Transition states reaction rate constants

Green W H, Moore C B and Polik W F 1992 Transition states and rate constants for unimolecular reactions Ann. Rev. Phys. Chem. 43 591-626... 

Given the foregoing assumptions, it is a simple matter to construct an expression for the transition state theory rate constant as the probability of (1) reaching the transition state dividing surface and (2) having a momenrnm along the reaction coordinate directed from reactant to product. Stated another way, is the equilibrium flux of reactant states across... 

The reaction coordinate is the C-O stretch vibration of the CO molecule in its transition state. The rate constant is... 

Activation energies and entropies of activation are in the same region as those for Sn2 reactions of neutral A-methylaniline. Large negative AS values are again in accord with increased charge separation with attendant solvation in the transition state. The rate constants at 298 K correlate with Hammett a values with p — 1.13 (r — 0.985) in keeping with a development of benzoate character in the transition state. 

Since both of these reactions proceed through similar transition states, their rate constants have similar pre-exponential factors, and the AH, corresponds to activation energies. Consequently, at process temperatures, i.e., T X 1000°C or less, the ratio of the rate coefficient of reaction (20) to that of (21) will be the order 10 or more. Therefore, C-Cl bond scission, i.e., reaction (20), will always dominate the unimolecular decomposition of CH3CI. 

As seen in Tables 22—25, the Arrhenius preexponential factors Aa for the initiation step are very low, 10 in 7, 10 in 20, 10 " in 41 and 1in 44. These are very low values for bimolecular reactions for which values of about 10 ° are observed and also predicted by the Transition State Theory Thus step (a) belongs to a class of slow reactions , some of which might have ionic transition states . The activation entropies AS obtained from the Transition State Theory rate constant expression... 

Thus, expression (59) enables us to describe the solid-state reaction rate constant dependence on the parameters of the potential barrier and medium properties in a wide temperature range, from liquid helium temperatures when the reaction runs by a tunneling mechanism to high temperatures (naturally, not exceeding the melting point) when the transition is of the activation type. 

Figure 16. Illustration of change of solid-state reaction rate constant in phase transition. Soft-mode splitting out occurs at point equalling 0,7i/4a, njla, 3 t/4o and n/a for curves 1-5, respectively. K( T) jump at Kq = 0 determined by difference in amplitude in two phases.

The term LFER is used for such correlations because they usually are linear correlations between logs of rate constants and logs of equilibrium constants for reactions of the compounds. According to transition-state theory, rate constants are exponentially related to the free energy of activation (AG ), and thermodynamics tells us that equilibrium constants are similarly related to AG°. If two reactions exhibit a LFER we can write... 

With this choice of dividing surfaces, a generalized expression for the transition state theory rate constant for a bimolecular reaction is given by ... 

G.W. Koeppl. Best Ab Initio Surface Transition State Theory Rate Constants for the D-1 H2 and H-FD2 Reactions. J. Chem. Phys. 59 3425 (1973). 

If multiple reaction channels are available for a reaction, which are characterized by conformationally distinct transition states, a rate constant is calculated for each... 

Green WH, Moore CB, Polik WF (1992) Transition states and rate constants for urumolecular reactions. Aim Rev Phy Chem, 43 591-629... 

In the subsections that follow we will focus on the factors that maximize the rate constant for elementary surface reaction steps. Again we will stress the need explicitly to include entropic contributions. According to transition-state reaction rate theoryl l, the rate of the elementary conversion step is defined as... 

Mondro SL, Linde SV, Hase WL. Reaction path and variational transition state theory rate constant for Li + HjO— Li (HjO) association. J Chem Phys. 1986 84 3783-7. 

Knutson et al. (280) measured the kinetics of the Diels-Alder reaction of maleic anhydride (MA) and 2,3-dimethyl-1,3-butadiene (DMB) in SCF propane solutions at 100-140°C and 46-141 bar. Reaction to the product 4,5-dimethyl-CM-l,2,3,6-tetrahydrophthalic anhydride (DMTA) was evaluated with excess DMB as a reactive cosolvent and 2,2,2-trifluoroethanol (TFE) as an unreac-tive cosolvent (Scheme 21). Near-critical effects and cosolvent effects on reaction rates were analyzed from transition state theory. Rate constants increased with increasing pressure at 140 C, but were not significantly affected at 100°C and 120 C at near-critical densities. A similar lack of pressure dependence has been reported by Reaves and Roberts (281) for the Diels-Alder reaction of MA with isoprene in subcritical propane at 80°C. This minimal pressure effect is in contrast to those noted above for Diels-Alder reactions in SCCO2 where the reactants were at approximately equal and dilute concentrations. The influence of the unreactive cosolvent, TFT, on reaction rates was found to be minimal. These results suggest that the local reactant composition, as well as pressure, temperature, and cosolvent, can be used to control the reaction rate of such reactions in the near-critical region. 

Hase, W. L. and D. M. Wardlaw (1989). Transition state theory rate constants for association reactions without potential energy barriers. In Bimolecular Collisions, M. N. R. Ashfold and J. E. Baggott (eds.). London, Royal Society of Chemistry, p. 171. 

H(v =l) + H reactions would be less than the conventional transition state theory rate constant. Generalized transition state theory would clearly be needed to describe the excited state reaction (of course summed over the final vibrational states). 

Miller W H 1974 Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants J. Chem. Phys. 61 1823-34... 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

---