London-Eyring-Polanyi-Sato method

A multidimensional PES for the reaction (6.45a) has been calculated by Wight et al. [1993] with the aid of the atom-atom potential method combined with the semiempirical London-Eyring-Polanyi-Sato method (see, e.g., Eyring et al. [1983]). Because of high exoergicity, the PES... 

In view of the high cost of ab initio quantum mechanical calculations, simplified procedures have been used in attempts to capture the essential features of potential energy hypersurfaces by approximate means. We discuss two of these, the BEBO (bond-energy-bond-order) method (Johnston and Parr, 1963 Johnston, 1966) and the LEPS (London-Eyring-Polanyi-Sato) method (Sato, 1955). 

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 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. 

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. 

Instead of performing the normal mode analysis we have used a more approximate method to take the qr- -coordinates into account. For the Cl - - CH4/CD4 reactions wc have in some work used a tanh-function in the breaking bond to interpolate between the saddle point and the product asymptote to get both the reaction thermicity and AfA" consistent with the ah initio calculations[18]. In addition, if the effective potential energy surface of the system is modeled by the semiempirical London-Eyring-Polanyi-Sato (LEPS) function, the correction is made directly in the Morse parameters for the two reactive bonds by adjusting the Sato parameters) , 19]. 

A generalization of the method of LONDON-EYRING-POLANYI-SATO (IiEPS) is proposed by J.POLAFYI /28/ for reactions involving three different atoms A,B,C by adjusting different values (S-, 82 S ) of the overlap integral for the three pairs of atoms (AB,AC,BC). 

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. ... 

We shall present results for several kinds of potential energy surfaces. Many of the surfaces are obtained by the London-Eyring-Polanyi-Sato (LEPS) method, involving a single adjustable (Sato) parameter, or by the extended LEPS method, in which different Sato parameters are used for different atomic pairs. These methods are reviewed elsewhere.For other calculations we used rotated Morse curves (RMC),semiempirical valence bond (VB) surfaces, and rotated-Morse-bond-energy-bond-order (RMBEBO) surfaces. 

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