A diagrammatical method, based on the second quantization formalism, timehyphen;independent Wick's theorem and Feynmanhyphen;like diagrams, is developed for the calculation of arbitrary matrix elements ofnhyphen;particle spinhyphen;independent operators between the states represented by antisymmetrized products of geminals of an arbitrary kind (i.e., strongly or weakly orthogonal, interacting, nonorthogonal or identical geminals). The method greatly facilitates any algebraic manipulation with geminal type functions, particularly when strong orthogonality is not assumed, and enables one to write down directly the algebraic expressions for the matrix elements of an arbitrary spinhyphen;independent operator between the single antisymmetrized products of arbitrary geminals, solely on the basis of simple graphs, which are easily constructed.
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