The Path Integral Monte Carlo Calculation of Electronic Forces

TL;DR

This paper introduces a Path Integral Monte Carlo method to calculate electronic forces, incorporating correlations and thermal effects, and applies it to molecular bonds, reaction barriers, and impurity interactions in metals.

Contribution

The paper presents a novel PIMC-based approach for evaluating electronic forces that naturally includes correlations and thermal effects, with a restricted approach for fermions to avoid the sign problem.

Findings

Accurate bond length for H₂ at low temperature.

Computed reaction barrier for H+H₂ → H₂+H.

Analyzed proton-proton interactions in electron gases at different densities and temperatures.

Abstract

We describe a method to evaluate electronic forces by Path Integral Monte Carlo (PIMC). Electronic correlations, as well as thermal effects, are included naturally in this method. For fermions, a restricted approach is used to avoid the ``sign'' problem. The PIMC force estimator is local and has a finite variance. We applied this method to determine the bond length of H$_2$ and the chemical reaction barrier of H+H$_2\longrightarrow $H$_2$+H. At low temperature, good agreement is obtained with ground state calculations. We studied the proton-proton interaction in an electron gas as a simple model for hydrogen impurities in metals. We calculated the force between the two protons at two electronic densities corresponding to Na ($r_s=3.93$) and Al ($r_s=2.07$) using a supercell with 38 electrons. The result is compared to previous calculations. We also studied the effect of temperature on the proton-proton interaction. At very high temperature, our result agrees with the Debye screening of electrons. As temperature decreases, the Debye theory fails both because of the strong degeneracy of electrons and most importantly, the formation of electronic bound states around the protons.