Adaptive hybrid density functionals

TL;DR

This paper introduces an adaptive hybrid density functional, aPBE0, which dynamically adjusts the exact exchange ratio for any chemical compound using data-efficient quantum machine learning, significantly improving accuracy in quantum chemistry calculations.

Contribution

The paper presents a novel adaptive hybrid density functional that optimizes exchange contributions on the fly with machine learning, enhancing accuracy over traditional fixed-parameter functionals.

Findings

aPBE0 improves atomization energy accuracy and cures the spin gap problem.

Enhanced energetics, electron densities, and HOMO-LUMO gaps in organic molecules.

Revision of QM9 dataset (revQM9) with superior quality metrics.

Abstract

Exact exchange contributions are known to crucially affect electronic states, which in turn govern covalent bond formation and breaking in chemical species. Empirically averaging the exact exchange admixture over compositional degrees of freedom, hybrid density functional approximations have been widely successful, yet have fallen short to reach high level quantum chemistry accuracy, primarily due to delocalization errors. We propose to `adaptify` hybrid functionals by generating optimal admixture ratios of exact exchange on the fly, i.e. specifically for any chemical compound, using extremely data efficient quantum machine learning models that carry negligible overhead. The adaptive Perdew-Burke-Ernzerhof based hybrid density functional (aPBE0) is shown to yield atomization energies with sufficient accuracy to effectively cure the infamous spin gap problem in open shell systems, such as carbenes. aPBE0 further improves energetics, electron densities, and HOMO-LUMO gaps in organic molecules drawn from the QM9 and QM7b data set. Obtained with aPBE0 in a large basis, we present a revision of the entire QM9 data set (revQM9) with an estimated quality vastly superior to the original containing on average, stronger covalent binding, larger band-gaps, more localized electron densities, and larger dipole-moments. While aPBE0 is applicable in the equilibrium regime, outstanding limitations include covalent bond dissociation when going beyond the Coulson-Fisher point.