Implications of the DFT+U method on polaron properties in energy materials

Abstract

To model polaronic behavior in strongly correlated transition-metal oxides with ab initio methods, one typically requires a level of theory beyond that of local density or general gradient density functional theory (DFT) approximations to account for the strongly correlated $d$-shell interactions of transition-metal oxides. In the present work, we utilize density functional theory with additional on-site Hubbard corrections $(\mathrm{DFT}+U)$ to calculate polaronic properties in two lithium ion battery cathode materials, ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ and ${\mathrm{Li}}_{x}{\mathrm{Mn}}_{2}{\mathrm{O}}_{4}$, and two photocatalytic materials, ${\mathrm{TiO}}_{2}$ and ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$. We investigate the effects of the $+U$ on-site projection on polaronic properties. Through systematic comparison with hybrid functional calculations, it is shown that $+U$ projection in these model materials can impact upon the band gap, polaronic hopping barrier, and polaronic eigenstate offset from the band edges in a nontrivial manner. These properties are shown to have varying degrees of coupling and dependence on the $+U$ projection in each example material studied, which has important implications for arriving at systematic material predictions of polaronic properties in transition-metal oxides.