Mean Amplitudes of Vibration in Molecules with Internal Rotation. IV. Theory with Application to Disulfur Dichloride

Abstract

A normal-coordinate analysis has been performed for disulfur dichloride, and used to calculate the mean amplitudes of vibration. A generalized definition of framework mean amplitudes is proposed, and is applicable to cases where the torsional mode (for internal rotation) is kinematically coupled with other normal modes of vibration. According to this definition the total mean-square amplitude is composed of a sum of the framework mean-square amplitude and the torsional mean-square amplitude; the latter quantity contains all contributions where the torsional coordinate is involved. Numerical results of framework and torsional mean amplitudes are reported for S2Cl2 at various temperatures as functions of the angle of rotation θ. The approximate formula for framework mean-square amplitudes, 〈Δρ2〉frm = (α + β cosθ + γ cos2θ) / ρ2, has been subjected to detailed studies. The α, β, and γ coefficients were evaluated in terms of certain mean-square amplitude quantities, and the following statement was deduced from the properties of their classical limits at high temperatures: α(θ, T), β(θ, T), and γ(θ, T) approach θ-independent values when T → ∞. Furthermore, it is explained why the above formula with constant coefficients may give a very good approximation even at low temperatures when the conditions of classical limits are not fulfilled. This feature was actually found for S2Cl2 even at absolute zero.