Vibration-rotation-inversion Hamiltonian of formaldehyde
Abstract
An expression for the Hamiltonian of a vibrating-rotating-inverting formaldehyde molecule is derived. In this derivation, we have used one curvilinear coordinate corresponding to the angle between the CO bond and the bisector of the angle HĈH, and five rectilinear coordinates (linearized valence coordinates). Making use of the zeroth-order Hamiltonian, we have fitted to least-squares (i) the three observed ΔG(v 4 + {1}/{2}) values for inversion of H 2CO and (ii) five of D 2CO, both belonging to the Ã1A 2 excited electronic states, in two separate calculations. For this, we have employed two model potential functions: one consisting of a sum of quadratic and Gaussian and the other a sum of quadratic and Lorentzian terms. In each case, the refined parameters, when transferred to the isotopic molecules (D 2CO and HDCO in the one case; H 2CO and HDCO in the other), could not account for their observed ΔG(v 4 + {1}/{2}) values to the expected degree. We attribute the discrepancies to the inadequacy of the model chosen for the formaldehyde molecule which takes into account only one large amplitude bending motion and which neglects vibration-inversion interactions. We have also obtained a number of quadratic squared sum relations among the Coriolis coupling constants ζ klα and the inertial constants a kαβ. These are applicable to any molecule undergoing a large amplitude bending motion provided the reference configuration is chosen as described in the text.
- Publication:
-
Journal of Molecular Spectroscopy
- Pub Date:
- January 1973
- DOI:
- 10.1016/0022-2852(73)90181-1
- Bibcode:
- 1973JMoSp..45..120M