Transition state theory zero-point energy

On this theory, it is assumed (a) that the motion of the reactant-state C-H/D bonds can be thought of as one stretching and two bending motions, and (b) that the bending motions are httle different in the transition state than in the reactant state. Then, the maximum possible isotope effect will be determined by the isotopic zero-point energy difference in the reactant-state C-H/D motion. For a stretching motion with a C-H frequency of 2900 and CD frequency 2130 cm , the isotopic... 

Fortunately, it is relatively simple to estimate from harmonic transition-state theory whether quantum tunneling is important or not. Applying multidimensional transition-state theory, Eq. (6.15), requires finding the vibrational frequencies of the system of interest at energy minimum A (v, V2,. . . , vN) and transition state (vj,. v, , ). Using these frequencies, we can define the zero-point energy corrected activation energy ... 

A final complication with the version of transition-state theory we have used is that it is based on a classical description of the system s energy. But as we discussed in Section 5.4, the minimum energy of a configuration of atoms should more correctly be defined using the classical minimum energy plus a zero-point energy correction. It is not too difficult to incorporate this idea into transition-state theory. The net result is that Eq. (6.15) should be modified... 

The motion in the reaction coordinate Q is, like in gas-phase transition-state theory, described as a free translational motion in a very narrow range of the reaction coordinate at the transition state, that is, for Q = 0 hence the subscript trans on the Hamiltonian. The potential may be considered to be constant and with zero slope in the direction of the reaction coordinate (that is, zero force in that direction) at the transition state. The central assumption in the theory is now that the flow about the transition state is given solely by the free motion at the transition state with no recrossings. So when we associate a free translational motion with that coordinate, it does not mean that the interaction potential energy is independent of the reaction coordinate, but rather that it has been set to its value at the transition state, Q j = 0, because we only consider the motion at that point. The Hamiltonian HXlans accordingly only depends on Px, as for a free translational motion, so... 

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