Ab-initio Calculation and Analytical Potential Function for C₂H

The ethynyl radical C₂H has been the subject of both experimental and the oretical investigations for its astrophsical interest. It is well established that it is linear and its ground state is ²Σ⁺. However, beyond these many questions about the strcture and spectra of this molecule are still open. The present work devotes to provide the molecular potential function of C₂H in the whole region as accurate as possible, and examine the dynamic feature which has been not yet dealt with.
Using UHF method the optimum geometry of C₂H has been found to be 1.226Å, 1.054Å and 180° with 6-311G basis. and to be 1.209Å, 1.057Å, and 180°with 6-311G^** basis for R_CC, R_CH and CCH respectively. As indicated earlier made by Z. H. zhu, the addiction of polarization functions to the basis set leads to significant improvement in bond angles but not in bond lengths. Based on the geometry of 6-311G^** basis, we have calculated the force field given in Table 2, the results of the force constants f_CC and f_CH, and the stretching vibration frequencies v₁(CH) and v₃(CC) are in good agrement with all the available experimental data. It is impossible to find the accurate dissocciation energy using basis 6-311G or 6-311G^** without configuration interaction. Therefore, the third-order perturbation with smaller basis set of 6-31G^* was used to the calculation of dissociation energy. The calculated De of C₂H is 12.06eV, which is remarkable satisfaction in comparison with thermodynamic determination of 12.1 leV.
The potential energ function would play the key role in examining the features of molecular dynamics. The ab-initio approach is likely to be valuable for some stationary regions, but it is extremely arduous and time-consuming task for giving an acceptable potential surface in the whole reactive region. Instead of that, we have used the so-called many-body expansion theory developed by J. N. Murrell and his coworkers, whivh is successful now in use for atom-diatom reactive collisions. The molecular potential function of many-body expansion for C₂H has been derived based on the energy, geometry and force field calculated above for its equilibrium configuration, in addition, the experimental data for diatomics. It is obvious from Fig.1 that there will be no activation energy for the molrcular formation processes of stable C₂H starting from either C₂+H or CH+C, which is significant for the interstallar molecules. From Fig.2 and 3, it seems to us that hydrogen atom is much liable to have the intramolecular migration along bond C-C, but the carbon atom is not the case.