# Quantum Simulation of non-Born-Oppenheimer dynamics in molecular systems by path integrals

## TL;DR

This paper introduces a path integral-based numerical algorithm to accurately compute non-Born-Oppenheimer energies in molecular systems, providing a nonperturbative alternative to traditional methods.

## Contribution

The authors develop a novel path integral approach combined with variational functions to treat non-Born-Oppenheimer molecular dynamics without relying on perturbation theory.

## Key findings

- Calculated non-Born-Oppenheimer energies for hydrogen molecules and ions.
- Results agree well with existing theoretical and experimental data.
- Demonstrated the method's potential as a nonperturbative testing tool.

## Abstract

A numerical algorithm based on the probabilistic path integral approach for solving Schroedinger equation has been devised to treat molecular systems without Born-Oppenheimer approximation in the non relativistic limit at zero temperature as an alternative to conventional Variational and perturbation methods. Using high quality variational trial functions and path integral method based on Generalized Feynman-Kac method, we have been able to calculate the non-Born-Oppenheimer energy for hydrogen molecule for the sigma state and hydrogen molecular ion. Combining these values and the value for ionization potential for atomic hydrogen, dissociation energy and ionization potential for hydrogen molecule have been determined to be 36 113.672(3) cm inverse and 124.446.066(10) cm inverse.respectively. Our results favorably compare with other theoretical and experimental results and thus show the promise of being a nonperturbative alternative for testing fundamental physical theories.