Finite-size effects in ionization potentials and electron affinities of metal clusters

Experimental ionization potentials (I) and electron affinities (A) of metal clusters MeN are compiled for a variety of systems and their size dependence is analyzed. In the theoretical part, we perform semiclassical density variational calculations using the spherical jellium model and the local density approximation. For alkali systems and, to some extent, also for some nonalkali systems, the calculated values of I and A reproduce very well the average size dependence of the measured quantities, if their common bulk limit W is adjusted to the experimental bulk work function. This holds even for rather small systems where I and A are no longer linear in N−1/3. We discuss the extent to which classical models for the energetics of charged metal spheres can account for the correct size dependence in the large-cluster limit. We point out that the deviation of the slope parameters α and β in the asymptotic expressions I∼W+α(e2/rs)N−1/3, A∼W−β(e2/rs)N−1/3 from the values (1)/(2) , which depends on the material via the Wigner–Seitz parameter rs, can be entirely accounted for by quantum-mechanical effects, namely the kinetic, exchange, and correlation energies and the diffuseness of the electron density.