Electronically Non-adiabatic reactions

All the reactions we have considered so far have been adiabatic, by which we mean that they occur on a single adiabatic PES that is unperturbed by other electronic states. In addition, we have assumed that the surface is the lowest (ground) electronic state connecting the reactants and products. If, for a specified reaction, there is an excited state PES near enough to the ground state for the two to interact, it is possible for the reaction to occur on both surfaces. Reactions that can occur on more than one PES are called non-adiabatic reactions. The reaction on one surface may give different products, or the same products but in different electronic states, than does reaction on another surface. When a reaction involves reactants and/or products in electronically excited states, non-adiabatic reactions must be considered. 

An example of this behavior is provided by the thermal decomposition of CO2 to CO and O atoms. In the absence of perturbation by an excited state adiabatic dissociation of the ground state, C02( Sg ) would result in formation of singlet ground state CO and an excited 0( D) atom as required by the Wigner-Witmer spin conservation rule [21] 

A reaction path following the lower branch of an avoided crossing between the ground state singlet PES and the excited state triplet PES 

The Landau-Zener model illustrates the important variables influencing the probability of non-adiabatic transitions, but as a ID model it is only applicable to bimolecular reaction of two atoms. For most reactions of interest it is too simple to provide accurate results. For reactions involving more than two atoms the PESs are multidimensional, as we have seen above, and the avoided crossing region on a multidimensional surface is described as a conical intersection [61]. The best method for handling this complex multidimensional reactive scattering problem is trajectory calculations. Fernandez-Ramos et al. [52] has discussed approaches to this problem as part of a recent review of bimolecular reaction rate theory. It is fortunate that the vast majority of chemical reactions occur adiabatically. It will only be necessary to delve into the theory of non-adiabatic reactions when a non-adiabatic reaction is present in a reaction model, experimental data are not available, and the reaction rate influences the overall rate appreciably. 

Some elementary chemical reactions follow a third order rate expression at all normally accessible experimental conditions, and according to the definitions of molecularity must be classified as termolecular. The most common example is the combination of two atoms in the presence of a third species. The rate expression is r = A ( J)[A] [M] for combination of Hke atoms. A, in the presence of the collider or heat bath species M. These reactions do not occur by the simultaneous collision of all three species, which is a very rare event, but by two bimolecular steps that take place within lpsec of one another. An energy transfer mechanism of the reaction may be written as follows  

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We would like to complete this section by briefly describing some of the recent developments on electronically non-adiabatic reactions. From the standpoint of the coupled-channels method, there is in principle no added difficulty in treating more than one electronic state of the reactive system. This may be done, for example, by keeping electronic degrees of freedom in the Hamiltonian and expanding the total scattering wavefunction in the electronic states of reactants and products. In practice, however, some new difficulties may arise, such as non-orthogonality of vibrational states on different electronic potential surfaces. There is at present a lack of quantum mechanical results on this problem. 

Introducing this expression in (77.IV) yields a rate equation for electronically non-adiabatic reactions... 

IV), the apparent activation energies depend solely on the solvent properties, so that the isotope substitution affects only the frequency factors through the proton vibration frequency Vy Therefore, from (83.IV) and (87.IV) for electronically non-adiabatic reactions, we get the equations... 

J. M. Bowman, S. C. Leasure, and A. Kuppermann, Large quantum effects in a model electronically non-adiabatic reaction ... 

Baer M 1985 The theory of electronic non-adiabatic transitions in chemical reactions Theory of Chemical Reaction Dynamics vol II, ed M Baer (Boca Raton, FL CRC Press) p 281... 

In a two-lowest-electronic-state Bom-Huang description for a chemical reaction, the nuclei can move on both of two corresponding PESs during the reaction, due to the electronically non-adiabatic couplings between those states. A reactive scattering formalism for such a reaction involving a triatomic system... 

A special case of a non-adiabatic reaction is electron transfer. The dynamics of electron-transfer processes have been studied extensively, and the most robust model used to describe... 

Figure 2.1(a) above illustrates the potential energy surface for a diabatic electron transfer process. In a diabatic (or non-adiabatic) reaction, the electronic coupling between donor and acceptor is weak and, consequently, the probability of crossover between the product and reactant surfaces will be small, i.e. for diabatic electron transfer /cei, the electronic transmission factor, is transition state appears as a sharp cusp and the system must cross over the transition state onto a new potential energy surface in order for electron transfer to occur. Longdistance electron transfers tend to be diabatic because of the reduced coupling between donor and acceptor components this is discussed in more detail below in Section 2.2.2. 

These monolayers provide a significant opportunity to compare the extent of electronic communication across the p3p bridge when bound to a metal electrode as opposed to being coupled to a molecular species, e.g. within a dimeric metal complex. Electronic interaction of the redox orbitals and the metallic states causes splitting between the product and reactant hypersurfaces, which is quantified by HabL the matrix coupling element. The Landau-Zener treatment [15] of a non-adiabatic reaction yields the following equation ... 

A two-state model is possible for PCET reactions that involve electronically adiabatic PT. This two-state model is convenient for the derivation of a rate expression in the limit of electronically non-adiabatic ET. The first step is to transform the VB basis set to another equivalent basis set. The new basis functions are defined to be the eigenvectors of the two matrices... 

The distance between the electron donor and acceptor affects the rates and mechanisms of PCET reactions in two different ways. First, an increase in this distance results in a decrease in the coupling between ET states (la/2a, aj2b, bj2a, bj2b). In the limit of electronically non-adiabatic electron transfer, a decrease in this coupling results in a decrease in the rate. Moreover, as the distance between the electron donor and acceptor increases, the interaction between the proton and the electron decreases. Thus, for a symmetric PT system with an initial state of la, EPT is favorable for short electron donor-acceptor distances and ET becomes equally favorable as this distance increases. 

On the other hand, for a non-adiabatic reaction, k i 1, /CeiVn = Vgi and the rate constant is given by Eq. 23 where Vei is the electron hopping frequency in the activated complex. The Landau-Zener treatment yields Eq. 24 for Vei [16, 17]. 

Lepetit B.. Launay J.-M. and M. Le Dourneuf (1986) Quantum mechanical study of electronically non-adiabatic colUnear reactions. I. Hyperspherical description of the clectronuclcar tlynamics Chem. Phys. 106, 103-110. 

The slow peak at 6 30 has a fast shoulder. A similar feature appears in other TOP spectra that sample v= 3 product near 6 180 , and this could be fit only by assuming it was due to HF(v>3) from reactants with approximately 1 kcal/mol internal excitation. This product, designated as v 3, could originate from spin-orbit excited F( P1/2) which lies 1.16 kcal/mol above the P3/2 ground state and constitutes 21Z of the F beam at 920 K, but the reaction between F( Px/2) And H2 can only occur by an electronically non-adiabatic process and is expected to be inefficient (25-26). It is more likely that the v 3 product is from the reaction of F(2p3/2> with H2(J=2) which is 1.03 kcal/mol above H2[Pg.485]

Spin-forbidden reactions are a subset of the broader class of electronically non-adiabatic processes, which involve more than one PES. The fundamental theory of how such processes occur is well understood (7-9), and a very large amount of research is being performed with the aim of elucidating more details in all the areas of nonadiabatic chemistry. It is not possible to present this work here, so I will instead provide an outline of the most important theoretical insights in the... 

In an electronically non-adiabatic process the description of the nuclear motion involves more than one PES. Electronic spectroscopy and photochemical reactions involve transitions between two or more PES in critical regions (avoided crossings, conical intersections, crossings) where the nature of the electronic wave function may change rapidly as a function of the nuclear displacement. This is illustrated in Scheme 4 which represents two different... 

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