Diffusion of Li and Na ions in TiO 2 , anatase, has been studied using theoretical (quantum chemical ab initio periodic Hartree-Fock and a modified semiempirical INDO) as well as electrochemical (chronocoloumetry) methods. On the basis of the theoretical calculations, the geometry of equilibrium and transition states for the impurities as well as the crystalline framework are analyzed and discussed. The calculated activation energies for Li + and Na + diffusion were found to be only slightly higher than 0.5 eV by both theoretical methods. The agreement of either theoretical method with the electrochemical experiments, 0.60 and 0.52 eV for Li + and Na + , respectively, is also remarkably good.
Theoretical MethodAb Initio Periodic Hartree-Fock Calculations. The structures of the alkali-doped crystal and the ion diffusion path were investigated by means of the ab initio quantum-chemical program Crystal95. 6 Using this program it is possible to treat not only molecules or clusters but, in particular, crystalline solids at an ab initio level of theory, since the Hartree-Fock one-electron eq are solved subject to periodic boundary conditions. 7 Whereas semiempirical and density-functional methods early on were applied to the solid state, especially in the discipline of solid state physics, ab initio calculations were not applied in a larger scale until the late 1980s and increasingly in the 1990s. Some examples include Al 2O3, 8 Li2O, Na2O and K2O, 9 LiOH‚H2O, 10 the TiO2 rutile 11,12 and anatase 13 phases, C-doped Si, 14 Li-doped NiO, 15 and bulk WO3. 16