Cartesian Dynamics of Simple Molecules II Non-Centrosymmetric Linear Triatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to non-centrosymmetric linear triatomic molecules. Analytical expressions for the stretching and bending mode frequencies are obtained, which are equivalent to those derived by conventional methods. For most molecules, the effects of the interaction between the outside atoms are shown to be negligible, but for N₂O, complex solutions are obtained unless this is included. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. For N₂O, frequency shifts resulting from isotopic substitution are explained by reference to the calculated eigenvectors.