A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

TL;DR

This study uses diffusion Monte Carlo to analyze the challenges of biases in calculations involving effective core potentials, demonstrating solutions to improve accuracy for molecules like BeH2 and C2H2.

Contribution

It identifies key issues in fixed-node DMC with ECPs and proposes practical upgrades to enhance computational accuracy and reliability.

Findings

Achieved chemical accuracy with improved DMC methods.

Addressed bias issues in fixed-node DMC with ECPs.

Validated results against independent correlated calculations.

Abstract

We study beryllium dihydride (BeH$_2$) and acetylene (C$_2$H$_2$) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the fixed-node DMC calculations that might appear with the use of effective core potentials (ECPs) or other nonlocal operators. This is especially relevant for the recently introduced correlation consistent ECPs (ccECPs) for $2s2p$ elements. Corresponding ccECPs exhibit deeper potential functions due to higher fidelity to all-electron counterparts, which could lead to larger local energy fluctuations. We point out that the difficulties stem from issues that are straightforward to address by upgrades of basis sets, use of T-moves for nonlocal terms, inclusion of a few configurations into the trial function and similar. The resulting accuracy corresponds to the ccECP target (chemical accuracy) and it is in consistent agreement with independent correlated calculations. Further possibilities for upgrading the reliability of the DMC algorithm and considerations for better adapted and more robust Jastrow factors are discussed as well.