one single potential energy surface. Our new implementation allowed to include for the first time also for H3+ all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. These new inclusions of all nonadiabatic effects could reduce also for H3+ the deviations to experimental data for most rovibrational levels to less than 0.1 cm−1 without any empirically adjustable parameters. For H3+, the accuracy is slightly improved when also relativistic and QED effects are taken into account. For two questionable assignments of observed transitions in H3+ we propose a new labeling.