The molecular structure and vibrational spectrum of the cyclopropenyl cation, C3H+3, and its deuterated isotopomers

Abstract

The equilibrium structure, harmonic vibrational frequencies, infrared intensities, anharmonic constants, vibration–rotation interaction constants and quartic and sextic centrifugal distortion constants of C3H+3, the cyclopropenyl cation, and its deuterated isotopomers have been determined via purely ab initio quantum-mechanical methods. Two one-particle basis sets have been employed in conjunction with second-order M≂ller–Plesset perturbation theory (MP2), singles and doubles configuration interaction (CISD), and singles and doubles coupled cluster (CCSD). The best estimate of the harmonic frequencies is obtained from MP2 with a triple zeta plus double polarization (TZ2P) basis set. The anharmonic analysis has been determined via second-order perturbation theory using a double zeta plus polarization (DZP) self-consistent-field (SCF) full quartic force field. A generalization of formulas for the anharmonic analysis of D3h symmetric tops is discussed. The complete quartic force field in symmetry internal coordinates is given. Additionally, the anharmonic constants, vibration–rotation interaction constants and quartic and sextic centrifugal distortion constants for C3H+3 and C3D+3 are reported. Predictions of the fundamental vibrational frequencies for C3H+3 and all its deuterated isotopomers are reported. At the TZ2P MP2 level of theory the equilibrium structure of cyclopropenyl cation is Re(C–C)=1.3647 Å, Re(C–H)=1.0753 Å. Coupling the TZ2P MP2 harmonic frequencies with the DZP SCF anharmonic corrections, the infrared active fundamentals of C3H+3 are predicted to occur at 3136, 1289, 939, and 773 cm−1, with those of C3D+3 predicted to occur at 2346, 1243, 684, and 567 cm−1.