Comparison of different approaches to the study of local defects in crystals. I. Theoretical considerations and computational schemes

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Abstract
The standard way of treating local defects in crystals is to correct the Green function of the perfect periodic host system so as to account for the defect. This approach, which is termed here as “perturbed crystal”, is compared with a “perturbed cluster” approach where instead the molecular solution for a cluster of atoms around and including the defect is corrected in order to account for the presence of the infinite surrounding medium. It is first shown that when a unique basis set is used to describe the crystal both, before and after the defect is created, the perturbed crystal approach is essentially simpler. When however the defect is complicated and the use of different basis sets is practically compulsory, then the other approach is more natural and the corresponding computational scheme is more easily implementable. New explicit formulae for the perturbed cluster approach are derived which are more powerful and general than those used in previous works.