Knowledge Bank

The single-center expansion configuration-interaction $method1$ has been used to examine the low lying electronically excited states of the $H3+$ molecule (equilateral triangular $H3+$ with $Dth$ symmetry). The expansion center for the electronic wavefunctions was placed in the plane of the molecule, equidistant from the three hydrogen nuclei. The wavefunction was expanded as a sum of two-electron configurations, each consisting of an antisymmetrized product of symmetry adapted Stater orbitals. The energy of each state was minimized with respect to the non-linear orbital parameters. For each of the electronic states considered, ($^\{3\}A\_\{1\}^\{\backslash prime\},\; ^\{1\}A\_\{2\}^\{\backslash prime\}^\{\backslash prime\},\; ^\{3\}A\_\{2\}^\{\backslash prime\}^\{\backslash prime\},\; ^\{1\}E\_\{1\}^\{\backslash prime\},\; ^\{3\}E\_\{1\}^\{\backslash prime\}$) the energy was evaluated at several values of the internuclear separation. Of the above states, only the $^\{1\}A\_\{2\}^\{\backslash prime\}^\{\backslash prime\}$ and the $^\{a\}A\_\{2\}^\{\backslash prime\}^\{\backslash prime\}$ states were found to be bound with respect to the symmetric stretching coordinate. The other states were purely repulsive. Comparisons, where possible, were made with previous $calculations2$, and the single-center method was found to compare favorably with other methods of calculation. The oscillator strengths of the allowed transitions, $^\{1\}A\_\{1\}^\{\backslash prime\}\backslash rightarrow\; ^\{1\}A\_\{2\}^\{\backslash prime\}^\{\backslash prime\}$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A1\prime \to 1E\prime$, were also calculated.