Vibrational adiabaticity

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)... 

The obtained PES forms the basis for the subsequent dynamical calculation, which starts with determining the MEP. The next step is to use the vibrationally adiabatic approximation for those PES degrees of freedom whose typical frequencies a>j are greater than a>o and a>. Namely, for the high-frequency modes the vibrationally adiabatic potential [Miller 1983] is introduced,... 

It is readily seen that when p is large enough and the hyperbolic sines in (4.18) can be replaced by exponents, the effect of the prefactor B, is to replace the potential V s) by the vibrationally adiabatic... 

In order to study the deviations from the vibrationally adiabatic approximation Benderskii et al. [1992b] have considered the situation when the transverse frequency co, switches instantaneously between two values, coi and CO2 (coi > CO2). If Ti and t2 = P the times of occurrence of the... 

In the vibrational-adiabatic limit this formula reduces to the familiar form... 

The adiabatic approximation in the form (5.17) or (5.19) allows one to eliminate the high-frequency modes and to concentrate only on the low-frequency motion. The most frequent particular case of adiabatic approximation is the vibrationally adiabatic potential... 

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. 

Such calculations have been performed by Takayanagi et al. [1987] and Hancock et al. [1989]. The minimum energy of the linear H3 complex is only 0.055 kcal/mol lower than that of the isolated H and H2. The intermolecular vibration frequency is smaller than 50cm L The height of the vibrational-adiabatic barrier is 9.4 kcal/mol, the H-H distance 0.82 A. The barrier was approximated by an Eckart potential with width 1.5-1.8 A. The rate constant has been calculated from eq. (2.1), using the barrier height as an adjustable parameter. This led to a value of Vq similar to that of the gas-phase reaction H -I- H2. 

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. 

Figure 5-3. Active site and calculated PES properties for the reactions studied, with the transferring hydrogen labelled as Hp (a) hydride transfer in LADH, (b) proton transfer in MADH and (c) hydrogen atom transfer in SLO-1. (i) potential energy, (ii) vibrationally adiabatic potential energy, (iii) RTE at 300K and (iv) total reaction path curvature. Reproduced with permission from reference [81]. Copyright Elsevier 2002...

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. 

J. Droe Prof. Zewail, have you analyzed the coherence pattern observed in Hgl from dissociating IHgl with respect to the extent of vibrational adiabaticity of the motion downhill from the energy barrier ... 

A. H. Zewail For vibrational adiabaticity we must complete the study of correlation of reaction product distribution to the nature of the initial excitation (see reply to Prof. Marcus below). You may be interested to know that for a given energy within our pulse we see tra-... 

A. H. Zewail With regard to Prof. Marcus s comment, we have observed the coherence-in-products first in the IHgl system where the wavepacket is launched near the saddle point. The persistence of coherence in products is fundamentally due to (1) the initial coherent preparation (no random trajectories) and (2) the nature of the potential transverse to the reaction coordinate (no dispersion). The issue of vibrational adiabaticity in the course of the reaction, as you pointed out, must await complete final-state analysis for well-defined initial energy. However, we do know that for a given energy of the initial wavepacket a broad distribution of vibrational coherence (in the diatom) is observed. 

Since the transverse vibration frequency at the barrier top is usually lower than co+, the vibrationally adiabatic barrier is lower than the bare one. 

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