Machine learning for a finite size correction in periodic coupled cluster theory calculations

TL;DR

This paper presents a Gaussian process regression model to accurately correct finite size errors in periodic coupled cluster calculations for metals, improving convergence to the thermodynamic limit.

Contribution

The authors develop a GPR-based finite size correction method for CCSD calculations that leverages the transition structure factor, enhancing accuracy and efficiency.

Findings

Effective correction of finite size errors demonstrated for lithium, sodium, and electron gas.

Improved convergence to thermodynamic limit compared to traditional methods.

Method reduces computational cost while maintaining accuracy.

Abstract

We introduce a straightforward Gaussian process regression (GPR) model for the transition structure factor of metal periodic coupled cluster singles and doubles (CCSD) calculations. This is inspired by the method introduced by Liao and Gr\"uneis for interpolating over the transition structure factor to obtain a finite size correction for CCSD [J. Chem. Phys. 145, 141102 (2016)], and by our own prior work using the transition structure factor to efficiently converge CCSD for metals to the thermodynamic limit [Nat. Comput. Sci. 1, 801 (2021)]. In our CCSD-FS-GPR method to correct for finite size errors, we fit the structure factor to a 1D function in the momentum transfer, $G$. We then integrate over this function by projecting it onto a k-point mesh to obtain comparisons with extrapolated results. Results are shown for lithium, sodium, and the uniform electron gas.