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Adiabatic global potential energy surfaces, for singlet and triplet states of AЈ and AЉ symmetries, were computed for an extensive grid for a total of 8469 conformations of H 3 ϩ system at full configuration interaction ab initio level and using an extended basis set that has also been optimized for excited states. An accurate ͑root-mean-square error lower than 20 cm Ϫ1) global fit to the ground-state potential is obtained using a diatomics-in-molecules approach corrected by several symmetrized three-body terms with a total of 96 linear parameters and 3 nonlinear parameters. This produces an accurate global potential which represents all aspects of ground-state H 3 ϩ including the absolute minimum, the avoided crossing and dissociation limits, satisfying the correct symmetry properties of the system. The rovibrational eigenstates have been calculated up to total angular momentum Jϭ20 using hyperspherical coordinates with symmetry adapted basis functions. The infrared spectra thus reproduced is within 1 cm Ϫ1 with respect to the experimental values for several transitions.

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A metallic isolated band in the middle of the band gap of several III-V semiconductors has been predicted as photovoltaic materials with the possibility of providing substantially enhanced efficiencies. We have investigated the electronic band structures and lattice constants of Ga n As m M and Ga n P m M with MϭSc, Ti, V, and Cr, to identify whether this isolated band is likely to exist by means of accurate calculations. For this task, we use the SIESTA program, an ab initio periodic density-functional method, fully self consistent in the localdensity approximation. Norm-conserving, nonlocal pseudopotentials and confined linear combination of atomic orbitals have been used. We have carried out a case study of Ga n As m Ti and Ga n P m Ti energy-band structure including analyses of the effect of the basis set, fine k-point mesh to ensure numerical convergence, structural parameters, and generalized gradient approximation for exchange and correlation corrections. We find the isolated intermediate band when one Ti atom replaces the position of one As ͑or P͒ atom in the crystal structure. For this kind of compound we show that the intermediate band relative position inside the band gap and width are sensitive to the dynamic relaxation of the crystal and the size of the basis set.

An analysis of the general representation of the occupation number matrix on density functional theory in conjunction with the generalized Hubbard model is presented. A central fact that will be addressed is that the total charge density cannot be broken down into simple atomic contributions. This fact means that the orbital occupations are not well defined. Different representations of the occupation number matrix, both that it conserves and that it does not conserve the number of electrons of the system, are compared. A localized basis set is used, which is suitable for large-scale electronic structure calculations based on the density functional theory. This methodology is applied to typical and well-analysed transition-metal oxide bulk systems and to Cr-doped zinc chalogenides and chalcopyrites. The bandgap, magnetic moment and detailed electronic structures are investigated and discussed with the different choices of the occupation number matrix. The results are in good agreement with previous theoretical and experimental studies.