Stable and transferable exchange-correlation potentials via machine-learned density-independent mapping.

Abstract

We present a machine-learning framework, density-independent mapping for exchange-correlation, for incorporating XC effects into density functional theory via a density-independent mapping from the external potential to the XC potential. By predicting the ground-state XC potential in a one-shot manner and holding it fixed throughout the self-consistent field (SCF) procedure, the approach entirely eliminates the need to evaluate the XC potential on the iteratively updated electron density, thereby enhancing numerical stability and efficiency. The model is implemented using kernel ridge regression and trained on a set of small neutral closed-shell molecular systems, representative of common chemical bonding motifs, achieving the predictive accuracy of hybrid functionals-with energy errors on the order of 10-3 kcal/mol-while bypassing expensive, iterative density-dependent XC evaluations during SCF. Further validation through infrared spectral predictions, molecular dynamics simulations, and structural perturbation tests demonstrates robust performance and reasonable transferability. This work establishes that machine-learned density-independent mapping represents a practical pathway for designing stable and transferable XC potentials.