Equilibrium geometries and electronic-structure properties have been obtained for cationic, anionic, and neutral Al n Na and Al n Na 2 (nϭ1 -12) clusters within the density-functional theory using the generalized gradient approximation for the exchange-correlation potential. The resulting geometries show that the sodium atom prefers to be on the periphery and does not get trapped. The stability has been investigated by analyzing the binding energy, the dissociation energy, and the second difference in energy. The results indicate that for neutral clusters, Al 4 Na and Al 7 Na are stable. Considerable enhanced stability is also seen for clusters. The stability of these clusters cannot be explained on the basis of a simple jellium model. The calculated vertical ionization potentials are in good agreement with their experimental counterparts. No consistent signature of a monovalent nature for Al is observed in these systems. The addition of sodium atoms is found to quench the weak magnetic moment of pure Al clusters and all Al n Na 2 clusters are found to be nonmagnetic.

We have investigated the ground-state geometries of Li n Be and Li n Mg (nϭ1-12) clusters using ab initio molecular dynamics. These divalent impurities Be and Mg induce different geometries and follow a different growth path for nϾ5. Li n Mg clusters are significantly different from the host geometries while Li n Be clusters can be approximately viewed as Be occupying an interstitial site in the host. Our results indicate that Be gets trapped inside the Li cage, while Mg remains on the surface of the cluster. Mg-induced geometries become three-dimensional earlier at nϭ4 as compared to the Be system. In spite of a distinct arrangement of atoms in both cases the character of the wave functions in the d manifold is remarkably similar. In both cases an eight valence electron system has been found to be the most stable, in conformity with the spherical jellium model.

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An algorithm based on local scaling transformations for electronic structure calculations that scales linearly with the size of the system is presented. The key feature of the method is the absence of the orthogonalization step during iterative minimization. We illustrate the feasibility and potential of the method by applying it to total energy calculations for a variety of small clusters, viz., Na 2 , Na 7 Al, Na 20 , Si 4 , and Al 13 . The method is easily parallelizable and therefore has the potential to deal with large real life systems.

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