The Hückel model for small metal clusters. II. Orbital energies, shell structures, ionization potentials, and extrapolation to the bulk limit

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Abstract
We analyze the results of HMO calculations (this paper and its preceding companion) for the neutral and cation alkali-like metal clusters, M2–M14. The filled HMO energy levels develop as well separated energy shells 1s, 1p, 1d, ... where s, p, and d denote the global nodal character of the Hückel orbitals. The HMO energy shells decrease in energy with increasing cluster size. By smoothly fitting the HMO orbital energies, we obtain trends in (a) atomization energies, (b) relative cluster stabilities, and (c) ionization potentials which are highly reminiscent of those derived from jellium calculations. The HMO atomization energies are best described by a classical drop model. When extrapolated to infinity, the HMO cohesive energies are within 15% of the experimental results for bulk Li→Cs. Thus we are able to unify within the single framework of HMO theory the quantum, jellium, and droplet models for alkali metal clusters. For the neutral clusters, HMO and local-spin-density atomization energies agree to within ∼4%. The HMO cation energies, modified by addition of a classical charge-correlation term, differ from the local-spin-density results by about 2%. Except for an exaggerated drop at the n=8 shell closing, the HMO ionization potentials are in good agreement with the experimental data for Na and K clusters.

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