Direct Dynamics Quasiclassical Trajectory Study of the Thermal Stereomutations of Cyclopropane

Abstract

Classical trajectories are computed for the stereomutations of cyclopropane-1,2-d2 at 695 K using direct dynamics on an AM1-SRP potential energy surface (AM1 with specific reaction parameters). The trajectories were initiated on a dividing surface, separating the cyclopropane reactants from the stereomutation products, with momenta and coordinates sampled from a 695 K Boltzmann distribution. The quasiclassical procedure was used, with two different sampling schemes, to ensure zero-point energy and vibrational quantization conditions for the energy levels on the dividing surface. From the product distribution, the ratio of rate constants for double and single methylene rotation, k12/k1, is 2.3 and 3.5 for the two sampling methods. These are between the values of 1.0 and 5−42 deduced from two separate experimental studies. A harmonic-oscillator/rigid-rotor transition-state theory calculation of k12/k1, assuming trimethylene as an intermediate, gives k12/k1 = 1.35 on the AM1-SRP potential energy surface. The lifetime distribution of reactive trajectories is nonexponential, in contrast to the nearly exponential decay computed from a Boltzmann average of RRKM rates. However, the initial 70% of the decay is single exponential, and the ratio of the time constants for decay of the single and double rotation rates is essentially the same as k12/k1 computed from the product ratios. Nearly all the trajectories cyclize on the first approach to a (90, 90) conformation. The data support a range of mechanistic descriptions. Most double rotations are conrotatory and occur via direct, short-lived trajectories. A quantity of 23% of trajectories have lifetimes >400 fs and include multiple independent rotations and both single and double rotation isomerizations.