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Keywords:

  • addition theorem;
  • Slater-type orbital;
  • exponential-type orbital

Abstract

The radial Slater-type orbitals (STO) equation image can be simply obtained by repeated parametric differentiation of the Yukawa Potential equation image with respect to α. A new compact two-range addition theorem (AdT) for the STO is herein derived by explicit parametric differentiation of the well-known Yukawa AdT. The resulting addition formula is combined with the single-range AdT for solid spherical harmonics equation image to present a new AdT for three-dimensional spherical coordinate STOs. We advance the proposition that this formula is “canonical” in the same sense that the Laplace expansion of the Coulomb potential is considered canonical. We demonstrate how this procedure can be employed for all exponential-type orbitals. © 2012 Wiley Periodicals, Inc.