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Electronic structure and response functions in random alloys: an application of block recursion and Green matrices

We present here a generalization of the recursion method of Haydock et al (1972 J. Phys. C: Solid State Phys. 5 2845) for the calculation of Green matrices (in angular momentum space). Earlier approaches concentrated on the diagonal elements, since the focus was on spectral densities. However, calculations of configuration averaged response functions or neutron scattering cross-sections require the entire Green matrices and self-energy matrices obtained from them. This necessitated the generalization of the recursion method presented here, with examples.