Vibrational frequencies of sodium clusters

The vibrational frequencies of NaN clusters (2 ≤ N ≤ 72) are calculated by direct diagonalization of the dynamical matrix. Density functional theory with a spherically averaged pseudopotential is used to compute the total energy. The geometry is optimized by the simulated annealing technique. Contributions to the Hessian matrix due to electron relaxation following the ionic displacements are calculated in linear response theory. The frequencies are in the range 0-220 cm-1 and the electron relaxation strongly modifies those of the modes dominated by radial oscillations, particularly the breathing mode frequencies that are proportional to N-1/3. The filling of atomic shells produces a stepwise behavior of the highest frequencies. The giant dipole resonance energies are obtained as a byproduct of the calculation. 28 refs., 9 figs