Effect of Molecular Vibrations on Gas Electron Diffraction. I. Probability Distribution Function and Molecular Intensity for Diatomic Molecules

General expressions and their practical approximations are presented for the molecular intensity of gas electron diffraction and the radial distribution function for an atom pair in the molecule which exerts moderately anharmonic intramolecular motion in thermal equilibrium. The calculations are based on a polynomial expansion of the probability distribution function of the internuclear distance around a Gaussian function representing harmonic vibration. The coefficients of the expansion for a diatomic system are calculated by the second-order perturbation method in terms of the coefficients of the potential energy expanded to the fourth order of the displacement in the internuclear distance. The structural parameters under various definitions (the mean internuclear distances, the mean square amplitudes, and the phase parameters) of a number of diatomic molecules are tabulated by the use of the spectroscopic values ωe, αe, and χe taken from the literature. The temperature dependence of the structural parameters is discussed.