GGA+Udescription of lithium intercalation into anataseTiO2

Abstract

We have used density-functional theory ͓generalized gradient approximation ͑GGA͔͒ to study lithium intercalation at low concentration into anatase TiO 2 . To describe the defect states produced by Li doping a Hubbard "+U" correction is applied to the Ti d states ͑GGA+ U͒. Uncorrected GGA calculations predict Li x TiO 2 to be metallic with the excess charge distributed over all Ti sites, whereas 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 Ti 3d site neighboring the intercalated lithium with a magnetization of 1 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 ͓001͔ direction. This challenges the previous interpretation of neutron diffraction data that there exist two potential energy minima separated by 1.6 Å along the ͓001͔ direction within each octahedron. Nudged elastic band calculations give barriers to interoctahedral diffusion of ϳ0.6 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 GGA+ U, compared to the experimental value of ϳ1.9 eV. Li-electron binding energies have also been calculated. The ͓Li i• -Ti Ti Ј ͔ complex has a binding energy of 56 meV, and a second electron is predicted to be bound to give ͓Li i• -2Ti Ti Ј ͔ 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.

Excess Electrons and Interstitial Li Atoms in TiO2 Anatase: Properties of the (101) Interface

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Insertion of Mono- vs. Bi- vs. Trivalent Atoms in Prospective Active Electrode Materials for Electrochemical Batteries: An ab Initio Perspective

“…Our study used a localized basis set which was tuned to reproduce the cohesive energies of the components (i.e., of TiO 2 , Li, Na, and Mg) as described in Section 2.1.1. This resulted in good agreement with previous plane wave calculations of the Li-TiO 2 system [114,115]. It also resulted in the formation of gap states which were Ti d states, as expected, see Figure 9 (this is what is often referred to as the Ti 3+ , see below about charge and oxidation states).…”

“…It also resulted in the formation of gap states which were Ti d states, as expected, see Figure 9 (this is what is often referred to as the Ti 3+ , see below about charge and oxidation states). Previously it had been shown (in plane wave calculations) that either a hybrid functional or a Hubbard U correction was needed to reproduce such states, or else the electron donated by Li would occupy a state in the conduction band [114,115]. That we were able to obtain the correct electronic structure at the GGA level at the least shows that it can be done effectively; it also poses a question of whether the previously reported inability of the GGA approximation to model the gap states has to do not only with the limitation of the GGA approximation itself but also with the use of specific computational setups.…”

Ultrafast sodium storage in anatase TiO2 nanoparticles embedded on carbon nanotubes

“…Indeed, a scenario of mix-valence states can help in significantly improving the electronic conductivity of TiO 2 [41][42][43][44]. The simplest way to achieve this is through the synthesis of oxygen-deficient TiO 2 À δ , in which trivalent Ti is partially produced.…”