Impact of the Electron Density on the Fixed-Node Errors in Quantum Monte Carlo

TL;DR

This paper investigates how increasing electron density, via nuclear charge, affects fixed-node errors in Diffusion Monte Carlo, revealing a linear relationship with the Hartree-Fock trial wave function.

Contribution

It provides a systematic analysis of fixed-node errors as a function of nuclear charge using different trial wave functions in quantum Monte Carlo.

Findings

Fixed node error increases linearly with nuclear charge for Hartree-Fock trial wave functions.

Comparison between Hartree-Fock and Configuration Interaction trial wave functions shows differences in fixed-node errors.

The study enhances understanding of how electron density influences quantum Monte Carlo accuracy.

Abstract

We analyze the effect of increasing charge density on the Fixed Node Errors in Diffusion Monte Carlo by comparing FN-DMC calculations of the total ground state energy on a 4 electron system done with a Hartree-Fock based trial wave function to calculations by the same method on the same system using a Configuration Interaction based trial wave function. We do this for several different values of nuclear charge, Z. The Fixed Node Error of a Hartree-Fock trial wave function for a 4 electron system increases linearly with increasing nuclear charge.