Transition state theory , development potential energy surfaces

The electronic partition function is usually equal to unity. In the transition state theory developed by Polanyi and Eyring, the transition complex is located at the top of the energy barrier (Figure 3.2) and the reaction can be presented a movement along a potential energy surface where the transition state is located at the saddle point. 

A collision theory of even gas phase reactions is not totally satisfactory, and the problems with the steric factor that we described earfier make this approach more empirical and qualitative than we would like. Transition state theory, developed largely by Henry Eyring, takes a somewhat different approach. We have already considered the potential energy surfaces that provide a graphical energy model for chemical reactions. Transition state theory (or activated complex theory) refers to the details of how reactions become products. For a reaction fike... 

The above discussion represents a necessarily brief simnnary of the aspects of chemical reaction dynamics. The theoretical focus of tliis field is concerned with the development of accurate potential energy surfaces and the calculation of scattering dynamics on these surfaces. Experimentally, much effort has been devoted to developing complementary asymptotic techniques for product characterization and frequency- and time-resolved teclmiques to study transition-state spectroscopy and dynamics. It is instructive to see what can be accomplished with all of these capabilities. Of all the benclunark reactions mentioned in section A3.7.2. the reaction F + H2 —> HE + H represents the best example of how theory and experiment can converge to yield a fairly complete picture of the dynamics of a chemical reaction. Thus, the remainder of this chapter focuses on this reaction as a case study in reaction dynamics. 

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

Dynamics on two-basin potential energy surfaces has been extensively explored in the context of chemical reactions over the past several decades [1-14]. Transition state theories (TST), first developed by Eyring [3] and Evans [4] and by Wigner [5] in the 1930s, have had great success in elucidating absolute reaction rates of chemical reactions. All the various forms of (classical) TST are based on two fundamental assumptions ... 

In 1984 Krauss and Stevens described tests and applications of the effective potential method used to gain knowledge of the electronic structure of the molecules in order to analyze the accuracy of the experimentally deduced dissociation energies of refractory metal salts [3]. They used the development of ab initio theoretical methods for the calculation of potential energy surfaces, which further allowed the direct computation of certain rate constants. Transition state theory was also utilized for this computation of some rate constants. However, as discussed by Krauss and Stevens, as of the mid 1980 s computational techniques were not yet readily applied to atmospheric science. Computing power and theoretical methods since these seminal reports have been greatly advanced. 

Henry Eyring and Michael Polanyi independently developed transition state theory, which gave a meaning to the activated complex (Figure 2.4). They explained chemical reactions in terms of the movement of a hypothetical particle on the potential surface defined by energy and the geometry of the atoms that participate in the reaction. The transition state is a saddle point on the potential surface between the reactant and the product. It was believed that the transition state should be passed extremely rapidly and that it would be almost impossible to observe it experimentally. 

We focus attention on both the theory of rates and the electronic mechanism for generic chemical processes. An exact quantum mechanical transition state theory was early developed by Miller [18] and rate expressions were derived from quantum scattering theory [19]. That approach and subsequent developments are based upon the reactive BO potential energy surfaces where the familiar case concerns a reaction accompanied by a smooth change in the overall electronic energy surface [20], The R-BO approach does not have such adiabatic changes of electronic states and it is of interest to see the way quantum scattering theory handles the problem in this new context. 

The determination of the specific sites at which the interaction between two chemical species is going to occur, is of fundamental importance to determine the path and the products of a given reaction. In principle, from a theoretical viewpoint, one should calculate the potential energy surface associated with the interacting species, to obtain the reaction coordinate that allows one to establish the path followed by the reacting molecules to reach the transition state and the final products. However, in practice, this procedure may be very complicated and, in general, it may not necessarily lead one to obtain simple chemically significant information to establish the behavior of a family of molecules with respect to a family of reactants. Thus, over the years, chemists have developed intuitive concepts and simple theories that have allowed them to understand the behavior of molecules under different circumstances, their reactive sites, and possible reaction mechanisms. 

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