The two polymorphs of TiO2, rutile and anatase, have been investigated at the ab initio level using different Hamiltonians with all-electron Gaussian and projector augmented plane wave basis sets. Their equilibrium lattice parameters, relative stabilities, binding energies, and band structures have been evaluated. The calculations have been performed at the Hartree-Fock, density functional theory (DFT), and hybrid (B3LYP and PBE0) levels. As regards DFT, the local density and generalized gradient (PBE) approximations have been used. Our results show an excellent agreement with the experimental band structures and binding energies for the B3LYP and PBE0 functionals, while the best structural descriptions are obtained at the PBE0 level. However, no matter which Hamiltonian and method are used, anatase is found more stable than rutile, in contrast with recent experimental reports, although the relative stabilities of the two phases are very close to each other. Nevertheless, based on the overall results, the hybrid PBE0 functional appears as a good compromise to obtain an accurate description of both structural and electronic properties of solids.

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We use state of the art ab initio calculations to obtain the diffusion properties of He in tungsten. The calculated migration energy of He is very low, around 0.06 eV. This value is much lower than the experimental field-ion microscopy results which lead to a migration energy of the order of 0.24-0.32 eV. The reason for this discrepancy is the high propensity for He to form He-He clusters characterized by a very large binding energy of the order of 1 eV. Such a large binding energy indicates that He atoms can be trapped by other He atoms and can explain the formation of He blisters close to the surface of He implanted tungsten.