Mean Amplitudes of Thermal Vibrations in Polyatomic Molecules. III. The Generalized Mean Amplitudes

Abstract

James' theory of the effect of molecular vibrations upon the diffraction pattern is revised and extended, including the parallel as well as perpendicular vibrations of atom pairs. Corresponding to these vibrations the mean square amplitudes, parallel and perpendicular, and the mean cross products are defined, and a method of calculating them by means of normal modes of vibration is derived. At the same time the effect of molecular symmetry upon mean amplitudes is discussed with the result that some of them are essentially reduced to zero because of the symmetry.