Theory of One-Electron Molecules. I.Li2+

Abstract

An accurate method for solving the one-electron Schrödinger 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 ${\sigma }_{g1\mathrm{}}$, a binding energy of 1.30 eV is found at a separation of 3.08 Å and a vibration frequency of 277 ${\mathrm{cm}}^{-1\mathrm{}}$. 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 ${\sigma }_{u1\mathrm{}}$ and ${\pi }_{u1\mathrm{}}$ states at $R=5.95\mathrm{}{a}_0$.