Secondary kinetic isotope effect in nucleophilic substitution: a quantum-mechanical approach

Four-dimensional time-independent quantum scattering calculations have been carried out on the perdeuterated exothermic and complex-forming gas-phase S(N)2 reaction Cl- + CD3Br --> ClCD3 + Br- and the reverse process Br- + CD3Cl --> BrCD3 + Cl-, employing a fine energetic resolution to resolve all scattering resonances. The two totally symmetric modes of the methyl group, C-D symmetric stretch and umbrella bend, are explicitly taken into account. Converged state-selected reaction probabilities and product distributions have been calculated up to 2960 cm(-1) above the vibrational ground state of CD3Br, i.e., up to initial vibrational excitation of the second overtone of the umbrella bending vibration. The inverse secondary kinetic isotope effect found experimentally is nicely confirmed by the calculated state-selected reaction probabilities. One contribution to this originates from excitation of the high-frequency symmetric C-D stretching vibration, which increases the reaction probability as a function of translational energy more than the corresponding vibration in the undeuterated system. Although transition state theory (TST) suffices to explain this effect qualitatively, the dynamics of S(N)2 reactions is well-known to show strong nonstatistical features. A striking example is given by the umbrella mode: Contrary to estimates obtained from TST, we find a significant enhancement of the reactivity in the perdeuterated system that is attributed to the increased density of states and the higher number of avoided crossings of the hyperspherical adiabats compared to the undeuterated system. Furthermore, compared to the system Cl- + CH3Cl'/CD3Cl', the influence of tunneling is negligible in this net-barrierless reaction. In the reverse endothermic reaction, the kinetic isotope effect of the umbrella mode is normal.