Analytic evaluation of two-center molecular integrals

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Abstract
By using the Fourier-transform technique, the explicit expressions for the one-electronndashtwo-center overlap integrals of Slater-type atomic orbitals up to 3d are derived. The final expressions are analytic, simple, and independent of local coordinates. Furthermore, they do not contain the non-closed-form of exponential integrals which were presented in expressions given in earlier work. It is shown that the two-electron–two-center Coulomb integrals, as well as the hybrid integrals, can simply be expressed in terms of these integrals. The numerical instability arising from the situation in which the exponents of the two orbitals are almost equal is discussed, and a solution for this problem based on a Taylor-series expansion of the integral is suggested.

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