The quantum mechanical three-body problem and its application to nonlinear, triatomic molecules: Part II. The effect of axis-switching

Abstract

In the course of a general investigation of the matrix elements of the electric dipole moment concerning triatomic, nonlinear molecules a theory of the “axis-switching” effect, recently discovered by Hougen and Watson, is presented. The essential difference between our method and theirs is due to our choosing the body-fixed system to be the instantaneous system of principal axes of inertia. This definition of the body-fixed system has the advantage of introducing the Eulerian angles independent of the equilibrium configuration of the molecule. Thus our set of Eulerian angles is the same for both electronic states involved in axis-switching. In consequence, the rotational part of the wave function is not influenced by axis-switching as long as only first-order corrections to the wave functions are taken into consideration. In this approximation the essential effect of axis-switching consists of the operator L 2 R α′ α appearing in the dipole moment in addition to the elements R α′ α of the rotation matrix.