London-Eyring-Polanyi-Sato potential

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] ... 

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. 

The first and second columns of the Tables give the reaction and potential energy surface used. Standard abbreviations are employed for the names of the potential surfaces. Thus. PK = Porter-Karplus potential surface No 2 for H+H2. LSTH = Liu-Siegbahn-Truhlar-Horowitz potential surface for H+Hg. YLL = Yates-Lester-LIu potential surface for H+Hp. LEPS = extended London-Eyring-Polanyi-Sato potential surface and DIM = diatomics-in-molecules potential surface. 

London-Eyring-Polanyi-Sato potential energy surface No. 3 of Persky and Komweitz. 

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... 

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. 

This expression has seen many developments through the years and has evolved into the so-called London-Eyring-Polanyi-Sato (LEPS) surface in which expression (30) is multiplied by an empirical factor (1 + k)" which is supposed to take account of overlap effects (90). The coulomb and exchange integrals are calculated from the singlet and triplet potential curves of the diatomics, given by the expressions... 

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. 

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. 

It appears to be difficult to state general conditions as to when reactive trajectories in reactions of an atom with a polyatomic molecule could be expected to be reasonably straight lines up to the barrier. In the case of A + BC reactions, however, the problem in question was studied in considerable detail for O + HCl (DCl) reactions [45-48] on two London-Eyring-Polanyi-Sato (LEPS) potential surfaces [49] usually referred to as Surface 1 and Surface II. The two surfaces, although perhaps not very accurate, nevertheless allow us to draw important conclusions of quite general validity. They differ mainly in the shape of the equipotential contours in the region near the H atom ... 

Molecular dynamics studies of diatomic model detonations were first carried out by Karo and Hardy in 1977 [14]. They were soon followed by other groups [15, 16]. These early studies employed predissociative potentials, in which the reactant dimer molecules are metastable and can dissociate exothermically. More realistic models, combining an endothermic dissociation of reactants with an exothermic formation of product molecules, were introduced by White and colleagues at the Naval Research Laboratory and U.S. Naval Academy, first using a LEPS (London-Eyring-Polanyi-Sato) three-body potential for nitric oxide [17], and later a Tersoff-type bond-order potential [18] for a generic AB model, loosely based on NO [19, 20]. 

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)... 

London-Eyring-Polanyi-Sato (LEPS) type potential that goes smoothly from reactant to products. This has been u,sed, for example, on the... 

BEBO = bond-energy-bond-order CID = collision-induced dissociation DC = dynamical correlation DIM = diatom-ics-in-molecules DMBE = double many-body expansion EHF = extended Hartree-Fock FFT = fast Fourier transform IVR = intramolecular energy distribution LEPS = London-Eyring-Polanyi-Sato MBE = many-body expansion MEP = minimum energy path PES = potential energy surface TST = transition-state theory. 

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... 

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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