Transition state theory angular momentum

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. 

RRKM theory, developed from RRK theory by Marcus and others [20-23], is the most commonly applied theory for microcanonical rate coefficients, and is essentially the formulation of transition state theory for isolated molecules. An isolated molecule has two important conserved quantities, constants of the motion , namely its energy and its angular momentum. The RRKM rate coefficient for a unimolecular reaction may depend on both of these. For the sake... 

Variational transition state theory was suggested by Keck [36] and developed by Truhlar and others [37,38]. Although this method was originally applied to canonical transition state theory, for which there is a unique optimal transition state, it can be applied in a much more detailed way to RRKM theory, in which the transition state can be separately optimized for each energy and angular momentum [37,39,40]. This form of variational microcanonical transition state theory is discussed at length in Chapter 2, where there is also a discussion of the variational optimization of the reaction coordinate. 

A transition-state theory (Safron et al, 1972) has been developed within the context of scattering theory, to provide suitable models for crossed molecular beam processes. As in the case of RRKM theory, it is based on the premise that the probability of complex decomposition is a product of a probability of break-up and a probability Of departure from the collision region. But it adds restrictions peculiar to bimolecular reactions, such as a limit on the maximum angular momentum that allows formation of the complex from reactants. Let p(E t) indicate the probability density for finding a product pair with kinetic energy E. This may be written as... 

Klippenstein and colleagues calculated rate constants for these barrierless reactions employing a method they termed variational reaction co-ordinate transition state theory (VRC-TST). In this version of TST, variational does not only refer to the procedure for finding the location of the transition state along the reaction co-ordinate, for each combination of energy (E) and total angular momentum (J), but also to a search for the optimum definition of the... 

A large number of approximate theories have been proposed for ion-dipole reactions. Some of these include the average dipole orientation (ADO) approximation and its extension to include conservation of angular momentum (the AADO method ), various transition-state theories involving variational and statistical modifications, the semiclassi-cal perturbed rotational state (PRS) approximation, classical trajectory studies, the adiabatic invariance method, and the statistical adiabatic channel model (SACM). 

Notably, adiabatic chaimel models and variational transition state theory yield identical rate estimates as long as they employ the same assumptions for the energy levels. However, the implementations of the two theories generally employ different assumptions (e.g., classical versus quantum) and so jdeld modestly different rate estimates. Furthermore, the adiabatic models sometimes implement additional constraints such as an assumed conservation of the orbital angular momentum. 

Study. The reason is that transition state theory concentrates on the behaviour of the system up to the dividing surface, whereas the product energy disposal is determined by the potential felt by the fragments as they separate. However, Marcus, Wardlaw and Klippenstein have proposed an extension that describes the evolution of the transitional modes along the reaction coordinate and that, at the same time, conserves angular momentum. 

In addition to the classical trajectory calculations, a variety of other theoretical studies have been done. Accurate quantum mechanical scattering results for zero total angular momentum have been reported for reaction (40). The reaction has also been studied by using transition-state theory (TST). Transition-state theory overestimates (compared to experiment) the thermal rate by a factor of about two. This may be caused by errors in the PES or to recrossings , that is, trajectories which pass through the transition state but quickly return to reactants rather than going on to form products (TST incorrectly counts these as reactive events). Studies are also being done to understand the spectroscopy of the transition state of this reaction. ... 

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