Fixed-node errors in real space quantum Monte Carlo at high densities: closed-shell atomic correlation energies

TL;DR

This paper investigates fixed-node errors in real space quantum Monte Carlo calculations of heavy noble gas atoms, including superheavy elements, revealing how these errors vary with atomic number and electron density.

Contribution

It provides a quantitative analysis of fixed-node errors across a range of noble gas atoms, including superheavy elements, and estimates the asymptotic behavior of atomic correlation energies.

Findings

Fixed-node errors decrease mildly with increasing atomic number.

Fixed-node biases increase with electron density.

Estimated linear term in asymptotic correlation energy expansion.

Abstract

We consider non-relativistic electron correlation energies of heavy noble gas atoms including the superheavy element Og. The corresponding data enables us to quantify fixed-node errors in real space quantum Monte Carlo methods as a function of the atomic number $Z$. We confirm that single-reference trial function nodes lead to an overall trend of mild decrease in recovered correlation energy with the increasing $Z$. This agrees with our previous study that has shown increasing fixed-node biases with the increasing electron density. We also estimate the value of the linear term in the asymptotic expansion of the atomic correlation energy.