Yukawa potential for realistic prediction of Hubbard and Hund interaction parameters for transition metals

The generalized Hubbard model is an important theoretical model for modeling strongly correlated materials. To be able to theoretically predict the properties of the materials, the model requires Hubbard’s $U$ and Hund’s $J$ parameter that represent the on-site Coulomb and exchange interaction, respectively. For bare Coulomb interactions, the analytic expression of $U$ and $J$ are analytically described by Racah’s $A,B,C$ parameters. However, the values of $U$ are too large for transition-metal-based materials. To obtain more accurate values for realistic materials, we employ a Yukawa-type screened Coulomb interaction, characterized by screening constant $\lambda$. We characterize $\lambda$ for transition metals. The modified $A,B,C$ parameters give a more realistic $U$ and $J$ values.