Theory of One-Electron Molecules. I. Li2+

An accurate method for solving the one-electron Schr\"odinger equation for small molecules is presented. For $\mathrm{Li}_{2}^{+}$, the valence-electron-core interaction is treated as an effective potential found by fitting the atomic energy levels. The intermolecular potentials for six low-lying electronic states of $\mathrm{Li}_{2}^{+}$ are calculated. For the ground state ${\ensuremath{\sigma}}_{g1}$, a binding energy of 1.30 eV is found at a separation of 3.08 \AA{} and a vibration frequency of 277 ${\mathrm{cm}}^{\ensuremath{-}1}$. From the intermolecular potentials, three cross sections are calculated for Li ions scattering from Li atoms: (i) elastic scattering, (ii) charge transfer, and (iii) inelastic scattering leaving the atom in a $2p$ excited state. This last process proceeds through a curve crossing of the ${\ensuremath{\sigma}}_{u1}$ and ${\ensuremath{\pi}}_{u1}$ states at $R=5.95{a}_{0}$.