Resolvent method for quantitative calculations on surface states and adsorption: General method

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Abstract
A new method is presented for the calculation of surface and adsorption effects on one-electron states in crystals. Conceptually, this method is similar to the Koster-Slater resolvent method for impurity states, which has often been applied to surface states in semi-infinite crystals. The elaboration is very different, however. The proposed scheme works for finite crystals, the resolvent matrix is calculated numerically instead of analytically, and the applicability of the method depends on a suitable algorthm for the numerical solution of the Koster-Slater equations. Such an algorithm is described. In comparison with the resolvent method for semi-infinite crystals, this method permits a more quantitative treatment of real crystals, such as transition metals or semiconductors. On the other hand, compared with standard molecular-orbital methods on finite clusters, it can handle much larger crystals.

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