Ionic vibrational breathing mode of metallic clusters

The energy of the vibrational mode with spherical symmetry, in which the ionic cores oscillate in the radial direction around the equilibrium geometry (ionic breathing mode) is calculated for trivalent (Al_N, 2≤N≤50) and monovalent (Na_N, 2≤N≤73; Cs_N, 2≤N≤74) metallic clusters. The ground-state total energy is calculated using density functional theory, with a spherically averaged pseudopotential to describe the ion–electron interaction and optimizing the geometry by the simulated annealing technique. The energy of the ionic mode is calculated by diagonalization of the dynamical matrix including the electronic relaxation in the linear response approximation. The compressibility and bulk modulus of the metallic cluster are obtained from the energies of the monopole oscillations. These energies present a linear behavior on the inverse of the cluster radius, which is analyzed using a semiclassical liquid drop mass formula for the total energy of the clusters and a scaling model. The values of the vibrational frequencies present electronic shell closing effects for the three metals.©1997 John Wiley & Sons, Inc.