Exploring DFT$+U$ parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling

TL;DR

This study uses Bayesian calibration with MCMC sampling to optimize Hubbard $U$ and $J$ parameters in DFT+$U$ for iron-based compounds, improving property predictions across different functionals.

Contribution

It introduces a Bayesian MCMC approach to systematically calibrate Hubbard parameters, enhancing the predictive accuracy of DFT+$U$ for correlated materials.

Findings

PBE functional shows the most transferable $U$ and $J$ parameters.

LDA requires the largest $U$ correction.

PBE predicts lattice parameters well without Hubbard correction.

Abstract

Density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard corrections to treat strongly correlated electronic states. Unfortunately, the exact values of the Hubbard $U$ and $J$ parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the $U$ and $J$ parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest $U$ correction. PBE has the smallest standard deviation and its $U$ and $J$ parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.