Valence Electron Studies with Gaussian-Based Model Potentials and Gaussian Basis Functions. II. Discussion of the One-Valence-Electron Molecular Theory and Applications to Li2+, Na2+, and LiH+

A one‐electron theory for one‐valence‐electron molecules is developed. It assumes nuclear‐nuclear repulsions to be between net core atomic charges, and that the potential seen by the valence electron is a superposition of atomic model potentials. The atomic model potentials are the core Coulomb potentials modified by Gaussian screened Coulomb potentials, as found in earlier atomic studies. Such model potentials are quite convenient for the use of Gaussian basis functions, which are also taken from the atomic studies, and for which potential energy matrix elements are simply calculated from physically based rules. The theory is applied to the ground states of ${\mathrm{Li}}_2^{+},{\mathrm{Na}}_2^{+}$ , and LiH⁺, using a variety of basis sets. Increasing the basis set flexibility lowers the energy, as in ordinary all‐electron variational calculations. Binding energies and internuclear distances from the most extended basis calculations are: ${\mathrm{Li}}_2^{+}{\mathrm{:\hspace{0.17em}D}}_e\text{=1.23\hspace{0.17em}}\mathrm{eV}$ , R_e = 5.8 a.u.; ${\mathrm{Na}}_2^{+}{\mathrm{:\hspace{0.17em}D}}_e\text{=0.97\hspace{0.17em}}\mathrm{eV},$ R_e = 6.7 a.u.; LiH⁺: D_e = 0.090 eV, R_e = 4.5 a.u. These are in excellent agreement with results from more elaborate all‐electron quantum mechanical studies, and we thus conclude that our simple, convenient theory simulates the true problem accurately.