Transition state theory long-range

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Phase space theory considers the long-range polarisation between the associating ion and neutral and this interaction has generally been described on the basis of the Langevin model [808]. As has been realised for some time [482, 486, 547, 614], the phase space theory is equivalent to transition state theory in the extreme case of a loose transition state. The term loose as used here means that the incipient fragments can each freely rotate [287, 333] within the confines of conservation of angular momentum. 

In summary, collision theory provides a good physical picture of bimolecular reactions, even though the structure of the molecules is not taken into account. Also, it is assumed that reaction takes place instantaneously in practice, the reaction itself requires a certain amount of time. The structure of the reaction complex must evolve, and this must be accounted for in a reaction rate theory. For some reactions, the rate coefficient actually decreases with increasing temperature, a phenomenon that collision theory does not describe. Finally, real molecules interact with each other over distances greater than the sum of their hard-sphere radii, and in many cases these interactions can be very important. For example, ions can react via long-range Coulomb forces at a rate that exceeds the collision limit. The next level of complexity is transition state theory. 

The phase behaviour of such colloidal suspensions should be nearly the same as those of the hypothetical hard-sphere atomic system. Kirkwood [6] stated that when a hard sphere system is gradually compressed, the system will show a transition towards a state of long-range order long before close-packing is reached. In 1957, Wood and Jacobson [7] and Alder and Wainwright [8] showed by computer simulations that systems of purely repulsive hard spheres indeed exhibit a well-defined fluid-crystal transition. It has taken some time before the fluid-crystal transition of hard spheres became widely accepted. There is no exact proof that the transition occurs. Its existence has been inferred from numerical simulations or from approximate theories as treated in this chapter. However, this transition has been observed in hard-sphere-Uke colloidal suspensions [9]. 

Georgievskii Y, Klippenstein SJ. (2005) Long-range transition state theory. J. Chem. Phys. 122 194103. 

Table 4.1. Components of the analytic expression for the long-range transition state theory capture rate for various asymptotic expansions of...

For radical-radical reactions, the full mode coupling and anharmonicity effects for the relative and overall rotational motions must be explicitly accounted for. We have derived a direct variable reaction coordinate transition state theory approach that appears to 3deld accurate rate coefficients for a number of alkyl radical reactions.This approach is analogous to that embodied in Eq. (4.10) for the long-range transition state, but includes variational optimizations of the form of the reaction coordinate and does not make the large orbital moment of inertia assumption. A detailed description of this approach was provided in some of our recent articles. 

Phase space orbiting transition state theory works much better for the calculation of KERDs than for that of the rate constants, thereby demonstrating that the former are controlled by the long-range part of the potential whereas the latter are governed by its shorter range. In addition, Klots has introduced a set of effective temperatures to parametrize the observed distributions. The SACM has also demonstrated its usefulness in the case of weakly bonded species. 

MC implemented in the framework of the transition state theory (Section 1.2.1.3) can provide estimates of rate constants for infrequent events. For the construction of polymer membrane models, filling a basic cubic volume element under periodic boundary condition, a rotational isomeric state Monte Carlo technique incorporating long-range interactions can be used. 

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