Knowledge Bank

The energies of the lower lying vibrational-rotational states of formaldehyde and deutero-formaldehyde are calculated by a variational technique with use of the full Watson Hamiltonian. First a study of different available force fields for formaldehyde was performed with the pure vibrational $(J=0)$ Hamiltonian. The vibrational basis functions are products of one-dimensional harmonic oscillator functions, one corresponding to each of the six normal coordinates; the integrals are evaluated by Gauss-Hermite quadrature. Results for different force fields in internal valence displacement coordinates are compared with experiment. The best presently available force field for formaldehyde is one which is obtained by transforming a Taylor series in valence coordinates which has been obtained by fitting theory to experiment within the framework of second order perturbation theory; stretching displacements $\Delta r$ are replaced by $\Delta r/r$ in such a way that the new force field is equal to the old one up through quartic terms in the Taylor series. For this force field vibrational-rotational states were calculated for low J values and compared with experimental data. The rotational basis functions are symmetric top functions and the integrals are calculated analytically. The mixing of states through anharmonic effects and Coriolis coupling will be discussed.