Classical trajectory analysis

The Restart check box can be used in ctiii junction with the explicit editing of a IIIX file to assign completely user-specified initial velocities. This may be useful in classical trajectory analysis of chemical reactions where the initial velocities and directions of the reactants are varied to statistically determine the probability of reaction occurring, or n ot, in the process of calculating a rate con -Stan t. 

Rather than solve a Schrodinger equation with the Nuclear Hamiltonian (above), a common approximation is to assume that atoms are heavy enough so that classical mechanics is a good enough approximation. Motion of the particles on the potential surface, according to the laws of classical mechanics, is then the subject of classical trajectory analysis or molecular dynamics. These come about by replacing Equation (7) on page 164 with its classical equivalent ... 

The F H- H — H —> F—H + H reaction is a common example of a reaction easily studied by classical trajectory analysis. The potential surface we are interested in is that for FH2. This potential surface may have many extrema. One of them corresponds to an isolated Fluorine atom and a stable H2 molecule these are the reactants. Another extremum of the surface corresponds to an isolated hydrogen atom and the stable H-Fmolecule these are the products. Depending on how the potential surface was obtained there may or may not be an extremum corresponding to stable H2F, but at the least you would expect an extremum corresponding to the transition state of the reaction being considered. 

Chymotrypsin, 170,171, 172, 173 Classical partition functions, 42,44,77 Classical trajectories, 78, 81 Cobalt, as cofactor for carboxypeptidase A, 204-205. See also Enzyme cofactors Condensed-phase reactions, 42-46, 215 Configuration interaction treatment, 14,30 Conformational analysis, 111-117,209 Conjugated gradient methods, 115-116. See also Energy minimization methods Consistent force field approach, 113 Coulomb integrals, 16, 27 Coulomb interactions, in macromolecules, 109, 123-126... 

A quantitative surface compositional analysis requires the comparison of the experimental yield of the individual clusters with corresponding yields obtained theoretically this may be done by numerical simulation of the complex collision process but the accuracy of the result cannot yet be ascertained. The accuracy of the compositional analysis depends to some extent on such poorly known factors as the interatomic potential, ionization cross-sections and quantum-mechanical corrections to a treatment based on classical trajectories. 

In the analysis of the data the authors applied a model that consisted of a Franck-Condon transition to three different surfaces. Once the molecule was on one of these surfaces it was allowed to undergo a classical trajectory to a final product. 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

A schematic illustration of a classical trajectory associated with a chemical reaction is shown in Fig. 4.1.17. A detailed description of the choice of initial coordinates and momenta as well as the analysis of the trajectory results is given in the following subsections. 

Another advantage of the quantum calculations is that they provide a rigorous test of approximate methods for calculating dissociation rates, namely classical trajectories and statistical models. Two commonly used statistical theories are the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and the statistical adiabatic channel model (SACM). The first one is thoroughly discussed in Chapter 2, while the second one is briefly reviewed in the Introduction. Moreover, the quantum mechanical approach is indispensable in analyzing the reaction mechanisms. A resonance state is characterized not only by its position, width and the distribution of product states, but also by an individual wave function. Analysis of the nodal structure of resonance wave functions gives direct access to the mechanisms of state- and mode-selectivity. 

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