Bayesian Calibration assisted by Markov Chain Monte Carlo sampling of parameter space of J and U values in DFT+U: Applications for Fe, Mn and Cu based compounds*

Density Functional Theory (DFT) fails to accurately determine the properties of strongly correlated materials (SCMs). One way to solve this problem is to add an additional Hubbard-like term (DFT+U). The strength of the on-site Coulomb and the on-site exchange interactions can be described by U and J parameters, respectively. At present, there exists no general method to evaluate these parameters for a given SCM system. These parameters are often determined using semi-empirical methods. We investigate the correlation between these parameters and the electronic density of SCMs using Bayesian Calibration assisted by Markov Chain Monte Carlo (MCMC) sampling of (U, J) parameter space for various Fe, Mn and Cu based SCMs. We also perform a comparative study of the available experimental data with the results of our theoretical calculations obtained using three different exchange correlation functionals, namely PBE, PBEsol and LDA, implemented in the VASP code. After sampling the (U, J) parameter space, we use the MCMC model to introduce an electronic density dependence of J and U values. This model can be further generalized to predict correct properties of SCMs without a need of tuning J and U values semi-empirically.