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Various properties of the general two-center two-electron integral over theexplicitly correlated exponential function are analyzed for the potential usein high precision calculations for diatomic molecules. A compact onedimensional integral representation is found, which is suited for the numericalevaluation. Together with recurrence relations, it makes possible thecalculation of the two-center two-electron integral with arbitrary powers ofelectron distances. Alternative approach via the Taylor series in theinternuclear distance is also investigated. Although numerically slower, it canbe used in cases when recurrences lose stability. Separate analysis is devotedto molecular integrals with integer powers of interelectronic distances$r_{12}$ and the vanishing corresponding nonlinear parameter. Several methodsof their evaluation are proposed.

Correlated exponential functions in high precision calculations for diatomic molecules