Chebyshev expansions for the scattering matrices in full-potential Korringa-Kohn-Rostoker band-structure calculations

The search for electronic energy bands in full-potential Korringa-Kohn-Rostoker (KKR) band theory requires the evaluation of the scattering matrices at many different energies for a certain number of wave vectors. We develop Chebyshev-function approximations for the scattering matrices, which can save a factor of 2 to 3 in computing time for the case of silicon. Moreover, the Chebyshev coefficients of the scattering matrices can be used in a polynomial expansion of the KKR secular matrix, which transforms the search for the energy bands to an eigenvalue problem. In a test calculation for silicon it turns out that if one wants to reproduce energy bands to within 1 mRy one needs to include cubic terms in the polynomial expansions. Calculations with polynomial coefficients from a Chebyshev series expansion are found to give more precise energy eigenvalues than calculations where the polynomial coefficients were obtained from a Taylor series expansion without using any additional computing time.