First Principles Calculation of Formation Energy for Nd-Fe-B compounds

The compound Nd$_{2}$Fe$_{14}$B is widely used in manufacturing permanent magnets. This interest has driven much of the research on the Nd-Fe-B system including the computational calculation of phase diagrams (CALPHAD). Formation energy of Nd-Fe-B compounds is required for CALPHAD input, and are calculated using Density Functional Theory (DFT). Hubbard U correction is used to account for the localized nature of Nd 4f electrons. Comparison between 2 methods of choosing Hubbard U value is drawn: a simplified implementation of DFT+U using effective Hubbard U value (U$_{eff}$ = U-J) and from constrained random phase approximation (cRPA) for bulk Nd. It is shown that the former method is insufficient to accurately calculate formation energy of several Nd-Fe-B compounds. Comparison is also drawn between 2 types of pseudopotentials, norm-conserving and ultrasoft pseudopotentials.