LEPS surface

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... 

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. 

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 parameter k is then chosen to give the LEPS surface some desired property, for example a specific activation energy (91-93). Further empirical parameters can give the surface added flexibility (94). 

We have already mentioned (expressions 30—33) the widely used LEPS surface for atom-diatom reactions. This may be regarded as purely empirical or semi-empirical in any modification in which some integrals are evaluated. Another system for which fairly elaborate potential functions have been used is for non-reactive atom-diatom scattering. The experiment for which the potential is designed is the change of rotational or vibrational state of a diatomic molecule by collision with a third atom, and also the quasi bound states, which may be observed spectroscopically, of van der Waals molecules such as Ar—H2 (133). 

As the LEPS surface comprises all vibrational degrees of freedom, it is possible to include the effect of bending in the analysis. To this end, we have carried out the equilibrium point quantization for this system at energies just... 

In the following, we will characterize the different dynamical regimes for CO2 on the LEPS surface. The scenario in a general way resembles the one for Hgl2. However, the initial bifurcations are of the second type described in Section IV.C.2 that is, the symmetric-stretch orbit undergoes a subcritical... 

Figure 16. Scattering resonances of the full rotational-vibrational Hamiltonian describing the dissociation of CO2 on a LEPS surface obtained by equilibrium point quantization with (2.8). The resonances with 7 = 0,..., 10 are given by dots. Their close vicinity explains the formation of hyphens , i.e., unresolved sequences of dots. Note that rotation is very slightly destabilizing in the present model. The successive hyphens are the bending progressions with V2 = 0,. .. 5. The solid line is given by the Lyapunov exponent of the symmetric-stretch periodic orbit 0 expressed as an imaginary energy.

The H3 potential surface which has been most widely used in transition state,2X4 classical dynamical,213 215 and quantum mechanical dynamical216-218 calculations has been the semi-empirical surface of Porter and Karplus.22 Because of the thin potential barrier of the PK surface, one would expect a larger amount of quantum mechanical tunnelling to be predicted at room temperature (this has been found to be the case in calculations performed by Johnston219 on barriers in the very similar LEPS surfaces). However, Karplus et a/.213-216 compared classical and quantum mechanical calculations on the PK surface and found that reaction cross-sections for both are very similar, and therefore that the tunnelling effect in the Ha system is small. 

Quantum mechanical and classical calculations have been performed [245] for H + Cl2 on a recently optimised extended LEPS surface [204]. The quantum mechanical results were transformed to three dimensions by the information theoretic procedure and are in good agreement with the distributions determined in the chemiluminescence experiments. However, three-dimensional trajectory calculations on the surface consistently underestimate (FR) at thermal energies and it is concluded that the LEPS surface which was optimised using one-dimensional calculations does not possess the angular dependence of the true three-dimensional surface. This appears to result from the lack of flexibility of the LEPS form. Trajectory studies [196] for H + Cl2 on another LEPS surface find a similar disposal of the enhanced reagent energy as was found for H + F2. The effect of vibrational excitation of the Cl2 on the detailed form of the product vibrational and rotational state distributions was described in Sect. 2.3. 

About 97% of the OH product from O + HBr is found to be in the v = 1 state [443]. This reaction is 58 kJ mole-1 exoergic, but has an activation energy of llkJmole l. Quantum mechanical calculations [445] for the collinear reaction O + HBr on an LEPS surface show that at thermal energies OH(v = 1) is the preferred product ( 62%). 

Fig. 16. Comparison of the experimental IF vibrational distribution from the reaction F + I2 (ref. 554) with the distribution derived from trajectory calculations using a LEPS surface. The trajectory results are represented as histograms with the hatched regions being two standard derivations centred around the mean vibrational population. (Reproduced from ref. 562 by permission of the authors and the Royal Society of Chemistry.)...

The Dlatomics-ln-Molecules Approach. The simple version of the DIM method that we employ is based on the Heitler-London approximation (28). In spirit, it is similar to the London-Eyring approach except that we use accurate diatomic potential curves (29a) rather than an approximate form for the diatomic triplet curve (e.g. the Sato parameter for LEPS surfaces) (29b). 

It is plausible that the variation in ff, in this homologous series of reactions is caused by the existence of a barrier along the reaction coordinate, the barrier height being negatively correlated with <7,. Mok and Polanyi have found using LEPS surfaces and the BEBO method that as the barrier height decreases, the location of the... 

The adiabatic correction is not always necessarily large. Consider the Cl+HCl- CIH+Cl exchange reaction on the extended LEPS surface of Ref. ( ). The coupling of the vibrational states is small, the adiabatic correction minor and the reaction proceeds nearly adiabatically. This statement can be easily verified from the reaction probabilities displayed in Fig. 3. The off-diagonal probabilities are small compared to the diagonal ones. Also the signature of resonance states in the th adiabatic surface U (r) is most noticeable in the Pp (E) or reaction probabilities... 

The computational approach of Kuppermann (1971) has recently been applied by Baer (1974) to H + Cl2 and D + Cl2 reactions, partly to improve upon previous calculations that neglected some closed channels. He used a LEPS surface with a barrier of 0-108eV in the entrance valley. Reaction probabilities for H + Cl2 from i = 0,1. 2 to rf < 7 showed that the 0 - 4 transition dominated at low energies, while 0 - 5 and then 0 -> 6 dominated as energies increased. The general trend was the same for vt = 1 or 2, but, in detail, the distributions of v depended on ly These dependencies were discussed in terms of a model of vertical non-adiabatic transitions between two displaced vibrational wells. Results with t,- = 0 for D + Cl2 showed that 0 — 5 dominated at low energies. Total transition probabilities were weakly dependent on both vt and isotopic masses. 

More recently an empirical extension of the LEPS surface has been introduced.229 This extension introduces three overlap type parameters ... 

The first full dynamics simulation of the Cl -I- CH3CI reaction in water was by Bergsma et al. Their model of this reaction system began with a LEPS surface for the reagents that was based in part on the gas phase curve calculated by Jorgensen and co-workers. > However, since that curve was calculated... 

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