GGA+Udescription of lithium intercalation into anataseTiO2

Abstract

We have used density-functional theory [generalized gradient approximation (GGA)] to study lithium intercalation at low concentration into anatase ${\text{TiO}}_{2}$. To describe the defect states produced by Li doping a Hubbard ``$+U$'' correction is applied to the $\text{Ti}\text{ }d$ states $(\text{GGA}+U)$. Uncorrected GGA calculations predict ${\text{Li}}_{x}{\text{TiO}}_{2}$ to be metallic with the excess charge distributed over all Ti sites, whereas $\text{GGA}+U$ predicts a defect state 0.96 eV below the conduction band, in agreement with experimental photoelectron spectra. This occupied defect state corresponds to charge strongly localized at a single $\text{Ti}\text{ }3d$ site neighboring the intercalated lithium with a magnetization of $1\text{ }\ensuremath{\mu}\text{B}$. This polaronic state produces a redshifted optical absorption spectrum, which is compared to those for the native O-vacancy and Ti-interstitial defects. The strong localization of charge at a single Ti center lowers the symmetry of the interstitial geometry relative to that predicted by GGA. The intercalated lithium sits close to the center of the octahedral site, occupying a single potential energy minimum with respect to displacement along the [001] direction. This challenges the previous interpretation of neutron diffraction data that there exist two potential energy minima separated by $1.6\text{ }\text{\AA{}}$ along the [001] direction within each octahedron. Nudged elastic band calculations give barriers to interoctahedral diffusion of $\ensuremath{\sim}0.6\text{ }\text{eV}$, in good agreement with experimental data. These barrier heights are found to depend only weakly on the position of the donated electron. The intercalation energy is 2.14 eV with GGA and 1.88 eV with $\text{GGA}+U$, compared to the experimental value of $\ensuremath{\sim}1.9\text{ }\text{eV}$. Li-electron binding energies have also been calculated. The $[{\text{Li}}_{\text{i}}^{\ifmmode\bullet\else\textbullet\fi{}}{\text{-Ti}}_{\text{Ti}}^{\ensuremath{'}}]$ complex has a binding energy of 56 meV, and a second electron is predicted to be bound to give $[{\text{Li}}_{\text{i}}^{\ifmmode\bullet\else\textbullet\fi{}}\text{\ensuremath{-}}2{\text{Ti}}_{\text{Ti}}^{\ensuremath{'}}]$ with a stabilization energy of 30 meV, indicating that intercalated lithium will weakly trap excess electrons produced during photoillumination or introduced by additional $n$-type doping.