Vibrationally non-adiabatic model

The vibrationally adiabatic approximation is hardly justified, because the reaction channel is curved. This means that motion along s couples with some vibrational modes, and also the vibrational modes couple among themselves. We have therefore to use the non-adiabatic theory and this means we need coupling coefficients B. The Miller-Handy-Adams reaction path Hamiltonian theory gives the following expression for the Bkk - 

If the derivative in the above formula is multiplied by an increment of the re-aetion path A, we obtain whieh represents a ehange of normal mode 

Curvature coupling constant B s links the motion along the reaction valley with the normal modes orthogonal to the IRC (Fig. 14.6)  

Intermolecular Motion of Electrons and Nuclei Chemical Reactions 

Bks (s) makes energy flow from the normal mode to the reaction path (or vice versa) much easier. 

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Energy Close to IRC Vibrational Adiabatic Approximation Vibrational Non-Adiabatic Model... 

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. 

The great majority of reactive collinear collisions have been studied computationally, with physical insight being extracted from the final numerical results. An alternative to this approach is the development of models that may be interpreted in terms of approximate analytical solutions. This has been done by Hofacker and collaborators. A non-adiabatic model was introduced (Hofacker and Levine, 1971) to describe population inversion in reactions. It makes use of reaction path coordinates and assumes harmonic vibrational motion perpendicular to the path. 

Figure 3.44. Dissociation of 02 adsorbed on Pt(lll) by inelastic tunneling of electrons from a STM tip. (a) Schematic ID PES for chemisorbed Of dissociation and illustrating different types of excitations that can lead to dissociation, (b) Schematic picture of inelastic electron tunneling to an adsorbate-induced resonance with density of states pa inducing vibrational excitation (1) competing with non-adiabatic vibrational de-excitation that creates e-h pairs in the substrate (2). (c) Dissociation rate Rd for 0 as a function of tunneling current I at the three tip bias voltages labeled in the figure. Solid lines are fits of Rd a IN to the experiments with N = 0.8, 1.8, and 3.2 for tip biases of 0.4, 0.3, and 0.2 V, respectively and correspond to the three excitation conditions in (a). Dashed lines are results of a theoretical model incorporating the physics in (a) and (b) and a single fit parameter. From Ref. [153].

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

The computational approach of Kuppermann (1971) has recently been applied by Baer (1974) to H + Cl2 and D + Cl2 reactions, partly to improve upon previous calculations that neglected some closed channels. He used a LEPS surface with a barrier of 0-108eV in the entrance valley. Reaction probabilities for H + Cl2 from i = 0,1. 2 to rf < 7 showed that the 0 - 4 transition dominated at low energies, while 0 - 5 and then 0 -> 6 dominated as energies increased. The general trend was the same for vt = 1 or 2, but, in detail, the distributions of v depended on ly These dependencies were discussed in terms of a model of vertical non-adiabatic transitions between two displaced vibrational wells. Results with t,- = 0 for D + Cl2 showed that 0 — 5 dominated at low energies. Total transition probabilities were weakly dependent on both vt and isotopic masses. 

Electron-jump in reactions of alkali atoms is another example of non-adiabatic transitions. Several aspects of this mechanism have been explored in connection with experimental measurements (Herschbach, 1966 Kinsey, 1971). The role of vibrational motion in the electron-jump model has been investigated (Kendall and Grice, 1972) for alkali-dihalide reactions. It was assumed that the transition is sudden, and that reaction probabilities are proportional to the overlap (Franck-Condon) integral between vibrational wavefunctions of the dihalide X2 and vibrational or continuum wave-functions of the negative ion X2. Related calculations have been carried out by Grice and Herschbach (1973). Further developments on the electron-jump mechanism may be expected from analytical extensions of the Landau-Zener-Stueckelberg formula (Nikitin and Ovchinnikova, 1972 Delos and Thorson, 1972), and from computational studies with realistic atom-atom potentials (Evans and Lane, 1973 Redmon and Micha, 1974). 

The main conclusion is that the success of this field is due to a close interconnection between analytical and computational approaches. The paper has clearly demonstrated that we need to take into account electron-phonon interactions. In other terms, there exists a timely need to include translational, rotational, vibrational contributions and non-adiabatic approaches in our models. Then the road will be open to complete non-equilibrium interpretations of the electronic properties of macromolecules [89]. 

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