Structures and electronic properties of copper clusters and bulk; comments on Mulliken–Walsh diagrams and on criticisms of the extended Hückel procedure

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Abstract
Structures, energy levels, and binding energies of small copper clusters are determined using a two‐step theory wherein (1) rigid atoms are superimposed giving rise to readily determined pairwise repulsion energies and (2) attractive energies due to electron delocalization are estimated with a molecular orbital theory derivable, with approximations, from the superimposed rigid atom Fock potentials. Optical spectra determined by Moskovits and Hulse for Ar matrix isolated Cu, Cu2, Cu3, Cu4, and Cu5 are interpreted in terms of molecular orbital energy levels. Matrix frequency shifts are seen to arise from antibonding interactions between Cu 4s and 4p orbitals with Ar matrix 3p orbitals. A fcc Cu13 cluster yields the major features of the Cu(100) surface photoemission spectrum due to Burkstrand et al. but not the lattice and force constants. The force constant is determined using a Poisson equation. It is suggested that small Cu microcrystals have structural and bond length disorder and may experience a phase transformation to fcc at a critical size. Less than bulk bond lengths in microcrystals are due to an absence of bulk coordination. It is suggested that the orbital energies, which are similar to extended Hückel ones, are obviously appropriate to Mulliken–Walsh diagrams and that past criticisms of extended Hückel orbital energy results have been premature.