The Green's function (GF) method has also been examined for the embedding problem. It has the advantage of being more consistent than any cluster method because it does not require unphysical splitting of the crystal electrons. In [A2,B25], the perturbed-cluster method has been proposed based on the HF one-particle GF (the resolvent of the HF operator). An approximate representation of the defect-containing crystal GF has been found. This allows one to obtain a simple analytical representation of the population matrix in the defect region and thereby perform self-consistent ab initio calculations of the defect electronic structure quite effectively. This theory has been implemented into the well-known EMBED computer code developed in Torino (C. Pisani).
Another technique based on a more general many-particle GF has been proposed in [B28,B29]. In this method, a special HF-like truncation procedure is used for the elements of the GF belonging to the outside region in order to simplify the problem and extract the cluster (i.e. the defect region) GF. It was shown in [B29] that the total crystal energy, density of states and electronic density matrix depend exclusively on the cluster GF, which turns out to be the key quantity of the theory. Then, in order to obtain the cluster GF taking into account correlation effects in the defect region, the Hedin's screened-exchange decomposition for the cluster self-energy (GW method) has been implemented. This method was tested on a model chemisorption problem (unpublished).