Morse oscillator reaction

They solved the equation of motion for the two reactants and their respective nearest neighbour shells with a potential energy of interaction between the two iodine atoms of the Morse oscillator type. A Monte Carlo technique was used and reaction occurred immediately the iodine atoms came into contact. The results of these simulations ate shown in Fig. 55. As the frequency of oscillation coe, of the iodine atom in the... 

The first applications of wavelet transforms to analyse time series in the field of chemical dynamics were those of Permann and Hamilton [47,48]. Their interest lay in modelling diatomic molecules, close to dissociation, perturbed by a photon. They modelled the reaction using the equation of motion for a forced and damped Morse oscillator, given by ... 

In order to illustrate the utility of the QNF technique for the computation of reaction rates in higher dimensional systems we consider a three DoF model system consisting of an Eckart barrier in the (physical) direction that is coupled to Morse oscillators in the qi direction and in the 3 direction. The Flamiltonian operator is... 

Figure 5.H The top panel shows the cumulative reaction probabilities A/"exact( ) (black oscillatory curve) and A/"weyi( ) (red smooth curve) for the Eckart-Morse-Morse reactive system with the Hamiltonian given by Eq. (66) with e = 0. It also shows the quantum numbers (rii, rii) of the Morse oscillators that contribute to the quantization steps. The bottom panel shows the resonances in the complex energy plane marked by circles for the uncoupled case e = 0 and by crosses for the strongly coupled case e = 0.3. The parameters for the Eckart potential are o = 1, A = 0.5, and 6 = 5. The parameters for the Morse potential are = 1, Dj 3 = 1.5, and Om = = 1. Also, h ff = 0.1.

However, whereas the natural collision coordinate v is a simple vibrational coordinate with a Morse oscillator-like potential energy curve throughout the course of the reaction, as can be seen by inspection of Figure 3, the hyperangular coordinate 0 is subject to a more complicated potential energy profile that changes very dramatically as a function of p (see Figures 4 and 5). 

It will be necessary to test the general applicability of equation (14) before it receives wide use. However, it should be quite accurate for large excitations as encountered in unimolecular reactions. For one and two separable Morse oscillators equation (14) has been found to be valid at low as well as high energies.By using equation (14) to derive quantal anharmonic densities of states for many different potential energy surfaces it may be possible to find a general semiempirical expression for quantal anharmonic densities of states. 

Fig. 1. Equipotential contours for energies between 1 and 20 kcal/mol (in 1 kcal/mol increments) for the rotated-Morse-oscillator-spline fit to the ah initio potential of Walch, Dunning, Raffenetti, and Bobrowicz (reference 6) for the collinear reaction 0( P) + H2 OH + H.

Figure. 1 Potential energy profiles together with some of the reactant energy levels for the H + H2O —> OH + H2 (a) and the H + H F —> F + H2 reaction (b). On panel (a) the energies of the stationary points are derived from the WSLFH PES [11], the initial energy levels for water are calculated with a DVR method using Radau coordinates, and the final levels for the products are obtained from the Morse potentials corresponding to the PES. On panel (b) the energies of the stationary points are obtained from the 6-SEC PES [13] both the initial and final energy levels are calculated from the Morse parameters obtained by fitting a Morse curve to the potential for the separated FIF and H2 oscillators.

Note added in proof In view of the failure of the harmonic oscillator model to account for the observed rate of activation in unimolecular dissociation reactions (the dissociation lag problem) these calculations have been repeated for a Morse anharmonic oscillator with transition between nearest and next-nearest neighbor levels [S. K. Kim, /. Chem. Phys. (to be published)]. The numerical evaluation of the analytical results obtained by Kim has not yet been carried out. From the results obtained by us and our co-workers [Barley, Montroll, Rubin, and Shuler, /. Chem. Phys. in press)] on the relaxation of vibrational nonequilibrium distributions of a system of Morse anharmonic oscillators it seems clear, however, that the anharmonic oscillator model with weak interactions (i.e., adiabatic perturbation type matrix elements) does not constitute much of an improvement on the harmonic oscillator model in giving the observed rates of activation. The answer to tliis problem would seem to lie in a recalculation of the collisional matrix elements for translational-vibrational energy exchange which takes account of the strong interactions in highly energetic collisions which can lead to direct dissociation. 

Harmonic bonds cannot be broken, and therefore, molecular mechanics with harmonic approximation is unable to describe chemical reactions. When instead of harmonic oscillators, we use the Morse model (p. 192), then the bonds can be broken. 

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