Bayesian Error Estimation in Density Functional Theory

TL;DR

This paper introduces a Bayesian-based method to estimate errors in Density Functional Theory calculations by creating ensembles of functionals and comparing them with experimental data, providing practical error bars for various molecular and solid-state properties.

Contribution

The paper presents a novel Bayesian approach to quantify uncertainties in DFT calculations by constructing ensembles of exchange-correlation functionals calibrated against experimental data.

Findings

Error estimates can vary significantly across different systems.

The method provides error bars that align with existing empirical experience.

Error fluctuations are useful for assessing the reliability of DFT predictions.

Abstract

We present a practical scheme for performing error estimates for Density Functional Theory calculations. The approach which is based on ideas from Bayesian statistics involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities like binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.