Intensities of Vibration-Rotation Bands with Special Reference to Those of HCl

Intensity formula for vibration bands. The intensities of vibration bands depend on certain matrix elements of the electric moment of the molecule. The electric moment of a diatomic molecule is a function of the nuclear separation and must be expanded in a power series about the equilibrium point. Matrix elements are calculated by perturbation methods for the fundamental and first two harmonic bands of the vibration spectrum, and it is found that, to a first approximation, for the ${\mathit{n}}^{\mathrm{th}}$ harmonic it is necessary to consider the ${(\mathit{n}+1)}^{\mathit{th}}$ power in the series expansion of the electric moment, and higher powers for better approximations. The formulas for the fundamental and first harmonic are given to a second approximation. The matrix elements are also calculated from wave functions due to Morse for a diatomic molecule, and it is shown that there is a negligible difference between the two methods of calculation for small quantum numbers. Formulas are also given for the ratio of the intensity of the first two harmonic bands to that of the fundamental.