Eyring potential energy surface

Before discussing the kinds of kinetic information provided by potential energy surfaces we will briefly consider methods for calculating these surfaces, without going into detail, for theoretical calculations are outside the scope of this treatment. Detailed procedures are given by Eyring et ah There are three approaches to the problem. The most basic one is purely theoretical, in the sense that it uses only fundamental physical quantities, such as electronic charge. The next level is the semiempirical approach, which introduces experimental data into the calculations in a limited way. The third approach, the empirical one, makes extensive use of experimental results. 

The semiempirical methods combine experimental data with theory as a way to circumvent the calculational difficulties of pure theory. The first of these methods leads to what are called London-Eyring-Polanyi (LEP) potential energy surfaces. Consider the triatomic ABC system. For any pair of atoms the energy as a function of intermolecular distance r is represented by the Morse equation, Eq. (5-16),... 

Fig. 1. Potential energy surface and classical trajectory calculations on the H + H2 hydrogen exchange reaction. Note the orbiting trajectory in the vicinity of Lake Eyring . Despite the unrealistic nature of a well near the transition state of this reaction, many of the modern ideas of chemical reaction theory can be seen in action already in this work. (See Ref. 1.)...

On the basis of London equation (9.31), Eyring and Polanyi calculated the potential energy surface, which is known as London-Eyring-Polanyi (LEP) surface. In this treatment, the coulombic energy A and exchange energy a for a diatomic molecule have been assumed to be the constant fractions of the... 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

The VB simplified model of ground-state potential energy surface H3 system considered as transition state and stabilization valleys of the H + H2 reaction is also an early problem, belonging to the history of physical chemistry under the name London-Eyring-Polanyi-Sato (LEPS) model that continues to serve as basis of further related developments [17,18], The actual analysis is a new a focus on the JT point of this potential energy surface able to absorb results of further renewed CASCCF type calculations on this important system. 

Henry Eyring, American chemist. Bom Colonia Juararez, Mexico, 1901. Ph.D. University of California, Berkeley, 1927. Professor Princeton, University of Utah. Known for his work on the theory of reaction rates and on potential energy surfaces. Died Salt Lake City, Utah, 1981. 

The London-Eyring-Polanyi-Sato (LEPS) method is a semi-empirical method.8 It is based on the London equation, but the calculated Coulombic and exchange integrals are replaced by experimental data. That is, some experimental input is used in the construction of the potential energy surface. The LEPS approach can, partly, be justified for H + H2 and other reactions involving three atoms, as long as the basic approximations behind the London equation are reasonable. 

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 ... 

The idea of the existence of a boundary between reactants and products can be traced to the scientific memoirs of Marcelin published in 1915 [26], It was not until 1931 that this idea began to percolate into the thinking of the chemistry community. In that year Eyring and Polanyi published their seminal article on the calculation of the absolute reaction rate for the collinear H + H2 reaction [27], It was in this article, which must be viewed as the origin of the modern theory of chemical reactions, that the concept of a TS separating reactants from products is first quantified. They defined it in terms of the morphology of the potential energy surface. 

More detailed expressions are available from absolute reaction rate theory (Pelzer and Wigner 1932 Evans and Polanyi 1935 Eyring 1935). This approach treats the forward and reverse reaction processes as crossings of molecular systems over a mountain pass on their potential energy surface. Systems at the pass are called activated complexes, denoted by t f... 

The use of the Slater (/w2//ti)W as the temperature independent factor does not obviously follow from a consideration of the potential energy surface, and thus its use must be regarded as an intermingling of the Eyring and the Slater approaches. 

Another early attempt to incorporate chemieal reactions into molecular dynamics of shock waves was the use of the LEPS (London, Eyring, Polanyi, Sato) potential [4], originally developed in the 1930 s to model the H3 potential energy surface. This method can be applied to systems in which each atom interacts with exactly two nearest neighbors, and is therefore suitable for modeling one-dimensional reactive chains [5-6]. It provides a more realistic treatment of energy release as a function of bond formation but is not readily extended to more complex systems. 

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