The electronic structure of atomic clusters is studied as a function of the geometrical parameters and number of atoms N in the clusters. Self-consistent electron wave functions and energies are calculated for the clusters with closed and open shells for N ranging from 4 to 40 and for the various radii of positive cluster cores. These calculations are done both for the homogeneous and inhomogeneous jellium models of the cluster core. The equilibrium values of jellium core radius have been obtained using ab initio Hartree-Fock calculations for the valence electrons. The importance of the role of nonlocal exchange interaction in the creation of the equilibrium cluster structure is also shown. An adiabatic type of collective vibration mode is predicted. Vibrational freuqencies and amplitudes are calculated for the ‘‘magic’’ number clusters. The influence of the geometrical parameters on the physical properties of clusters is discussed.

• Received 26 October 1993

DOI:https://doi.org/10.1103/PhysRevA.50.1459