Cartesian Dynamics of Simple Molecules I Diatomics and Centrosymmetric Triatomics

A simple spring model for molecular vibrations is described in which Cartesian co-ordinates are used for both longitudinal and transverse displacements. The transverse restoring forces are shown to be electrostatic in origin and much weaker than the elastic longitudinal forces. The technique is applied to diatomic and centrosymmetric triatomic molecules. In the latter case, an analytical expression for the bending mode frequency is obtained which is equivalent to that derived by conventional methods using bending constants and internal co-ordinates. The model offers certain advantages when applied to the dynamics of crystals, for which Cartesian co-ordinates, aligned with the unit cell axes, are the natural choice. Reference is made to recent work on molecular and ionic crystals using extensions of this model.