Free energy methods in Coupled Electron Ion Monte Carlo

TL;DR

This paper introduces a method to efficiently compute free energies in first-principles simulations using Quantum Monte Carlo, enabling more accurate phase diagram predictions for condensed systems like hydrogen.

Contribution

It derives a relation to estimate free energies with Reptation Quantum Monte Carlo from less demanding Variational Monte Carlo results, facilitating large-scale simulations.

Findings

Good agreement between RQMC-based transition pressures and direct observations.

The method enables accurate phase transition predictions in hydrogen.

Supports future large-scale and quantum proton simulations.

Abstract

Recent progress in simulation methodologies and in computer power allow first principle simulations of condensed systems with Born-Oppenheimer electronic energies obtained by Quantum Monte Carlo methods. Computing free energies and therefore getting a quantitative determination of phase diagrams is one step more demanding in terms of computer resources. In this paper we derive a general relation to compute the free energy of an ab-initio model with Reptation Quantum Monte Carlo (RQMC) energies from the knowledge of the free energy of the same ab-initio model in which the electronic energies are computed by the less demanding but less accurate Variational Monte Carlo (VMC) method. Moreover we devise a procedure to correct transition lines based on the use of the new relation. In order to illustrate the procedure, we consider the liquid-liquid phase transition in hydrogen, a first order transition between a lower pressure, molecular and insulating phase and a higher pressure, partially dissociated and conducting phase. We provide new results along the T = 600K isotherm across the phase transition and find good agreement between the transition pressure and specific volumes at coexistence for the model with RQMC accuracy between the prediction of our procedure and the values that can be directly inferred from the observed plateau in the pressure-volume curve along the isotherm. This work paves the way for future use of VMC in first principle simulations of high pressure hydrogen, an essential simplification when considering larger system sizes or quantum proton effects by Path Integral Monte Carlo methods.