Analysis of numerical methods for evaluating the Fock exchange integral in a plane-wave basis
نویسندگان
چکیده
A. Singular integration algorithm A convenient method for numerical evaluation of singular integrals is to introduce an auxiliary function in order to transform the argument of the numerical integral into a nonsingular argument. The complete result involves also evaluating the singular integral of the auxiliary function, which can be accomplished by using analytic or efficient numerical methods. This idea was first proposed by Gygi and Baldereschi13 and further developed by Massidda, Posternak, and Baldereschi;14 several other schemes have appeared in the more recent literature.3,4,7 Following the work of Duchemin and Gygi,7 Eq. (1) can be evaluated according to
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