AN AB INITIO CALCULATION OF THE ROVIBRONIC ENERGIES OF THE ${CH^{+}}_{2}$ MOLECULE

$^{1}$W. P. KRAEMER, P. JENSEN, AND P. R. BUNKER, Can. J. Phys. 72, 871-878 (1994). $^{2}$P. JENSEN, M. BRUMM, W. P. KRAEMER, AND P. R. BUNKER, J. Mol. Spectrosc., in press. $^{3}$W. REUTER AND S. D. PEYERIMHOFF, Chem. Phys. 160, 11-24 (1992). $^{4}$M. RÖSSLEIN, C. M. GABRYS, M.-F. JAGOD, AND T. OKA, J. Mol. Spectrosc. 153, 738-740 (1992).Author Institution: Bergische Universität - Gesamthochschule Wuppertal, D-42097 Wuppertal, Germany.; Karl-Schwarzschild-Strasse, 1 Postfach 1523, D-85740 Garching, Germany.; National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6.In a recent $paper^{1}$ we reported the results of an ab initi calculation of the vibronic (i.e., N = 0) energy levels of the ${CH^{+}}_{2}$ molecular ion in both the $\tilde{X} {^{2}A_{1}}$ and $\bar{A} {^{2}}B_{1}$ electronic states. These two electronic states become degenerate $(^{2}\Pi)$ when the molecule is linear, and in the vibronic calculation we used the theory that we have given in another $paper^{2}$ in order to allow for the effects of the electronic angular momentum in this situation (i.e., the Renner effect). In the present work we extend the ${CH^{+}}_{2}$ calculation to include N > 0 rovibronic energies and we take into account the effect of spin-orbit coupling by using the ab initi value of the spin-orbit matrix element from Reuter and $Peyerimhoff^{3}$. The only experimental data available for ${CH^{+}}_{2}$ come from a measurement of the $\nu_{3}$ fundamental band of the ground $state^{4}$ in which the $\nu_{3}$ vibrational term value was determined to be $3131.37 cm^{-1}$. In our ab initi calculation we obtain $3114.1 cm^{-1}$ for this term value. Thus, to make our predictions as reliable as possible, we calculate the rovibronic energies after adjusting one parameter in the potential so that we fit the observed value of the $\nu_{3}$ vibrational term value. Using this slightly adjusted ab initi potential we predict a large number of rovibronic term values in the $\tilde{X}$ and $\bar{A}$ states that have not yet been spectroscopically characterized, and we compare our results for the line positions and spin splittings in the $\nu_{3}$ band with the observations