Phonon Frequencies and Cohesive Energies of Copper, Silver, and Gold

The static dielectric functions of copper, silver, and gold are investigated in the noninteracting band scheme using the exchange-correlation corrections due to Singwi et al. in the $s-s$ part of the dielectric function. These dielectric functions are further used in conjunction with Harrison's model potential to investigate the electronic contribution to the phonon frequencies. The direct ion-ion-interaction contribution to phonon frequencies is evaluated by Ewald's method and the contribution due to exchange-overlap potential is calculated using an overlap potential calculated by Moriarty. The calculated phonon frequencies for copper and silver along the three principal symmetry directions [100], [110], and [111] are in good agreement with experimental values except for transverse branches in the [100] and [110] directions for copper. The results for gold are compared with the calculations of Moriarty. The effective ion-ion potential and form factors for all these metals are also calculated. The calculated cohesive energies of these metals are in poor agreement with the experimental values while good agreement is obtained with the calculations of Moriarty for silver and gold.