Vibrationally adiabatic model

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)... 

Since chemical reactions usually show significant nonadiabaticity, there are naturally quantitative errors in the predictions of the vibrationally adiabatic model. Furthermore, there are ambiguities about how to apply the theory such as the optimal choice of coordinate system. Nevertheless, this simple picture seems to capture the essence of the resonance trapping mechanism for many systems. We also point out that the recent work of Truhlar and co-workers24,34 has demonstrated that the reaction dynamics is largely controlled by the quantized bottleneck states at the barrier maxima in a much more quantitative manner than expected. 

Vibrationally adiabatic model an ultra simple model 123... 

The quantization of the transition state number of states (Eq. (2.8)) can be justified for a separable reaction coordinate or for a vibrationally adiabatic model [21, 22]. Furthermore, in these cases, one may also include the effect of... 

Collinear models may be extended to include the centrifugal forces that arise from rotation of the three-atom axis. This has been done by Wyatt (1969), who studied H + H2 reactive collisions with a vibrational adiabatic model. The required coordinates are (xAB,xBC), and new ones (0, axial orientation. Transforming (xAB,xBC) to curvilinear coordinates (s, r) he expressed the total wavefunction as... 

The results of the present calculations that the zero-point vibrational energy of the reactants can pass smoothly into that of the intermediate complexes is entirely consistent with the basic postulate of Eyring s theory that activated complexes are created from the reactants in equilibrium states. It is easy to show that the vibrationally adiabatic model, coupled with the assumption that collision cross sections are the same for all vibrational levels, leads to the conclusion that there is a Boltzmann distribution between the vibrational levels in the activated state. Thus, consider the situation represented by the energy diagram shown in Fig. 6 two levels are shown for the initial and activated states— the ground level and the nth vibrationally excited... 

Jaquet and Miller [1985] have studied the transfer of hydrogen atom between neighbouring equilibrium positions on the (100) face of W by using a model two-dimensional chemosorption PES [McGreery and Wolken 1975]. In that calculation, performed for fairly high temperatures (T> rj the flux-flux formalism along with the vibrationally adiabatic approximation (section 3.6) were used. It has been noted that the increase of the coupling to the lattice vibrations and decrease of the frequency of the latter increase the transition probability. 

The exchange reactions (6.20) and (6.21) have been among the basic objects of chemical-reaction theory for half a century. Clearly further investigation is needed, incorporating real crystal dynamics. It is worth noting that the adiabatic model, upon which the cited results are based, can prove to be insufficient because of the low frequency of the promoting vibrations. 

In the meantime other experiments have also improved our range of observational results. For example, Watts et al. carried out experiments very similar to the NO/Ag(lll) experiments described above.32 A critical difference in this work was the substitution of Cu(110) in place of the Ag(lll). Despite the chemically distinct metal surface, nearly identical results were obtained as those in Refs. 24 and 25, including surface temperature and incidence energy dependence. While it is not unlikely that the bond softening of NO is similar on Ag(lll) and Cu(110), there is no a priori reason to believe that these two metals would exhibit the same incidence energy and surface temperature dependence in vibrational excitation experiments. More importantly, there has not been a theoretical attempt to explain why these two chemically distinct systems behave so similarly within the context of electronically adiabatic models. 

Figure 32. Vibronic periodic orbits of a coupled electronic two-state system with a single vibrational mode (Model IVa). All orbits are displayed as a function of the nuclear position x and the electronic population N, where N = Aidia (left) and N = (right), respectively. As a further illustration, the three shortest orbits have been drawn as curves in between the diabatic potentials Vi and V2 (left) as well as in between the corresponding adiabatic potentials Wi and W2 (right). The shaded Gaussians schematically indicate that orbits A and C are responsible for the short-time dynamics following impulsive excitation of V2 at (xo,po) = (3,0), while orbit B and its symmetric partner determine the short-time dynamics after excitation of Vi at (xo,po) = (3, —2.45).

The most extensive potential obtained so far with experimental confirmation is that of Le Roy and Van Kranendonk for the Hj — rare gas complexes 134). These systems have been found to be very amenable to an adiabatic model in which there is an effective X—Hj potential for each vibrational-rotational state of (c.f. the Born Oppenheimer approximation of a vibrational potential for each electronic state). The situation for Ar—Hj is shown in Fig. 14, and it appears that although the levels with = 1) are in the dissociation continuum they nevertheless are quasi bound and give spectroscopically sharp lines. 

Another way of calculating the distribution of product states would be to apply an extension of RRKM that Wardlaw, Klippenstein, and I developed. However, judging from your observations, the reaction is highly vibrationally nonadiabatic, considering, for example, the considerable difference in vibrational quantum number vco in HCO and CO and the major change in bending — rotational state. In that case a Franck-Condon approach would seem to be much more appropriate than any adiabatic or near-adiabatic or statistically adiabatic model. 

Romelt, J. (1983). Prediction and interpretation of collinear reactive scattering resonances by the diagonal corrected vibrational adiabatic hyperspherical model, Chem. Phys. 79, 197-209. 

Hofacker and Levine have proposed a non-adiabatic model in which the product vibrational distributions are described by a single parameter g, taken as a measure of the attractive character of the potential energy surface. In this model, g /2 is equal to Eyfhcw. We find that the BaX vibrational distributions are fit moderately well to the functional form given by Hofacker and Levine and that the parameter g increases monotonically along the series. Such a model shows promise as a means of relating the details of the product internal state distribution to the potential energy surface of the reaction. 

---