# Path Integral Monte Carlo Simulation on Molecular Systems with Multiple Electronic Degrees of Freedom

## TL;DR

This paper introduces a new method for simulating molecular systems with multiple electronic states using path integral Monte Carlo, validated on simple models and real molecules.

## Contribution

A novel path integral Monte Carlo scheme for molecular systems with multiple electronic states is proposed and validated.

## Key findings

- The method can reproduce exact results for a model system with nonadiabatic couplings.
- Thermodynamic equilibrium properties of H2 and C2 are accurately computed.
- An open-source implementation of the algorithm is provided.

## Abstract

We present an imaginary time path-integral formalism
for molecular
systems including nuclear and electronic degrees of freedom based
on the previous work of [SchmidtJ. R.; TullyJ. C.J. Chem. Phys.2007, 127, 09410317824728
10.1063/1.2757170]. To sample the resulting path integral expression efficiently,
a path integral Monte Carlo scheme is proposed, allowing the computation
of finite temperature equilibrium properties of molecular systems
including multiple low-lying electronic states directly from ab initio
potential energy surfaces. Finally, we show how this generalized approach
in combination with the Monte Carlo scheme can reproduce exact results
for a simple model system including nonadiabatic couplings as well
as thermodynamic equilibrium properties of H2 and C2. Our implementation of the algorithm is available as an open-source
code.