Data-driven complete basis set limit estimates from a minimal auxiliary basis

TL;DR

This paper introduces a data-driven method using Kernel-Ridge-Regression with minimal auxiliary basis sets to efficiently estimate the complete basis set limit energy from a single quantum chemistry calculation.

Contribution

It presents a novel approach combining physical baselines with machine learning to accurately estimate CBS energies from minimal basis calculations.

Findings

KRR with Chebyshev polynomial approximation improves efficiency

Single calculation estimates CBS energy accurately

Method outperforms traditional extrapolation techniques

Abstract

Quantum chemistry calculations are often performed using atom-centered basis sets which are chosen to balance accuracy and cost. While they are systematically improvable, the total energy converges slowly with basis set size towards the complete basis set (CBS) limit. Common extrapolation methods require several intermediate-quality calculations to afford an estimate of the CBS energy. We propose combining a pairwise interaction model with a minimal complementary auxiliary basis set (CABS) baseline to estimate the CBS energy from a single quantum chemistry calculation in a minimal basis set via Kernel-Ridge-Regression (KRR), which is more efficient than both direct and $\Delta$-machine learning. We show that KRR on standard molecular representations can be improved by approximating atom-wise local kernels using Chebyshev polynomials which allows us to train KRR models efficiently on moderate compute resources, further enabling a data-driven approach towards CBS combining physical baselines capturing leading order effects with data-efficient machine learning models.