Guillemin—Zener Energy of H2+

Abstract

The energy of the H₂⁺ ground state 1sσ calculated with the Guillemin—Zener approximate wavefunction, ${\psi }_s{\mathrm{=N}}_s\exp \text{(−Raλ/2)}\cosh \text{(Rbμ/2)}$ lies within 0.0005 e²/a₀ of the exact for the full range of internuclear separations. In the limit of zero separation, ${\psi }_s{\mathrm{=N}}_s\exp {\mathrm{(-r}}_{\mathrm{A}}{\mathrm{-r}}_{\mathrm{B}})\cosh {\mathrm{[(r}}_{\mathrm{A}}{\mathrm{-r}}_{\mathrm{B}}\mathrm{)/}\sqrt{3}]$ . The energy still lies within 0.0010 e²/a₀ when the additional requirement is imposed that Hψ_s remains finite at the nuclei. The Guillemin—Zener energy is less accurate for the first excited 2pσ state.