Theoretical calculations of the ring-puckering vibration for trimethylene oxide (TMO) and its deuterated derivatives: The rigid model for the large-amplitude ring-puckering vibration

Abstract

The Hougen-Bunker-Johns model (J. Mol. Spectrosc.34, 136 (1970)) has been extended to a four-membered ring molecule allowing for large-amplitude out-of-plane ring vibration, usually described as a ring-puckering vibration. This model has been used for the trimethylene oxide molecule (TMO) and its symmetrically deuterated derivatives, namely for TMO-β-d2, TMO-α,α′-d4, and TMO-d6. The large-amplitude ring-puckinger vibration energy levels have been calculated using a zeroth-order Hamiltonian in which the small-amplitude vibrations are omitted. The calculations have been carried out using the Numerov-Cooley method for two different forms of the double-minimum potential function: (i) a two-parameter polynomial quadratic-quartic function and (ii) a three-parameter function being a sum of the quadratic and Lorentz terms. It has been shown that: (i) satisfactory agreement between the experimentally observed ring-puckering bands and theoretically calculated ones has been obtained using only two ring-puckering transitions for the fitting of the potential function parameters, (ii) the values of the potential function parameters are different for four TMO molecules, (iii) the model satisfactorily reproduces the intensities of the ring-puckering transitions.