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We have performed density-functional calculations on the Ti 4 O 7 Magnéli phase. Our results provided a consistent description of the high-temperature ͑T Ն 298 K͒ phase, the intermediate-temperature ͑120 K Յ T Յ 140 K͒ phase, and the low-temperature ͑T Յ 120 K͒ phase. The established model for the electronic structure of the low-and intermediate-temperature phases of Ti 4 O 7 states that Ti 3+ -Ti 3+ pairs, bonded through nonmagnetic metal-metal bonds, form ordered bipolarons in the low-temperature phase, and that these bipolarons exist but are disordered in the intermediate-temperature phase. In this work we propose a different picture for the Ti 4 O 7 low-and intermediate-temperature electronic structure. We argue that, in the lowtemperature phase, a combination of a strong on-site Coulomb repulsion and electron-phonon coupling results in the localization of unpaired electrons in the Ti 3+ ions forming the pairs. The electrons are accommodated in specific t 2g -like orbitals for two reasons: to minimize the direct Coulomb repulsion, and to minimize the indirect interaction that results from lattice distortion. The localized electrons are antiferromagnetically coupled, producing bipolarons with zero spin. This orbital ordering results in the widening of the gap between the fully occupied and unoccupied levels. This is a bipolaronic state, but there is no bond in between the Ti 3+ forming the pairs. In the intermediate phase, a subset of the bipolarons dissociate but the electrons remain strongly localized: this state consists of a mixture of polarons and bipolarons placed in a superstructure with long-range order. This model provides a consistent explanation of the observed electric and magnetic properties of Ti 4 O 7 .

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He-atom scattering is a well established and valuable tool for investigating surface structure. The correct interpretation of the experimental data requires an accurate description of the He-surface interaction potential. A quantum-mechanical treatment of the interaction potential is presented using the current dominant methodologies for computing ground state energies (Hartree-Fock, local and hybrid-exchange density functional theory) and also a novel post-Hartree-Fock ab initio technique for periodic systems (a local implementation of Møller-Plesset perturbation theory at second order). The predicted adsorption well depth and long range behavior of the interaction are compared with that deduced from experimental data in order to assess the accuracy of the interaction potential.