First Principles Hartree–Fock Description of Lithium Insertion in Oxides: I. The End Members TiO2and LiTiO2of the System LixTiO2

First principles periodic Hartree–Fock calculations are reported for theP42/mnm(rutile),I41/amd(anatase),Pbca (brookite),Pnma(ramsdellite),Pcbn(colombite),Fd m(spinel), andImma(orthorhombic) polymorphs of TiO2, from which the predicted order of stability is The calculated difference in energy between the rutile and anatase structures is 0.02–0.06 eV, in good agreement with a recent local density approximation (LDA) estimate of 0.033 eV and an experiment enthalpy difference of 0.05 eV. The corresponding Hartree–Fock and LDA differences for the brookite structure are 0.06 and 0.058 eV, respectively. The calculated volumes, which are based on isotropic volume-optimized Hartree–Fock energies, are also in good agreement with recent LDA calculations and with experiment. Spin-unrestricted calculations are reported for theFm m,Imma,Pnma, andP42/mmmof LiTiO2, where the stability is in the order The only reported phase for LiTiO2isFm m, for which the calculated volume is in good agreement with experiment. From the relative stabilities of TiO2and LiTiO2, the relative lithium insertion potentials corresponding to TiO2 LiTiO2are deduced, with a maximum variation of 1.6 eV for the different polymorphic routes. The maximum voltage predicted is that for theImmaroute which is ~1 eV larger than that forPnma. Direct comparisons with the calculated energy forC2/mLi0.5MnO2 LiMnO2lead to an estimate of the voltage forImmaTiO2 LiTiO2of ~1.3 eV, which is ~2.5 eVanodicto the Mn system. The corresponding values for thePnmapolymorphic route are ~3 and ~3.5 eV, respectively. Mulliken population analyses indicate that lithium is completely ionized in LiTiO2and that the charge transfer is predominantly to the oxygen sublattice. There is a rehybridization of the titanium valence orbitals leading to a slight increase in the 3dpopulation and strong localization of spin density at the titanium sites with local moments of ~1B.