Self-consistent Green matrix approach

A rigorous mathematical basis for the separation of cluster and background is provided by Green-function (GF) techniques. There are essentially two possible ways the perturbed-crystal and the perturbed-cluster approaches. In the former approach it is assumed that the defect introduces a perturbation relative to the perfect crystal, locahzed to the cluster. If the GF of the perfect crystal is known in any localized basis representation, and the matrix elements of the perturbation can be constructed, the GF of the perturbed crystal can be calculated [294]. The perturbed-crystal approach looks conceptually hke the cleanest and most sophisticated solution as far as the description of the crystalline background is concerned. The problems arise more with the cluster. The perturbation should be constructed self-consistently and at the same... 

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