Fitting valence charge densities at a crystal surface

A procedure is reported for obtaining a much better initial parameterization of the charge density than that possible from a neutral atom model. This procedure involves the parameterization of a bulk charge density model in terms of simple variables such as bond lengths, which can then be transferred to the problem of interest, for instance a surface. Parameterization is accomplished through the fitting of density functional theory calculations for a variety of crystal distortions. The details of the parameterization are discussed for the specific case of silicon. This parameterized model can then be applied to surfaces or to other problems where an initial higher-order model is needed without the addition of any extra fitted parameters. The non-convexity of the charge density problem is also discussed.