The Chadi total energy algorithm for determining surface geometries

The Chadi total energy minimization technique is probably the simplest, physically realistic approach for determining the surface geometries of solids and has proved highly successful in predicting the surface relaxation and reconstruction of a wide variety of covalent solids. One of the basic assumptions of this method has been that the tight-binding parameters, which describe the dependence of the electronic energy of the system upon the surface configuration of atoms, simply vary as the inverse square of the appropriate interatomic distance. More recent work, however, has shown that there are now strong grounds for doubting the validity of this 1/d² approximation, and has suggested that a better representation of the spatial dependence of the LCAO model Hamiltonian parameters might be obtained from self-consistent bandstructure calculations performed at different lattice constants. The purpose of this paper is to assess the relative merit of these two alternative models by employing them in a direct determination of some of the lattice dynamical properties of silicon, and to discuss the implications of the results of these calculations for surface structure analyses within the Chadi formalism.