The Theory of Surface Chemistry and Bonding

The goal of theoretical surface chemistry is to understand the surface chemical bond, and from this to be able to describe and predict the properties of atoms and molecules adsorbed on surfaces. The primary properties of interest include adsorption sites and geometries, bond lengths and angles, the electronic structure of adsorbed species, adsorption energies, diffusion energies, and the 

The basic approach of chemical theory to surface science is to model a surface with a cluster of a finite number of atoms, with one or more adsorbate atoms or molecules bonded to various sites on the cluster. In parallel with the chemical theory there is also the solid state physics approach. This starts from an extended surface surface model, where an array of atoms perfectly periodic in two dimensions represents both the substrate and any adsorbates. Many theoretical techniques have been developed for the extended-surface model. We can only refer the interested reader to the literature/87,88,89,90,91,92,93,94/ and remark that the relative merits of the cluster and extended-surface approaches are still very much under active debate. It is clear that certain properties, such as bonding, are very localized in character and are well represented in a cluster. On the other hand, there are properties that have a delocalized nature, such as adsorbate-adsorbate interactions and electrostatic effects, for which an extended surface model is more appropriate. 

The cluster approach is, like the extended-surface approach, characterized by many different calculational schemes. A recent review stresses electronic aspects of bonding. In this review we have chosen to concentrate on geometric aspects. We shall discuss a number of major techniques in order of increasing computational complexity the extended H uckel theory, self-consistent Xa scattered wave calculations, and self-consistent ab initio Hartree-Fock and valence bond methods. In that order these techniques allow increasing accuracy. However, the cluster size must decrease simultaneously due to calculational complexity, ultimately reducing the degree of analogy with surfaces. 

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals 

On minimizing the total energy, one obtains a set of secular equations 

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