LEPS potential

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),... 

It should also be mentioned that a theoretical model using an empirical LEPS potential energy surface has successfully been used to reproduce the vibrational population distribution of the products of this surface reaction.40 This approach confines itself to the assumptions of the Born-Oppenheimer approximation and underscores one of the major questions remaining in this field do we just need better Born Oppenheimer potential surfaces or do we need a different theoretical approach ... 

Reaction of gas-phase molecules with metal surfaces modified LEPS potentials... 

Several researchers have used modified forms of the LEPS potential (see section 1.2 for a discussion of the modifications) to study the dynamics of H2 on the surfaces of various metals. Initial studies of this type were restricted to rigid surfaces, and the parameters in the LEPS surfaces were either determined by fitting to available experimental or theoretical data, or systematically varied to produce potential energy surfaces with specific properties. 

In a series of studies, McCreery, Wolken and coworkers have used a LEPS potential to model reaction of H2 and HD with the W(OOl) surface ... 

This model includes a LEPS potential contribution which mimics a reaction involving three atoms confined to motion along a line. Only one bond can be formed, either between atoms A and B or between atoms B and C. The potential function has the form... 

Porter and Karplus [19] constructed a LEPS potential for H + H2 including overlap and three-center terms in order to evaluate the energies of nonlinear configurations more realistically. Kuntz et al. [313] employed a modified LEPS function in a detailed investigation of metathetical reactions involving three atoms. Three adjustable parameters were included, instead of just S2. This provided a more flexible potential, and it was possible to vary the nature of the potential surface quite considerably. Other potentials based on pairwise interactions have been used for calculations where AB is ionic [72-74, 306],... 

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 ... 

The reaction 0( P) + H2 OH + H is important in combustion and as a prototypical oxygen atom reaction. A considerable number of theoretical and experimental investigations of this reaction that have been reported are quoted in the trajectory study [63] devoted primarily to the effects of reagent rotation in this reaction. The work in [63] is based on Johnson-Winter LEPS potential surface [64] from which also the relevant parameters were derived for the kinematic mass model analysis [61] of the trajectory results in question. 

Consider a diatomic, AB, interacting with a surface, S. The basic idea is to utilize valence bond theory for the atom-surface interactions, AB and BS> along with AB to construct AB,S For each atom of the diatomic, we associate a single electron. Since association of one electron with each body in a three-body system allows only one bond, and since the solid can bind both atoms simultaneously, two valence electrons are associated with the solid. Physically, this reflects the ability of the infinite solid to donate and receive many electrons. The use of two electrons for the solid body and two for the diatomic leads to a four-body LEPS potential (Eyring et al. 1944) that is convenient mathematically, but contains nonphysical bonds between the two electrons in the solid. These are eliminated, based upon the rule that each electron can only interact with an electron on a different body, yielding the modified four-body LEPS form. One may also view this as an empirical parametrized form with a few parameters that have well-controlled effects on the global PES. 

Figure 25. Two-dimensional contour plots for a LEPS potential of Hj/NiilOO) based upon the ab initio calculations of Siegbahnet al. (1988). The data are from Kara and DePristo (1989).

The particular model used in the original simulation i- of this reaction was that of a Cl + CI2 like reaction as modeled by a LEPS potential energy surface. The barrier for this symmetric reaction was normally taken to be 20 kcal/mol (—33 kT at room temperature). Other simulations used 10 and 5 kcal/mol barriers. The reactants were placed in either a 50 or 100 atom solvent (Ar in the earliest simulations Ar, He, or Xe in the later work) with periodic truncated octahedron boundary conditions. To sample the rare reactive events, as described previously, this system was equilibrated with the Cl—Cl—Cl reaction coordinate constrained at its value at the transition state dividing surface (specifically, the value of the antisymmetric stretch coordinate was set equal to zero). From symmetry arguments, this constraint is the appropriate one (except in the rare case where the solvent stabilizes the transition state sufficiently such that a well is created at the top of the gas phase barrier). For each initial configuration, velocities were chosen for all coordinates from a Boltzmann distribution and molecular dynamics run for 1 ps both forward and backward in time. 

Fig. 6-12 Contour diagram of LEPS potential energy surface for F + H2 system. (Adapted from Muckerman [44].)...

We will first make use of the half-empirical LEPS potential surface, constructed by WESTON /27/yfor two reasons 1. A correction for the bent configurations of the linear collision complex H-H-H was introduced by MORTENSEN and PITZER /71a/ 2. The.transition probabili-ties k, were calculated exactly by MORTENSEN /52,71b/ using both quasiclassical and quantum-mechanical methods. For this purpose the wave function is written as... 

The LEPS potential used is described in Ref. L34J. The bound... 

The H- F2 reaction was the first one. beyond H- H2 and Its Isotopes, for which it was meaningful to compare large scale DW calculations with experiment (Clary and Connor [21]). This reaction has the advantage that a reasonable LEPS potential surface Is available (Jonathan et al. [49]) and the product distributions are insensitive to variations in j and Etr for the thermal energy range. This last property allows a fixed energy calculation for H+F2(v=0. j=0) to be meaningfully compared with thermal infrared chemiluminescence data (Polanyi and Sloan [69]. Brandt and Polanyi [11]). 

Table II shows there have been many SSDW calculations for the F- H2 reaction using the Muckerman 6 LEPS potential surface. The first DW...

The less anisotropic LEPS potential gave a differential cross section that was distributed in both the forward and backward regions. The DIM-3C differential cross section, however, showed only backward scattering - which was in good agreement with experiment [2]. Since the anisotropy in the differential cross section directly reflected aristropy in the molecular potential, thus comparison suggested that the H+Cfi,H potential should be very anisotropic. 

We have used this ab initio data to parameterise a LEPS potential energy surface. Thus our predictions should be realistic. 

We have calculated [53], the full photodissociation spectrum for the dissociation of H2 0 into OH(X tt)+H on the first absorption band, the A state. A LEPS potential was used for the dissociating state in which the Sato parameters were made 0 dependent and were varied to obtain a good fit to the ab initio data of Staemmler and Palma [43]. 

In this expression VhCN accurate global potential for HCN [26], one which determines spectroscopically accurate energy levels for HCN and HNC, and which dissociates correctly. VcN Vhh re experimentally determined Morse potentials for CN and H2, respectively. The specific combination of these diatomic potentials with the two HCN potentials is such that all six pair potentials associated with HHCN are included. V CHH V nHH re 3-body LEPS potentials for CHH and NHH, respectively. They are included so that the four possible 3-body potentials in HHCN are included. V4 is the four-body potential for HHCN, and is generally represented by sums of Gaussian functions which are centered on the stationary points of the full potential. 

The first question is whether such a potential is realistic for our problem. Figure 9 compares it to the LEPS potential [2,11] for the four-center case, while Fig. 10 shows the potential for a six-center atomic configuration. It is to be expected [14,23] that a six-center bond switching will have a significantly lower barrier than the four-center case. 

Figure 9 An equipotential contour plot for the potential energy (in kJ/mol) specified by Eqs. (1-3) and the LEPS potential [11] for a rectangular configuration of atoms in the four-center N2 + N2 - 2NN reaction. The axes are the old and new bond distances (in A) which specify a rectangular configuration.

---