Ewald summation expressions are derived for the energy, interatomic forces, pressure tensor, electric fields, and electric field gradients in a periodic computer simulation system of molecules with charges, induced dipoles, and quadrupoles. The full expressions including quadrupolar multipole interactions are given; those involving dipoles are included for completeness. The expressions apply not only to molecules with permanent multipoles, but also to systems of polarizable ions where the multipoles are induced by the interionic interactions. The expressions which allow for this generalization consider the ions to be spherically polarizable, but include the consequences of the coupling between dipolar and quadrupolar induction. The phonon dispersion curves of MgO and the structural lattice constants of Al2O3 in its corundum phase are discussed as specific examples. In simulations with a dipole- and quadrupole-polarizable interaction model, a full Ewald summation of quadrupolar interactions is shown to have a significant effect.

The structural and bonding properties of small neutral alkali halide clusters, (AX) n with nр10, A ϭLi ϩ ,Na ϩ ,K ϩ ,Rb ϩ , and XϭFϪ , are studied using the ab initio perturbed ion ͑PI͒ model and a restricted structural relaxation criterion. A trend of competition between rocksalt and hexagonal ringlike isomers is found and discussed in terms of the relative ionic sizes. The main conclusion is that an approximate value of r C /r A ϭ0.5 ͑where r C and r A are the cationic and anionic radii͒ separates the hexagonal from the rocksalt structures. The classical electrostatic part of the total energy at the equilibrium geometry is enough to explain these trends. The magic numbers in the size range studied are nϭ4, 6, and 9, and these are universal since they occur for all alkali halides and do not depend on the specific ground-state geometry. Instead those numbers allow for the formation of compact clusters. Full geometrical relaxations are considered for (LiF) n (nϭ3 -7) and (AX) 3 clusters, and the effect of Coulomb correlation is studied in a few selected cases. These two effects preserve the general conclusions achieved thus far. ͓S0163-1829͑97͒01848-1͔

Putative global minima of neutral ͑Al n ͒ and singly charged ͑Al n + and Al n − ͒ aluminum clusters with n = 13-34 have been located from first-principles density functional theory structural optimizations. The calculations include spin polarization and employ the generalized gradient approximation of Perdew, Burke, and Ernzerhof to describe exchange-correlation electronic effects. Our results show that icosahedral growth dominates the structures of aluminum clusters for n = 13-22. For n = 23-34, there is a strong competition between decahedral structures, relaxed fragments of a fcc crystalline lattice ͑some of them including stacking faults͒, and hexagonal prismatic structures. For such small cluster sizes, there is no evidence yet for a clear establishment of the fcc atomic packing prevalent in bulk aluminum. The global minimum structure for a given number of atoms depends significantly on the cluster charge for most cluster sizes. An explicit comparison is made with previous theoretical results in the range n = 13-30: for n = 19, 22, 24, 25, 26, 29, 30 we locate a lower energy structure than previously reported. Sizes n = 32, 33 are studied here for the first time by an ab initio technique.

A systematic theoretical study of stoichiometric clusters (N aI) n up to n = 15 is performed using the ab initio Perturbed-Ion (PI) model. The structures obtained are compared to previous pair potential results, and observed differences between (N aI) n clusters and previous ab initio results for other alkali halide clusters are discussed. (N aI) n clusters with n up to 15 do not show yet a marked preference for geometries which are fragments of the bulk lattice. Instead, stacks of hexagonal rings or more open structures are obtained as ground structures in clusters with n = 3, 6, 7, 9, 10, 12, 13 and 15, indicating that convergence to bulk structure is not achieved yet at this size range. Low lying isomers which are fragments of the crystal lattice exist, nevertheless, for those cases. The binding energies show that clusters with n = (4), 6, 9 and 12 molecules are specially stable. The binding energy has been decomposed in contributions which allow for an intuitive interpretation. Some electronic properties like ionization potentials and electronic energy levels are also studied.