Barrier Heights and the Separation of Torsional Motion from Frame Vibrations in Electron Diffraction

A method is presented for determining the barrier height hindering internal rotation from electron‐diffraction data. The method is based on simple assumptions regarding the variation of the contribution of the frame vibrations as a function of the equilibrium positions on the circle of rotation. These assumptions, combined with the occurrence of two or more different interatomic distances which are affected by the torsional motion, permit a separation of the contribution of the torsional motion from that of the frame vibrations. The assumed form for the functional variation of the squared amplitude of the contribution from the frame vibrations is $\text{α{1+β}\exp {\mathrm{[-(\pi -|\phi }}_e{\mathrm{|)}}^2\mathrm{]\}}$ , where α and β are constants and φ_e is the equilibrium angle for an interatomic distance on the circle of rotation, where φ_e=0 corresponds to the trans distance. When the variation is assumed to be constant, β=0, some typical values obtained from electron‐diffraction data are 12.8 kcal mole⁻¹ for Cl₃CCCl₃, 4.3 kcal mole⁻¹ for F₃CCF₃, and 1.1 kcal mole⁻¹ for Cl₃SiSiCl₃. It was found that a value of β=3.76 and a barrier height of 3.4 kcal mole⁻¹ afforded a very good fit to the diffraction data for Cl₃CNO₂. Errors in the barrier heights are estimated to extend to 30% above and 20% below the given values. Further studies on Cl₃CNO₂ indicated that the barrier height is relatively insensitive to the assumptions made concerning the variation of the contribution of the frame vibrations, but strongly dependent on the assumed form for the potential barrier. Comparisons are made with the results of other methods for computing the barrier heights, and quite satisfactory agreement is obtained.