Transition state vibrationally adiabatic

If K is adiabatic, a molecule containing total vibrational-rotational energy E and, in a particular J, K level, has a vibrational density of states p[E - EjiJ,K). Similarly, the transition state s sum of states for the same E,J, and Kis [ -Eq-Ef(J,K)]. The RRKM rate constant for the Kadiabatic model is... 

Quack M 1981 Faraday Discuss. Chem. Soc. 71 309-11, 325-6, 359-64 (Discussion contributions on flexible transition states and vibrationally adiabatic models statistical models in laser chemistry and spectroscopy normal, local, and global vibrational states)... 

As stated by inequality (2.81) (see also section 4.2 and fig. 30), when the tunneling mass grows, the tunneling regime tends to be adiabatic, and the extremal trajectory approaches the MEP. The transition can be thought of as a one-dimensional tunneling in the vibrationally adiabatic barrier (1.10), and an estimate of and can be obtained on substitution of the parameters of this barrier in the one-dimensional formulae (2.6) and (2.7). The rate constant falls into the interval available for measurements if, as the mass m is increased, the barrier parameters are decreased so that the quantity d(Vom/mn) remains approximately invariant. 

I would like to ask Prof. J. Troe whether he could discuss some typical situations where the SAC approximation may fail. For example, consider the F + HBr — FHBr — HF(u) + Br reaction with energy E just above the potential barrier V41. In this situation, the adiabatic channels in the transition state ( ) should be populated only in the vibrational ground state, and they should, therefore, yield products HF(u = 0) + Br, according to the assumption of adiabatic channels. This is in contrast with population inversion in the experimental results that is, the preferred product channels are HF(i/) + Br, where v = 3, 4 [1] see also the quantum scattering model simulations in Ref. [2]. The fact that dynamics cannot be rigorously adiabatic (as in the most literal interpretation of SAC) has been discussed by Green et al. [3], and the most recent results (for the case of ketene) are in Ref. 4. 

These relaxation times correspond to rates which are about 106 slower than the thermal vibrational frequency of 6 x 1012 sec 1 (kBT/h) obtained from transition state theory. The question arises how much, if any, of this free energy of activation barrier is due to the spin-forbidden nature of the AS = 2 transition. This question is equivalent to evaluating the transmission coefficient, k, that is, to assess quantitatively whether the process is adiabatic or nonadiabatic. 

In this case, again only a one-dimensional instanton exists. The transverse frequency increases when moving along the MEP from the well to the transition state. So we have an effect of dynamically induced barrier formation in which the height of the vibrationally adiabatic barrier exceeds V. The analysis of this squeezed potential by Auerbach and Kivelson [1985] shows that the vibrationally adiabatic approximation is valid when... 

PES is characterized by an early transition state that is, the saddle point is strongly shifted toward the reactant valley so that the reaction barrier is overcome without appreciable lengthening of the Cl-Cl bond. Since the angle between the valleys is less than 90° and the intramolecular vibration frequencies are much greater than a>0, criterion (2.86) indicates that this reaction takes place in the vibrationally adiabatic regime. 

The dynamics of a reaction that proceeds directly over the transition state is expected to be qualitatively different from that of a resonance-mediated reaction. In particular, one expects that the branching ratios into the product rovibrational states will be very different between the direct and the resonant mechanisms. For example, if a given Feshbach resonance corresponds to trapping on the v = 1 vibrationally adiabatic curve, then one might expect that the population of the v = l vibrational state of the product molecule may be greatly enhanced by the resonant mechanism. Similarly, the rotational product distribution resulting from the fragmentation of a resonance molecule may show a quite distinct pattern from that of a direct reaction. Indeed, Liu and coworkers [94], and Nesbitt and coworkers [95] have noted distinct rotational patterns in the F+HD resonant reaction. 

---