On the representation of potential energy surfaces of polyatomic molecules in normal coordinates: II. Parameterisation of the force field

By substituting the standard mass-weighted normal coordinates with either Morse-like or Gauss-like coordinates, it is demonstrated that significant improvements can be made to the vibrational spectra of polyatomic molecules calculated variationally. Quartic force fields in the form of Taylor expansions are generated by density functional theory for water, formaldehyde and methane, and their vibrational spectra calculated by the perturbation normal coordinate code SPECTRO. These are then compared with three sets of spectra arising from the variational code MULTIMODE. Initial spectra are obtained using the identical Taylor expansion force fields. A subsequent set of spectra are then obtained for which the symmetric normal coordinates of the force fields are replaced by Morse-like coordinates and a final set of spectra are obtained for which the asymmetric normal coordinates of the force field are replaced by Gauss-like coordinates. The restriction is imposed that the complete set of derivatives to quartic are preserved under these coordinate transformations.