Frequency Factor for the Arrhenius Form of the Rate Constant for Cyclobutane

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Abstract
Slater's theory is developed starting from the solution to Lagrange's equations of motion and based on symmetry coordinates. From the fundamental frequencies of cyclobutane the potential constants for the Eu vibrations are calculated and a normal‐coordinate analysis of cyclobutane is made. Using this analysis and Slater's theory, the frequency factor in the Arrhenius form of the rate constant is predicted for three different sets of critical coordinates. Using P1=ΔR12+ΔR34 as a critical coordinate, a value for the frequency factor two orders of magnitude less than the reported experimental values is predicted. When P2=ΔR12+ΔR23 is used as a critical coordinate, a frequency factor of an order of magnitude less than the experimental values is predicted. With P3=0.891124 ΔR12+0.761947 Δr2 as the critical coordinate, a frequency factor of ½ the experimental values is predicted. An examination of the activation energy which ranges between 61.8 and 65 kcal/g‐mole shows that the degree of distortion of cyclobutane at the critical configuration is sufficiently large to warrant the consideration of anharmonic terms in the potential energy. Investigation of the pressure dependence of K/K∞ shows that a curve identical in shape to the experimental curve is obtained when P3 is the critical coordinate and the effective number of oscillators is 16.

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