Transition state theory reaction pathways

Three possibilities were considered to account for the curved Arrhenius plots and unusual KIEs (a) the 1,2-H shift might feature a variational transition state due to the low activation energy (4.9 kcal/mol60) and quite negative activation entropy (b) MeCCl could react by two or more competing pathways, each with a different activation energy (e.g., 1,2-H shift and azine formation by reaction with the diazirine precursor) (c) QMT could occur.60 The first possibility was discounted because calculations by Storer and Houk indicated that the 1,2-H shift was adequately described by conventional transition state theory.63 Option (b) was excluded because the Arrhenius curvature persisted after correction of the 1,2-H shift rate constants for the formation of minor side products (azine).60... 

The kinetic model for proton transfer based upon transition state theory that incorporates a tunneling contribution to the overall reaction rate assumes that tunneling occurs near the region of the transition state (pathway a in Scheme 2.5). There is, however, another possibility for the reaction path for proton transfer. In lieu of thermally activating the vibration associated with the proton-transfer coordinate to bring it into the region of the transition state, the proton may instead... 

The mechanism of action of enzymes can best be described with the aid of transition state theory. On the pathway from substrate A to product B in a reaction catalyzed by a chemical catalyst or an enzyme A passes through a transition state A which is found at the highest point of the energy diagram (fig. 2.1). The energy difference between the ground state of A and the transition state A represents the activation energy. The transition state as such can not be isolated. It is the state of A in which the bonds... 

The reaction pathway is shown schematically in Fig. 10.4. The assumptions implicit in transition-state theory are discussed next. 

In addition to experiments, a range of theoretical techniques are available to calculate thermochemical information and reaction rates for homogeneous gas-phase reactions. These techniques include ab initio electronic structure calculations and semi-empirical approximations, transition state theory, RRKM theory, quantum mechanical reactive scattering, and the classical trajectory approach. Although still computationally intensive, such techniques have proved themselves useful in calculating gas-phase reaction energies, pathways, and rates. Some of the same approaches have been applied to surface kinetics and thermochemistry but with necessarily much less rigor. 

The application of isotope effects studies of reaction mechanism includes comparison of experimental values of isotope effects and predicted isotope effects computed for alternative reaction pathways. On the basis of such analysis some of the pathways may be excluded. Theoretical KIEs are calculated using the method of Bigeleisen and Mayer.1 55 KIEs are a function of transition state and substrate vibrational frequencies. Equilibrium isotope effects are calculated from substrate and product data. Different functionals and data sets are used in these calculations. Implementation of a one-dimensional tunnelling correction into conventional transition-state theory significantly improved the prediction of heavy-atom isotope effects.56 Uncertainty of predicted isotope effect can be assessed from the relationship between KIEs and the distances of formed or broken bonds in the transition states, calculated for different optimized structures.57 Calculations of isotope effects from sets of frequencies for optimized structures of reactants and transition states are facilitated by adequate software QUIVER58 and ISOEFF.59... 

All of the ab initio calcnlations that include electron correlation to some extent clearly favor the concerted pathway for Reaction 4.1. All of these computations also identified a transition state with Q symmetry, indicating perfectly synchronons bond formation. One method for distinguishing a synchronous from an asynchronous transition state is by secondary kinetic isotope effects (KIEs). Isotopic snbstitution alters the frequencies for all vibrations in which that isotope is involved. This leads to a different vibrational partition function for each isotopicaUy labeled species. Bigeleisen and Mayer determined the ratio of partition functions for isotopicaUy labeled species. Incorporating this into the Eyring transition state theory results in the ratio of rates for the isotopicaUy labeled species (Eq. (d. ))." Computation of the vibrational frequencies is thus... 

Unimolecular gas phase studies try to isolate reacting molecules from their environment. Insofar as this is successful, gas phase studies provide the most unambiguous data on the intramolecular forces which control reaction rates and pathways. The energetic and conformational requirements of transition state species are of paramount interest, and with the stringent limitations placed on the data by modern reaction rate theories, the results may be critically examined and meaningfully evaluated. A critical survey of the data leading to the rejection of some and a selection of the best parameters in others, has been one of our primary concerns. Transition state theory has been assumed, and the methods and criteria employed in the calculations are based on this theory. They are outlined very briefly for each... 

Computational quantum chemistry has been used in many ways in the chemical industry. The simplest of such calculations is for an isolated molecule this provides information on the equilibrium molecular geometry, electronic energy, and vibrational frequencies of a molecule. From such information the dissociation energy at 0 K is obtained, and using ideal gas statistical mechanics, the entropy and other thermodynamic properties at other temperatures in the ideal gas state can be computed. Such calculations have provided information on heats of formation of compounds and, when used with transition state theory, on reaction pathways and reaction selectivity. As these applications are well documented in the literature, they are not discussed here. 

While it is true that once there is confidence that the correct mechanism has been identified that transition state theory will usually yield a reasonable description of the energetics, it is also true that ignorance of the correct pathway can lead to results that are completely misleading. As a result, work has concentrated on important new developments in the area of determining the relevant reaction pathways in complex systems. In particular, sophisticated techniques have been set forth that are aimed at uncovering the optimal reaction pathway in cases where intuition does not suffice as a guide. 

Chapter is the remarkable ability to finally predict quantatively reaction pathways and transition states for geochemically interesting reactions. At the same time, the rigorous molecular theory proposed here also paves the way to a solid foundation of the treatment of transition-state theory in water-rock kinetics. 

In general, proton transfer occurs via a combination of over-barrier and through-barrier pathways. The rate constant of over-barrier transfer is usually calculated by standard transition state theory (TST) [22] by separating the reaction coordinate from the remaining degrees of freedom. If tunneling effects and the curvature of the reaction path are neglected, this leads to the expression... 

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