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We have calculated the average magnetic moments per atom $\overline{\ensuremath{\mu}}$ of nickel clusters $({\mathrm{Ni}}_{N})$ as a function of cluster size in the range $5l~Nl~60$. The cluster geometries have been taken from molecular-dynamics simulations with a semiempirical many-body potential for $Nl~20$, and for $Ng20$ the same potential was used for a steepest-descent relaxation of icosahedral structures. The spin-polarized electronic structure has been calculated for those optimized geometries with a self-consistent tight-binding method considering the $3d$, $4s$, and $4p$ valence electrons. The results are discussed in comparison with recent experimental data and other theoretical calculations. The theory explains perfectly the magnetic moments up to $N\ensuremath{\approx}16$ and the decreasing tendency of $\overline{\ensuremath{\mu}}$ with cluster size. With respect to the oscillations of the measured magnetic moment for larger $N$, the theory gives an explanation for the minima, which appear to be associated with an icosahedral growth pattern. The observed maxima are more difficult to reproduce and we discuss some plausible alternatives.

The adsorption of molecular hydrogen on a metal-organic framework (MOF) material, MOF-5, has been studied using the density-functional formalism. The calculated potential-energy surface shows that there are two main adsorption regions: both near the ${\text{OZn}}_{4}$ oxide cores at the vertices of the cubic skeleton of MOF-5. The adsorption energies in those regions are between 100 and 130 meV/molecule. Those adsorption regions have the shape of long, wide, and deep connected trenches and passage of the molecule between regions needs to surpass small barriers of 30--50 meV. The shape of these regions, and not only the presence of metal atoms, explains the large storage capacity measured for MOF-5. The elongated shape explains why some authors have previously identified only one type of adsorption site, associated to the Zn oxide core, and others identified two or three sites. One should consider adsorption regions rather than adsorption sites. A third region of adsorption is near the benzenic rings of the MOF-5. We have also analyzed the possibility of dissociative chemisorption. The chemisorption energy with respect to two separated H atoms is 1.33 eV/H atom; but, since dissociating the free molecule costs 4.75 eV, the physisorbed ${\text{H}}_{2}$ molecule is more stable than the dissociated chemisorbed state by about 2 eV. Dissociation of the adsorbed molecule costs less energy, but the dissociation barrier is still high.

The dissociation of ${\mathrm{Na}}_{\mathit{N}}^{+}$ clusters (N\ensuremath{\le}37) has been studied using two cluster models and two different approximations to the exchange and correlation effects. First we show that the jellium model with the usual local-density approximation to exchange and correlation leads to dissociations mostly involving ${\mathrm{Na}}_{2}$ and ${\mathrm{Na}}_{8}$. This prediction does not agree with recent experimental results, which indicate that most ${\mathrm{Na}}_{\mathit{N}}^{+}$ clusters dissociate emitting a neutral monomer. The explicit introduction of the ions eliminates many dissociations involving ${\mathrm{Na}}_{2}$ in favor of the channel involving a Na monomer. Furthermore, a nonlocal description of exchange and correlation lowers the stability of ${\mathrm{Na}}_{8}$ in favor, again, of dissociation through the monomer channel. In summary, the combined effect of these two improvements leads to a satisfactory description of the dissociation of ${\mathrm{Na}}_{\mathit{N}}^{+}$ in comparison with experiment.

Ab initio density-functional molecular dynamics simulations were performed in order to study the melting behavior of the NaSn alloy. This alloy exhibits a phase transition at 756 K to a high-temperature solid showing rotational disorder, which has been described as an assembly of rapidly rotating Sn 4 tetrahedral clusters surrounded by mobile Na cations. Various simulation temperatures and volumes were considered in order to distinguish the features of both solid β-NaSn and plastic α-NaSn phases. The results show that the ability of Na cations to diffuse is strongly linked to the deformation of Sn 4 tetrahedra. In addition, the α-NaSn phase seems to be characterized by a sizable degree of structural disorder, with frequent breaking of the Sn 4 tetrahedral units. The influence of the volume of the simulation cell on the dynamical behavior of the alloy was found to be very important, with increasing disorder as the volume was reduced. Finally, strong correlations between structural and electronic properties were found, with increased disorder leading to more metallic behavior.