Quantum Mechanical Effects on Reaction Coordinate Motion

Like Eq. (27.2), Eqs. (27.11) and (27.12) are also hybrid quantized expressions in which the bound modes are treated quantum mechanically but the reaction coordinate motion is treated classically. Whereas it is difficult to see how quantum mechanical effects on reaction coordinate motion can be included in VTST, the path forward is straightforward in the adiabatic theory, since the one-dimensional scattering problem can be treated quantum mechanically. Since Eq. (27.12) is equivalent to the expression for the rate constant obtained from microcanonical variational theory [7, 15], the quantum correction factor obtained for the adiabatic theory of reactions can also be used in VTST. 

Quantum Mechanical Effects on Reaction Coordinate Motion 

Rather than compute the reaction probabilities for all quantum states that contribute significantly to the sum in Eq. (27.14), we approximate the probabilities for all excited states by the probabilities for the ground state with the energy shifted by the difference in adiabatic barrier heights (relative to a single overall zero of energy) for the excited state, V (n, A), and ground state, [16  

We first consider the case where the reaction probabilities are computed for the adiabatic model with the reaction-path curvature neglected, the so-called vibrationally adiabatic zero-curvature approximation [36]. We approximate the quantum mechanical ground-state probabilities P (E) for the one-dimensional scattering problem by a uniform semiclassical expression [48], which for E is given by 

When one uses CVT, one must replace by an approximation that is con- 

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In the previous sections, we quantized the F — 1 degrees of freedom in the dividing surface, but we still treated the reaction coordinate classically. As discussed, such quantum effects, which are usually dominated by tunneling but also include nonclassical reflection, are incorporated by a multiplicative transmission coefficient k(T). In this section, we provide details about methods used to incorporate quantum mechanical effects on reaction coordinate motion through this multiplicative factor. 

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