Bayesian Calibration assisted by Markov Chain Monte Carlo in DFT+U for Iron Compunds

Density Functional Theory (DFT) revolutionized condensed matter physics by mapping the electron problem solved by the Schrodinger’s Equation to a series of mean field electron independent equations. In DFT, the most crucial approximation is from the exchange correlation functional. Although many have attempted the development of accurate functionals, they all fail to reproduce the behavior of strongly correlated materials when kinetic energy is as large as the Coulomb interaction. To solve this problem, local exchange correlation functionals are corrected by a Hubbard term. This is DFT+U which depends on two extra parameters, U (on-site coulomb interaction) and J (on-site exchange interaction). These parameters are usually fitted from experimental values or obtained by using density functional perturbation theory. Either way the quality of the parameter values can only be assessed by comparing to experimental data. In this work, we use uncertainty quantification methods to study the dependence of different experimental observables where we evaluate the relevance of errors by utilizing Bayesian Calibration facilitated by Markov Chain Monte Carlo simulation with a number of strongly correlated materials.