Mutual conversion of three flavors of Gaussian type orbitals

Mutual expansion formulas are developed for three types of Gaussian orbitals: Hermite Gaussians, Cartesian Gaussians, and spherical Gaussians. Overlap, kinetic energy, and Coulomb energy matrix elements are presented for generalized spherical basis functions proportional to \documentclass{article}\pagestyle{empty}\begin{document}$r^{n+s}\exp(-\alpha r^{2})Y^{m}_{n}(\hat{\mathbf{r}})$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$Y^{m}_{n}$\end{document} represents spherical harmonics, where − n ≤ m ≤ n , and where s =0,2,4,… . Hartree–Fock benchmark calculations on isolated, neutral 2 He, 6 C, and 12 Mg atoms indicate that inclusion of the s ≥2 generalized functions is slightly unfavorable if the electronic ground state energy is to be minimized. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001