Charge redistribution at Pd surfaces: ab initio grounds for tight-binding interatomic potentials

TL;DR

This paper uses ab initio calculations to show that charge distribution at Pd surfaces remains unchanged from bulk to surface, challenging existing neutrality assumptions and revealing new insights into band energy variation.

Contribution

It provides a self-consistent parametrization of charge redistribution for late transition metals like Pd, invalidating previous neutrality rules and refining tight-binding models.

Findings

Charge remains unchanged from bulk to surface at Pd.

Orbital neutrality requires different level shifts per orbital.

Band energy variation with coordination number differs from the square root law.

Abstract

A simplified tight-binding description of the electronic structure is often necessary for complex studies of surfaces of transition metal compounds. This requires a self-consistent parametrization of the charge redistribution, which is not obvious for late transition series elements (such as Pd, Cu, Au), for which not only d but also s-p electrons have to be taken into account. We show here, with the help of an ab initio FP-LMTO approach, that for these elements the electronic charge is unchanged from bulk to the surface, not only per site but also per orbital. This implies different level shifts for each orbital in order to achieve this orbital neutrality rule. Our results invalidate any neutrality rule which would allow charge redistribution between orbitals to ensure a common rigid shift for all of them. Moreover, in the case of Pd, the power law which governs the variation of band energy with respect to coordination number, is found to differ significantly from the usual tight-binding square root.