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

Density-functional theory has gained popularity because of its ability to predict properties of a large group of materials a priori. However, this triumphant ability stops short for strongly correlated materials where the non-universality of the exchange-correlation functionals becomes substantial. One solution to this problem is to introduce a Hubbard correction for the treatment of the strongly correlated electronic states at the mean-field level, used in the so-called DFT+U approaches. Unfortunately, this U correction turns the theory into a semiempirical method as the exact values of the correction parameters U and J are unknown and their parameterization can vary considerably from one material to another composed of the same strongly correlated atoms. In this study, we select a group of iron-based compounds to explore the space of the U and J correction parameters that simultaneously improve the prediction results for all the studied materials. We perform this exploration using a Bayesian calibration assisted by Markov chain Monte Carlo sampling to determine the distribution of the correction parameters. The following are the main findings of this study: LDA requires a significantly larger U parameter compared with the GGA functionals. The U and J obtained for PBE are the most transferable to other iron-based compounds. The Dudarev approximation can result in a closer prediction to the Lichtenstein approach in PBE compared to that of in LDA and PBEsol. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction for iron-based compounds.