Tight transition state theory

Figure 23. Plot of experimental ( ) and theoretical three-body rate constants as a function of cluster size for the clustering of one CO molecule to copper clusters, Cun. Note the dramatic increase in reactivity (almost four orders of magnitude) within the first seven atom additions to the clusters. The overall trend represents a transition from termolecular to effective bimolecular behavior. The solid line (theory) was obtained assuming a loose transition state while the dotted line shows the results for a tight transition state for monomer and dimer only (upper limit). Taken with permission from ref. 155.

The preexponential factor involves the entropy change in going from reactants to the transition state the more highly ordered and tightly bound is the transition state, the more negative A S° will be and the lower the preexponential factor will be. Transition state theory thus automatically takes into account the effect of steric factors on rate constants, in contrast to collision theory. 

Important milestones in the rationalization of enzyme catalysis were the lock-and-key concept (Fischer, 1894), Pauling s postulate (1944) and induced fit (Koshland, 1958). Pauling s postulate claims that enzymes derive their catalytic power from transition-state stabilization the postulate can be derived from transition state theory and the idea of a thermodynamic cycle. The Kurz equation, kaJkunat Ks/Kt, is regarded as the mathematical form of Pauling s postulate and states that transition states in the case of successful catalysis must bind much more tightly to the enzyme than ground states. Consequences of the Kurz equation include the concepts of effective concentration for intramolecular reactions, coopera-tivity of numerous interactions between enzyme side chains and substrate molecules, and diffusional control as the upper bound for an enzymatic rate. 

For all the dissociating halotoluenes examined, the formation of tight transition states typical of rearrangement reactions is confirmed by the negative S% values found by fitting the dissociation rate vs internal energy curves, calculated on the basis of the RRKM theory, with the experimental PEPICO data145. 

Chemical kinetic rate methods including conventional transition state theory (TST), canonical variational transition state theory (CVTST) and Rice-Ramsper-ger-Kassel-Marcus in conjunction with master equation (RRKM/ME) and separate statistical ensemble (SSE) have been successfully applied to the hydrocarbon oxidation. Transition state theory has been developed and employed in many disciplines of chemistry [41 4]. In the atmospheric chemistry field, conventional transition state theory is employed to calculate the high-pressure-limit unimole-cular or bimolecular rate constants if a well-defined transition state (i.e., a tight... 

Several approaches to the issue of tight binding ionic mobility in the channel system can be explored. In the past decade, quantum transition state theory has matured to the point that it is possible to consider sophisticated treatments that include formally accurate... 

The upper limits are provided by the collision frequency of the radical-molecule pair which is about 1011 3 1/mole-sec at 400°K. This result can also be arrived at from transition state theory by assuming that the centers of the colliding pair lie on a spherical shell 3.5 A in radius and 0.10 A thick. This corresponds to a tight transition state since the small amplitude of motion of 0.10 A is characteristic of bond vibration amplitudes in molecules. The only bimolecular reactions whose A-factors come close to this upper limit are the methathesis reactions of I atoms (27) for which the A-factors equal, or slightly exceed, the collision frequency. 

Transition state theory, if valid, can also be used to determine the tightness or looseness of the transition state molecular configuration as compared to that of the reactants. When transition state theory is formulated in thermodynamic terms it is found that the high pressure Arrhenius A- factor is given by... 

The variational version of RRKM theory (VTST) can be used to locate the transition state on the basis of the minimum sum of states. However, if this level of effort does not appear appropriate for the particular reaction, it is perfectly possible to fit a given data set with the vibrator model of the RRKM theory simply by adjusting the transition-state vibrational frequencies until a fit is obtained (as was done in the calculations of figures 7.3 and 7.4). In fact, such a fitting procedure is one means for determining whether the reaction is characterized by a loose or a tight transition state. 

Figure 11. Kinetic energy release distribution for metastable loss of CH4 from nascent Co(C3Hg)+ collision complexes. The "unrestricted" phase space theory curve assumes the entrance channel contains only an orbiting transition state, the exit channel has only an orbiting transition state (no reverse activation barrier), and there are no intermediate tight transition states that affect the dynamics. The "restricted" phase space theory calculation includes a tight transition state for insertion into a C-H bond located 0.08 eV below the asymptotic energy of the reactants.

The Transition-State Theory Definition of the Reaction Rate Constant Loose and Tight Transition States... 

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