Effect of Isotopic Substitution on the Dipole Moment of Molecules of Symmetrical Configuration

摘要

As is well known, molecules of symmetrical configuration possess no permanent dipole moment. Upon isotopic substitution, however, a dipole is produced due to the changed zerohyphen;point motion of vibration and the asymmetry of the restoring forces.This effect is calculated for two molecules: O16C12O18, and CH3D.A normal coordinate treatment is carried out for these two molecules using a simplified form for the force fields as an approximation to the general quadratic force fields of both CO2and CH3D. It is assumed therefore that the omitted terms play a negligible part in dipole moment calculations. The vibrational wavefunctions for the nuclear skeletons of the systems are calculated, including the effect of the cubic terms in the potential function as perturbations to the simple harmonic wavefunctions. The shift from the equilibrium separation of the atoms is then calculated by taking the quantum mechanical average values of the position coordinates.Finally, the dipole moment is given by the product Dgr;mgr;=part;mgr;/part;rlang;Dgr;rrang;Av, where part;mgr;/part;ris the change in bond moment with respect to internuclear distance which is determined from experiment, and lang;Dgr;rrang;Avis the shift or displacement from the equilibrium separation of the nuclei.The calculations yielded the following results: for O16C12O18, a permanent dipole moment of the order of 10mdash;3D, and for CH3D, a permanent dipole moment of the order of 10mdash;3D, for the vibrational ground states.