Optimization of an exchange-correlation density functional for water

TL;DR

This paper introduces a Bayesian-based method called DPPS to optimize density functionals, specifically applied to water, improving the accuracy of density functional theory for liquid water and related systems.

Contribution

The paper presents a novel Bayesian optimization scheme for energy functionals, applied to water, revealing limitations of current approximations and enhancing functional performance.

Findings

The optimized functional vdW-DF-w performs well for condensed water systems.

DPPS constrains functional parameters to stay close to ab initio data.

The method provides insights into DFT limitations for water.

Abstract

We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the \correct" parametrization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.