Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach: Application to the fundamental bands of CH 2

Abstract

The present paper describes a method for calculating the linestrengths and (if the molecules are in thermal equilibrium) absolute intensities for triatomic molecules using the rotation-vibration energies and wavefunctions obtained in the MORBID (Morse oscillator rigid bender internal dynamics) approach [P. Jensen, J. Mol. Spectrosc. 128, 478–501 (1988)] together with ab initio dipole moment values. A computer program that carries out these calculations has been written and used to compute the rotation-vibration spectrum of X ̃ 3B 1 12CH 2 in the wavenumber region around 1000 cm −1, containing the observed ν 2 fundamental band [M. D. Marshall and A. R. W. McKellar, J. Chem. Phys. 85, 3716–3723 (1986), and references therein], and around 3000 cm −1, where the stretching fundamental bands ν 1 and ν 3 are found together with the 3 ν 2 band. No transitions belonging to these latter bands have been observed and one of the aims of the present work is to provide the best possible theoretical predictions to guide the experimental search for them. It is found that the strongest transition in the region around 3000 cm −1 is the ν 3 5 14 ← 4 13 line calculated to have a frequency of 3285.49 cm −1 and an integrated intensity of 1.04 × 10 3 mole −1 cm at an absolute temperature of 293 K. The integrated intensity of this line is about half of the integrated intensity of the weakest ν 2 transition observed, the 5 23 ← 5 32 line observed at 910.1660 cm −1. Even when the decrease in peak absorption due to Doppler line broadening is taken into account, it should not be entirely out of the question to observe at least stronger ν 3 lines.