The relationship between the Dyson equation and the embedding method, in the Green’s function calculation of a defect in a solid, was considered. It was shown that, if the Green’s function was expanded by using the same basis set, the Green’s function matrix of the embedding method was related to that of the Dyson-equation method by a simple Dyson-type equation. With increasing number of basis functions, the Green’s functions which were calculated by using the 2 methods rapidly converged towards each other within the interior of the perturbed volume. They differed persistently on the boundary surface because the Dyson-equation method failed to incorporate the boundary condition on the Green’s function.

Comparison of the Embedding and Dyson-Equation Methods in the Green’s-Function Calculation of Defects in Solids. H.Ishida, M.I.Trioni: Physical Review B, 2001, 63[15], 155108 (7pp)