Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers

TL;DR

This paper introduces a NOON-based measure to estimate and understand the bias in fixed-node diffusion Monte Carlo calculations caused by single Slater determinant trial states, providing insights into bias cancellation.

Contribution

It proposes a novel NOON-based metric to evaluate the appropriateness of SD trial states and predict bias in FN-DMC energy differences.

Findings

NOON-based measures reflect bias magnitude and sign

The measure provides insights into bias cancellation mechanisms

Application to small complexes and bond breaking shows effectiveness

Abstract

Accuracy of the fixed-node diffusion Monte Carlo (FN-DMC) depends on the node location of the best available trial state $\Psi_T$. The practical FN-DMC approaches available for large systems rely on compact yet effective $\Psi_T$s containing explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FN-DMC energy differences. It remains a challenge, how to estimate inequivalency or appropriateness of SDs. Here we use the differences of a measure based on Euclidean distance between the natural orbital occupation number (NOON) vector of the Slater determinant (SD) from the exact solution in the NOON vector space, that can be viewed as a measure of SD inequivalency and a measure of the expected degree of nondynamic-correlation-related bias in FN-DMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si$_2$ vs. N$_2$. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing new insights to the nature of bias cancellation in SD FN-DMC energy differences.