Data-Driven Complete Basis Set Limit Estimates from a Minimal Auxiliary Basis

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 toward the complete basis set (CBS) limit. Common extrapolation methods require several intermediate-quality calculations to afford an estimate of the CBS energy. We propose 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 Δ-machine learning and 40× faster than triple-ζ single-point calculations. The spatial and alchemical gradients from minimal basis and minimal CABS are more accurate than double-ζ (DZ) calculations. 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 10×–50× times faster on moderate compute resources, thereby enabling a data-driven approach toward the mean-field CBS, combining physical baselines capturing leading-order effects with data-efficient machine learning models.