Two-Center Exchange Integrals between Slater-Type Atomic Orbitals

A novel general formula is developed which expresses two‐center charge distributions over Slater‐type atomic orbitals as expansions over terms of the form ${\text{(ξ\hspace{0.17em}−\hspace{0.17em}1)}}^k{\mathrm{(\xi }}^2{\text{\hspace{0.17em}−\hspace{0.17em}1)}}^{\text{M/2}}\mathrm{ex}\mathrm{(-\hspace{0.17em}\alpha \xi )}{\mathfrak{Y}}_{\mathrm{lm}}\mathrm{(\eta ,\phi )}$ , where $\mathrm{(\xi ,\; \eta ,\; \phi )}$ are elliptic coordinates. The formula is applied to derive compact expressions for the calculation of two‐center exchange integrals arising from large basis sets. The program structure is discussed and computing times are quoted for these type integrals.