Nonadiabatic rotational states of the hydrogen molecule

TL;DR

This paper introduces a new computational approach for accurately calculating nonadiabatic rotational energy levels in four-particle systems like hydrogen molecules without separating nuclear and electronic motions.

Contribution

It develops a novel method using explicitly correlated exponential basis functions and analytic formulas, enabling precise calculations of rotationally excited states without adiabatic approximation.

Findings

Achieved energy level accuracy of 10^{-12} to 10^{-13}

Demonstrated high numerical efficiency for hydrogen molecule states

Provided formulas for coupling between rotational and electronic angular momenta

Abstract

We present a new computational method for the determination of energy levels in four-particle systems like H$_2$, HD, and HeH$^+$ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schr\"odinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present results for various states of the hydrogen molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of $10^{-12}$-$10^{-13}$, which corresponds to an uncertainty of $10^{-7}$-$10^{-8}$ cm$^{-1}$.