Single-Center Calculations on the Electronically Excited States of Equilateral H3+ Ion

Abstract

A theoretical investigation of the excited electronic states of the equilateral triangular H₃⁺ ion is reported. Ab initio calculations were performed for the lowest energy states of symmetries ${}^3{A}_1{\mathrm{\prime ,}}^1{A}_2{\mathrm{″,}}^3{A}_2{\mathrm{″,}}^1\mathrm{E\prime }$ , and ${}^3\mathrm{E\prime }$ , using the single‐center expansion configuration‐interaction method. For each state we have obtained the potential‐energy curve in $D_{\text{3h}}$ symmetry. The calculated state energies are expected to be in error by at most 0.01 hartree (6 kcal/mole). Two of the excited states ${}^1\mathrm{E\prime }$ and ${}^3\mathrm{E\prime }$ were found to be purely repulsive with respect to the totally symmetric nuclear coordinate, while three excited states ${}^1{A}_2{\mathrm{″,}}^3{A}_2\mathrm{″,}$ and ${}^3{A}_1\prime$ showed minima with respect to the totally symmetric nuclear coordinate. However, arguments based on group‐theoretical correlation between our calculated $D_{\text{3h}}$ state energies and the energies of possible dissociation products suggest that none of the excited states considered achieves an absolute energy minimum in $D_{\text{3h}}$ symmetry. For the allowed electric dipole transitions ${}^1{A}_2{\mathrm{″\hspace{0.17em}\leftarrow \hspace{0.17em}}}^1{A}_1\prime$ and ${}^1{\mathrm{E\prime \hspace{0.17em}\leftarrow \hspace{0.17em}}}^1{A}_1\prime$ we have calculated the vertical (Franck–Condon) transition energies, oscillator strengths, and polarizations. The nature of the excited‐state energy curves, at the ground‐state equilibrium geometry, indicates that in every case only continuum absorption from the ${}^1{A}_1\prime$ ground state would be observed experimentally.