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We present an efficient approach to evaluate two-center two-electronintegrals with exponential functions and with an arbitrary polynomial inelectron-nucleus and electron-electron distances. We show that the masterintegral with the single negative power of all distances can be obtained fromthe second order differential equation in $r$, the distance between nuclei. Forparticular values of nonlinear parameters corresponding to the James-Coolidgebasis, we find a fully analytic expression. For integrals with arbitrary powersof all distances, we construct recursion relations which starts from the masterintegral. The presented approach opens a window for the high precisioncalculations of relativistic effects in diatomic molecules.

Two-center two-electron integrals with exponential functions