Heterogeneous catalysis is an important global industry, but there are many gaps in our understanding of catalytic selectivity. Reactivity indices are helpful for predicting selectivity, and it would be useful to have a reactivity index which can be applied to metal surfaces and adsorbates. The local softness is a reactivity index based on Pearson’s theory of hard and soft acids and bases. It is the derivative of the local electron density with respect to the chemical potential, at constant external electric potential. It can be calculated simply for molecules or nanoparticles which have a band gap. However, the calculation for conductors is less straightforward.

In this work, a method was developed to calculate the local softness of metal surfaces using density functional theory. This required a solution to the problem of increasing the chemical potential while keeping the external electric potential constant, which is difficult to do in charged cells with periodic boundary conditions. This problem was solved by correcting for a shift in energy reference with charge and by extrapolating to an infinitely sized unit cell. The local softness was visualised using isosurfaces and colourplots and was used to compare predicted reactivity between different sites on various metal surfaces.

In order to get a measure of the softness of individual atoms on a surface, Bader’s theory of atoms in molecules was used to integrate the local softness over the regions of atomic volume. The resulting reactivity index, the atomic softness, was used to predict the adsorption energy of carbon monoxide on eighteen different metal surfaces. The local and atomic reactivity indices were also used to study directing effects for aromatic adsorbates on the Pt{111} surface. The local and atomic softness were found to be useful for predicting reactivity trends between different sites on metal surfaces and for adsorbates.