Reaction, coordinate field

Kramers solution of the barrier crossing problem [45] is discussed at length in chapter A3.8 dealing with condensed-phase reaction dynamics. As the starting point to derive its simplest version one may use the Langevin equation, a stochastic differential equation for the time evolution of a slow variable, the reaction coordinate r, subject to a rapidly statistically fluctuating force F caused by microscopic solute-solvent interactions under the influence of an external force field generated by the PES F for the reaction... 

Calculations within tire framework of a reaction coordinate degrees of freedom coupled to a batli of oscillators (solvent) suggest tliat coherent oscillations in the electronic-state populations of an electron-transfer reaction in a polar solvent can be induced by subjecting tire system to a sequence of monocliromatic laser pulses on tire picosecond time scale. The ability to tailor electron transfer by such light fields is an ongoing area of interest [511 (figure C3.2.14). 

Another technique is to use an ah initio method to parameterize force field terms specific to a single system. For example, an ah initio method can be used to compute the reaction coordinate for a model system. An analytic function can then be fitted to this reaction coordinate. A MM calculation can then be performed, with this analytic function describing the appropriate bonds, and so on. 

Ermer (179) describes more extended force-field calculations, following a reasonable reaction coordinate from the twist to the distorted chair form. The barrier (AH ) between these is found to be 7.21 kcal/mol, implying that the interconversion is fast except at very low temperatures. 

In 1983, Huskey and Schowen tested the coupled-motion hypothesis and showed it to be inadequate in its purest form to account for the results. If, however, tunneling along the reaction coordinate were included along with coupled motion, then not only was the exaltation of the secondary isotope effects explained but also several other unusual feamres of the data as well. Fig. 4 shows the model used and the results. The calculated equilibrium isotope effect for the NCMH model (the models employed are defined in Fig. 4) was 1.069 (this value fails to agree with the measured value of 1.13 because of the general simplicity of the model and particularly defects in the force field). If the coupled-motion hypothesis were correct, then sufficient coupling, as measured by the secondary/primary reaction-coordinate amplimde ratio should generate secondary isotope effects that... 

The combination of modem valence bond theory, in its spin-coupled (SC) form, and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wavefunction, is demonstrated to provide quantitative and yet very easy-to-visualize models for the electronic mechanisms of three gas-phase six-electron pericyclic reactions, namely the Diels-Alder reaction between butadiene and ethene, the 1,3-dipolar cycloaddition of fulminic acid to ethyne, and the disrotatory electrocyclic ringopening of cyclohexadiene. 

This methodology has two chief drawbacks. A philosophical drawback is that movement along the reaction coordinate raises the force-field energy instead of lowering it, which... 

MCSCF calculations in practice require much more technical expertise than do singleconfiguration HF analogs. One particularly difficult problem is that spurious minima in coefficient space can often be found, instead of the variational minimum. Thus, convergence criteria are met for die self-consistent field, but the wave function is not really optimized. It usually requires a careful inspection of the orbital shapes and, where available, some data on relative energetics between related species or along a reaction coordinate to ascertain if this has happened. 

Suppose the reactive polyatomic molecule of interest can undergo uni-molecular reaction to form several products, and we imagine carrying out a constrained reaction path analysis for each of the product channels. To carry out the analysis of a particular constrained reaction path, Zhao and Rice adopted a system-bath model [74] in which the reaction path coordinate delines the system and all other coordinates constitute the bath. The use of this representation permits the elimination of the bath coordinates, which then increases the efficiency of calculation of the optimal control field for motion along the reaction coordinate. 

In this chapter Prof. Rice has advocated two techniques that should be useful for evaluations of optimal fields for laser control of chemical reactions (i) reduced space of eigenstates for representations of nuclear wavepackets and (ii) the use of effective reaction coordinates. Both techniques have already been used for efficient evaluations of reaction probabilities in model reactions. See, for example, Ref. 1 for the prediction of population inversion and Ref. 2 for the demonstration of rather strong deviations of chemical reactions from the reaction path, specifically in the case of hydrogen transfer reactions. 

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