London-Eyring-Polanyi-Sato function

The traditional approach for performing classical trajectory simulations is to represent V(q) by either an empirical analytic function, with adjustable parameters, or as an analytic function fit in total or in part to ab initio potential energies. A widely used empirical potential is the London-Eyring-Polanyi-Sato function for triatomic systems. Since the number of independent coordinates is 3N — 6 for a nonlinear system with N atoms, to fit V(q) with potential energies for each internal coordinate at NP different positions, a total of (] p)3N-6 initio points are required. Thus, only for reactive systems with a small number of atoms is it practical to derive y(q) completely from... 

LEPS (London-Eyring—Polanyi—Sato) Potential—approximate polyatomic potential surface obtained from diatomic Morse functions and related repulsive functions. 

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]. 

The potential energy surface used for the CH4 + OH CH3 + H2O reaction combines an accurate potential function for H2O [31] with a London-Eyring-Polanyi-Sato (LEPS) function to describe the C-H and OH reactive bonds. The potential has accurate reactant and product ro-vibrational energy levels, correct bond dissociation energies and transition state geometries in reasonable accord with ah initio data [13,14]. It also incorporates the zero point energies of all modes not explicitly treated in the RBA calculations. 

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)... 

The PE function was proposed by London for H + H2 —> H2 + H, collinear system and subsequently was modified by Eyring, Polanyi and Sato. One widely used form of the LEPS function is given by... 

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