Potential energy surface London-Eyring-Polanyi

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... 

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. 

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]. 

Several important modifications have been made of the semiempirical procedure of Eyring and Polanyi for calculating the potential-energy surface. Sato [4] has used the Heitler-London formulation to obtain the following... 

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. 

The formalism for the quasiseparation of nuclear coordinates from electronic coordinates was introduced by Born and Oppenheimer in 1927 [12]. However, it was the 1929 paper by London [13] and the 1931 paper by Eyring and Polanyi [14] that introduced the potential-energy surface (PES) for a chemical reaction and thus created the conceptual framework for modern kinetic theory. The following year Pelzer and Wigner [15] identified the saddle point on the PES as the TS. The stage had been set. 

In 19, four years after the breakthrough of the Heitler-London quantum treatment of the H + H problem, Eyring and Polanyi provided the first potential energy surface describing the motion of three atoms (Fig. 2) ... 

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. 

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

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. 

We notice that the molecule can pass either an early barrier located in the entrance channel (where r the gas phase equilibrium distance) or a late barrier in the exit channel where r > If the barrier is late, then vibrational excitation of the incoming molecule enhances the dissociative sticking process if it is early, the dissociation is enhanced by increasing the translational energy of the molecule. This early and late barrier discussion is therefore identical to the one known from gas-phase reaction dynamics [123]. Thus it is natural to try to use similar model potentials in molecule surface interaction to those which have been used in gas-phase dynamics. Such a model potential is the one due to London, Eyring, Polanyi, and Sato, in short, denoted the LEPS potential. 

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. 

The hydrogen exchange reaction H -I- H2 H2 + H is the simplest of all neutral reactions. It can be studied experimentally using isotopes (D + H2 —> DH + H) or ortho- and para-H2, i.e. H + para-H2 —> ortho-H2 -H H. In para-H2 the nuclear spins are anti-parallel in ortho-H2 the nuclear spins are parallel. Eyring and Polanyi (1931) carried out the first quantum-mechanical calculation of the H3 potential surface, but the remarkable fact is that it was not until 1965 that Kuntz, Nemeth and l.C. Polanyi using the London equation calculated the PES for H3. In contrast, an extensive body of data from crossed-beam reaction studies and modern and accurate ab initio calculations (see below) demonstrate that there is no potential well but a saddle point on the H3 energy surface. 

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