Separability between valence and conduction bands in transition metal clusters

Simplified theories of transition metal electronic structure have been postulated for many decades. We test one such approximation, namely separate treatments of d (valence) and s/p (conduction) electrons in transition metal clusters, within a density functional theory (DFT) formalism. Two different basic approaches are considered: (a) an independent-band approximation, in which the d- and s/p-bands interact only via the p-dependent components of the Kohn-Sham operator; and (b) a more realistic approximation, in which the lowest-energy d- and s/p-orbitals (separately derived) are allowed to interact through explicit off-diagonal coupling matrix elements. The results are presented for the energy differences among three structural forms (icosahedral, cuboctahedral, and truncated decahedral) of 13-atom Ni and Pt clusters. We demonstrate that an explicit decoupling of the d- and s/p-bands does not produce accurate results for the clusters considered, not even for nickel, i.e., the transition metal for which d-s/p mixing should be at its minimum. By contrast, allowing the lowest-energy orbitals of the two separate bands to interact improves the results considerably, and ensures a fair description of metal-metal bonding. This finding suggests that simplified models that exclude explicit d-s/p coupling should be employed with caution.