Vibrationrotationinversion Hamiltonian of formaldehyde
Abstract
An expression for the Hamiltonian of a vibratingrotatinginverting 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 zerothorder Hamiltonian, we have fitted to leastsquares (i) the three observed ∆G(v _{4} + {1}/{2}) values for inversion of H _{2}CO and (ii) five of D _{2}CO, both belonging to the Ã^{1}A _{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 _{2}CO and HDCO in the one case; H _{2}CO and HDCO in the other), could not account for their observed ∆G(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 vibrationinversion interactions. We have also obtained a number of quadratic squared sum relations among the Coriolis coupling constants ζ _{kl}^{α} and the inertial constants a _{k}^{αβ}. 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:
 10.1016/00222852(73)901811
 Bibcode:
 1973JMoSp..45..120M