Reaction coordinate relaxation method

The Locally Updated Plane.s- (LUP) minimization is related to the chain method, but the relaxation is here done in the hyperplane perpendieular to the reaction coordinate, rather than along a line defined by the gradient. Furthermore, all the points are moved in each iteration, rather than one at a time. 

The second use of Equations (2.36) is to eliminate some of the composition variables from rate expressions. For example, 0i-A(a,b) can be converted to i A a) if Equation (2.36) can be applied to each and every point in the reactor. Reactors for which this is possible are said to preserve local stoichiometry. This does not apply to real reactors if there are internal mixing or separation processes, such as molecular diffusion, that distinguish between types of molecules. Neither does it apply to multiple reactions, although this restriction can be relaxed through use of the reaction coordinate method described in the next section. 

Consideration of the thermodynamics of a representative reaction coordinate reveals a number of interesting aspects of the equilibrium (Fig. 5). Because the complex is in spin equilibrium, AG° x 0. Only complexes which fulfill this condition can be studied by the Raman laser temperature-jump or ultrasonic relaxation methods, because these methods require perturbation of an equilibrium with appreciable concentrations of both species present. The photoperturbation technique does not suffer from this limitation and can be used to examine complexes with a larger driving force, i.e., AG° 0. In such cases, however, AG° is difficult to measure and will generally be unknown. 

Jaume et al. (1984) studied the contribution of solvent relaxation to the reaction coordinate of the F (H20) + CH3F(H20)SN2 reaction. Potential energy calculations were performed using the ab initio MO method with the 3-21G basis set. The authors found large variation of the solvation parameters along the reaction path and concluded that solvent coordinates are an important part of the reaction coordinate. They showed that the solvent acts not only as a medium for the reaction but also as a rectant. Thus, the solvent does not adjust its position to the changing chemical system but rather takes part in it. 

A wide variety of problems are amenable to the Redfield methodology in addition to those discussed here. Some of the most important, in our view, are as follows. First, problems involving the interaction of strong laser fields with a condensed-phase system are often difficult to solve because the construction of a small, physically intuitive zeroth-order quantum subsystem Hamiltonian is difficult the numerical methods described above will make it possible to expand the size of the quantum subsystem and allow the problem to be attacked much more easily. A second class of problems involves relaxation of complex systems (e.g., vibronic or vibrational relaxation of a molecule in a liquid) [42,43, 72]. A third class of problems would be concerned with chemical dynamics in which the system could not be described easily by a single reaction coordinate, for example, general proton transfer reactions [98] or the isomerization of retinal in bacteriorhodopsin [120]. A low-dimensional system probably is adequate for these cases, but a nontrivial number of quantum levels will still be required. 

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