Gaussian product rule for two-electron wave functions

The Gaussian product rule for two-electron wave functions is introduced. The two-electron Gaussian product rule enables a new way for solving two-electron integrals. The solution is demonstrated with an example of the two-center two-electron integral in solid harmonic Gaussian basis. The solution is obtained by expanding inverse inter-electron separation and integrating in spherical coordinates. The resulting integral separates into four integrals, three of which are straightforward to solve. The remaining integral can be solved with Boys-like functions. It is demonstrated that the solution can deliver results with accuracy comparable with that of the McMurchie-Davidson scheme.