Hydrogen molecule ion: Path integral Monte Carlo approach

TL;DR

This paper employs path integral Monte Carlo methods to analyze the quantum dynamics of electrons and nuclei in the hydrogen molecule ion, highlighting the significance of non-adiabatic effects and coupling between particles.

Contribution

It introduces a non-adiabatic simulation approach for the hydrogen molecule ion, revealing detailed electron-nuclear coupling effects beyond the Born--Oppenheimer approximation.

Findings

Coupling effects significantly alter nuclear pair correlation and bond length.

Non-adiabatic correction impacts the binding energy.

Electronic distribution is less affected by non-adiabatic effects.

Abstract

Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born--Oppenheimer and non-adiabatic simulations, and inspecting projections of the full three-body dynamics onto adiabatic Born--Oppenheimer approximation. Coupling of electron and nuclear quantum dynamics is clearly seen. Nuclear pair correlation function is found to broaden by 0.040 a_0 and average bond length is larger by 0.056 a_0. Also, non-adiabatic correction to the binding energy is found. Electronic distribution is affected less, and therefore, we could say that the adiabatic approximation is better for the electron than for the nuclei.