Abstract

A very simple method for deriving formulas for integrals over Slater—Zener type atomic orbitals is given. Essentially, the method obtains integrals over orbitals having higher n and l quantum numbers from the integral over 1 s orbitals by repeated application of operators involving the orbital exponents and the positions of the orbital centers. The method is made practicable by using a symbolic algebra expert system to derive the formulas. Formulas for overlap integrals (and their derivatives) over 1 s, 2 s, and 2 p atomic orbitals are given directly in Cartesian coordinates, thus avoiding the transformation from a local to a molecular coordinate system.

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