VIBRATIONAL FREQUENCIES OF SODIUM CLUSTERS

The vibrational frequencies of Na-N clusters (2 less than or equal to N less than or equal to 72) are calculated by direct diagonalization o f the dynamical matrix. Density functional theory with a spherically a veraged pseudopotential is used to compute the total energy. The geome try is optimized by the simulated annealing technique. Contributions t o the Hessian matrix due to electron relaxation following the ionic di splacements are calculated in linear response theory. The frequencies are in the range 0-220 cm(-1) and the electron relaxation strongly mod ifies those of the modes dominated by radial oscillations, particularl y the breathing mode frequencies that are proportional to N--1/3. The filling of atomic shells produces a stepwise behavior of the highest f requencies. The giant dipole resonance energies are obtained as a bypr oduct of the calculation. (C) 1995 John Wiley & Sons, Inc.