Nonadiabatic corrections to the wave function and energy

TL;DR

This paper develops a systematic perturbative approach to calculate nonadiabatic corrections in small molecules, deriving explicit formulas and validating them through numerical comparisons with experiments on hydrogen molecules.

Contribution

It introduces a perturbative expansion around the adiabatic approximation with explicit formulas for corrections, validated against numerical and experimental data.

Findings

Good agreement with experimental dissociation energies for H₂ and D₂.

Derived closed-form formulas for leading nonadiabatic corrections.

Validated the perturbative approach with numerical results.

Abstract

Nonadiabatic corrections in molecules composed of a few atoms are considered. It is demonstrated that a systematic perturbative expansion around the adiabatic solution is possible, with the expansion parameter being the electron-nucleus mass ratio to the power 3/4. Closed form formulae for the leading corrections to the wave function and to the energy are derived. Their applicability is demonstrated by a comparison of numerical results for the hydrogen molecule with the former nonadiabatic calculations and the experimental values. Good agreement with the recent experiment is achieved for the ground state dissociation energy of both H$_2$ and D$_2$.