Extended-Hückel study of the (111), (100), and (110) surfaces of copper

We have found that the energy bands of bulk copper can be fit equally well with a set of Hamiltonian parameters Hᵢⱼ and overlap parameters Sᵢⱼ=δᵢⱼ corresponding to Wannier basis functions or by a set (Hᵢⱼ^', Sᵢⱼ^') corresponding to atomic basis functions or by any of a continuum of sets (Hᵢⱼ^'', Sᵢⱼ^'') between (Hᵢⱼ, Sᵢⱼ) and (Hᵢⱼ^', Sᵢⱼ^'). Using the Wannier parameters in thin-film calculations we previously obtained surface-charge deficits of -0.198e, -0.269e, and -0.354e for the (111), (100), and (110) films, respectively. Using atomic parameters we obtain a surface-charge surplus of $0.256e$ for a (111) film. Using a set of intermediate parameters we obtain deviations from surface-charge neutrality of $0.0079e$, -0.0013e, and -0.0452e for the (111), (100), and (110) films. We give a physical explanation of why one would expect a set of intermediate parameters to yield approximate surface-charge neutrality on all three surfaces. Exact surface-charge neutrality can be obtained by making small surface-parameter shifts. We discuss the effect of the new parameters on the surface states, the most interesting of which is the (111) state in the L_2^'-L₁ gap. It is shifted downward but still lies 0.1 eV above EF rather than the 0.4 eV below EF needed if it is to be used to explain the photoemission data of Gartland and Slagsvold.