Recrossing phenomenon

Early in the development of VTST calculations on simple three atom systems compared rates obtained by exact classical dynamics with conventional TST and VTST, the same potential energy surface and classical partition functions being used throughout. These calculations confirmed the importance of eliminating the recrossing phenomenon in VTST. While TST yielded very much larger rate constants than the exact classical calculations, the VTST calculations yielded smaller rate constants, but never smaller than the exact classical values. 

Boltzmann s constant. Actually, the TST expression only holds if all molecules which pass from the reactant over the TS go on to product. To allow for recrossings , where a molecule passes over the TS but is refiected back to the reactant side, a transmission coefficient, k, is sometimes introduced. This factor also allows for the quantum mechanical phenomenon of tunnelling, i.e. molecules that have insufficient energy to pass over the TS may tunnel through the barrier and appear on the product side. The transmission coefficient is difficult to calculate, but is usually close to one, and rarely falls outside the range 0.5-2. At low temperatures the tunnelling contribution... 

Over the years, TST has been modified and corrected for kinetic effects of tunneling, barrier recrossing and medium viscosity, yet, developing a theory that will explain such a phenomenon is an on-going challenge. The next section describes attempts to lay a general foundation for such a theory. 

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