Eyring-Polanyi equation

Transition State Theory (TST) connects thermodynamic properties of adsorbates and of the transition state (TS) with the rate constant. Two main assumptions are made in TST. The first is that the time scale to either break or form a bond is longer than the time needed for energy redistribution among internal energy levels of a state along the reaction coordinate. This means that states, either initial or final, can be described using thermodynamics. The second assumption is that the molecules at the TS are in quasi-equilibrium with the reactants. Under these assumptions, the reaction rate constant is described by the Eyring-Polanyi equation [15] ... 

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),... 

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... 

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. 

Initially, Hine (1966a) related PLM to the London-Eyring-Polanyi approach to three-center reactions. Since this method cannot easily be applied to most systems of interest, approximate methods have to be used. One of these minimizes bond motions and bond distortions. The geometric changes in pentadienyl or cyclohexadienyl anions brought about by protonation (Bates et al., 1967) in equation (192) are assumed to be roughly parallel to changes in bond order (BO). For deuteriation on the end carbons, 27(BO)2 = 2(2/3)2 + 2(l/3)2 = 10/9 for deuteriation... 

For their calculations, Polanyi and co-workers and Karplus, Porter, and Sharma (20) have employed versions of the LEPS (London-Eyring-Polanyi-Sato) potential, which has some connection with formal theory since it is based on the London equation for a system of three atoms [320] ... 

In the London-Eyring-Polanyi-Sato (LEPS) method224 the original London equation is multiplied by an empirical factor which is supposed to account for the effect of overlap. 

During the three productive years of a postdoctoral stay in Mark s Laboratory, Robert extended Einstein s equation (originally derived for linear stress gradient) to parabolic Poiseuille flow. There were excursions with Eirich into kinetic theory and viscosity of gaseous paraffins, as well as viscosity, surface tension, and heat of vaporization correlations of chain molecular fluids. The latter made use of the recently formulated transition-state theory of Eyring, Polanyi, and Wigner. 

The pre-exponential factor of this Arrhenius equation was given without demonstration as a known result of the theory of the transition state established by Wigner, Eyring, Polanyi, and Evans in 1930 (Laidler and King 1998). 

The use of known diatomic potentials to estimate the three-atom potential function is at the heart of the so-called London-Eyring-Polanyi(-Sato) (LEP(S)) method. This is a semi-empirical scheme based on the London equation, originally intended to deal with four one-electron S-state atoms. In its most primitive form, we begin by writing the potential between two atoms as a stun of a coulomb (Q)... 

DIM/LEPS The method of diatomics-in-molecules (DIM) is based on the definition of states for the atoms in the system (molecule) that are coupled to describe states of diatomic, triatomic, etc., groups. The simplest form of DIM is the LEPS (London-Eyring-Polanyi-Sato) equation. ... 

Semiempirical potential energy calculations of triatomic reactive systems are usually carried out using either the London equation, as in the London-Eyring-Polanyi-Sao (LEPS) method, ... 

For many years the Tafel equation was viewed as an empirical equation. A theoretical interpretation was proposed only after Eyring, Polanyi and Horiuti developed the transition-state theory for chemical kinetics, in the early 1930s. Since the Tafel equation is one of the most important fundamental equations of electrode kinetics, we shall derive it first for a single-step process and then extend the treatment for multiple consecutive steps. Before we do that, however, we shall review very briefly the derivation of the equations of the transition-state theory of chemical kinetics. 

Equation (9.31) is known as London equation and has been used by Eyring and Polanyi (1931) in their semiempirical calculation of a PES for H-H-H system and then used by many workers for a variety of reactions. The... 

The physicists developed impressive equations which were supposed to represent the solutions to chemical problems, and they became discouraged because the chemists found it too difficult to test the equations numerically. In contrast, the chemists, such as Polanyi, Pauling, and Eyring, made whatever additional assumptions were required in order to get numerical solutions quickly and easily. The chemists approach resembled engineering empiricism. They invented simple formulas which superficially agreed with the physicists theoretical results on the one hand, and which possessed... 

The Arrhenius equation, interpreted using the theory of Eyring, Evans, and M. Polanyi, seems at first glance to contain virtually all the information one would need to know about reaction kinetics. However, as hinted at previously, a number of reactions have been observed to exhibit behavior that does... 

Simultaneous with Eyring s work, Evans and Polanyi [17] developed equivalent rate equations, but Eyring and Wynne-Jones [18] immediately extended TS to solutions by connecting with the macroscopic thermodynamic quantities AH and AS, thus providing the link from molecular collision theory all the way to these phenomenological macroscopic quantities. 

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