Calculation of the CASSCF Potential Energy Surface, the Dipole Moment Surfaces, the Rotation-Vibration Energies and the Vibrational Transition Moments for $C_{3}$($\tilde{X} ^{1}\Sigma_{3}^{+}$)

$^{1}$C. A. Schmuttenmaer, R. C. Cohen, N. Pugliano, J. R. Heath, A. L. Cooksay, K. L Buarow and R. J. Saykally, Science 249 , 897 (1990). $^{2}$ F. J. Northrup, T. J. Sears, and E. A. Rohlfing, J. Mol. Spectorsc, 145 , 74 (1991) and references therein. $^{3}$ P. Jenson, J. Mol. Spectrosc. 128 , 478 (1988).Author Institution: Physical Chemistry Institute, Justus Liebig University Giessen; Theoretical Division, Sandia National Laboratories; Department of Chemistry and Minnestoa Supercomputer Institute, University of Minnesota, MinneapolisThe $C_{3}$ molecule is of major importance in combustion processes, and it plays a role in astrochemistry. It has a very anharmonic bending mode with a bending fundamental energy observed $experimentally^{1}$ $63 cm^{-1}$, and a rather irregular vibrational energy level pattern caused by substantial interactions between the bending and stretching $motions^{2}$. We have carried out an ab initio calculation of the CASCF potential energy surface and the corresponding diploe moment surfaces for $C_{3}$ employing a very large basis set and have used the ab initio results for a further calculation of the rotation vibration energies in the lower part of the energy spectrum using the MORBID $approach^{3}$. The ab initio calculation reproduces qualitatively the $observed^{2}$variation of the bending energy pattern with stretching excitation. We conclude from the ab initio results obtained in the present work, and from a fitting to experimental data carried out with the MORBID computer program, that the equilibrium structure of $C_{3}$ is linear. Using the MORBID rotation-vibration wavefunctions and the ab initio dipole moment, we have calculated the vibrational transition moments for selected vibrational transitions. We determine transition moments of 0.44 and 0.35 Debye, respectively, for the $\nu_{2}$ and $\nu_{3}$ bands. The ab initio dipole moment values have further been used to calculate the line strengths, integrated absorption coefficients, and peak absorption coefficients of the low-J transitions in the $v_{2}$ and $v_{3}$ bands of $^{12}C_{3}$; these results are in keeping with recent experimental $observatioins^{1}$