Transition state theory intramolecular reactions

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. 

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... 

The competition between intramolecular vibrational relaxation and chemical reaction has been discussed in terms of the applicability of transition state theory to the kinetic analysis [6], If the environment functions mainly as a heat bath to ensure thermalization among the vibrational modes in the excited complex, then transition state theory is a good approximation. On the other hand, when the reaction is too fast for thermalization to occur the rate can depend upon the initial vibronic state. Prompt reaction and prompt intersystem crossing are, by definition, examples of the latter limit. 

Intramolecular hydrogen transfer is another important class of chemical reactions that has been widely studied using transition state theory. Unimolecular gas-phase reactions are most often treated using RRKM theory [60], which combines a microcanonical transition state theory treatment of the unimolecular reaction step with models for energy redistribution within the molecule. In this presentation we will focus on the unimolecular reaction step and assume that energy redistribution is rapid, which is equivalent to the high-pressure limit of RRKM theory. 

Kinetic theory and transition-state theory try to calculate the rates of chemical reactions starting from a model of molecular interactions. A less ambitious task is to correlate reaction rates with phenomenological laws of various macroscopic processes which have been established experimentally. This type of theory can be termed a phenomenological theory of reaction rates. For the purpose of calculating theoretical reaction rates, chemical reactions are divided into three categories bimolecular associations, uni-molecular dissociations, and intramolecular transformations. 

The structures of intermediates and transition states in the reaction of tertiary phosphines with unsaturated carboxylic acids have been calculated at the B3LYP level of theory using the 6-31-l-G(d,p) basis set. Analysis of the results has shown that [1,3]-intramolecular migration of carboxylic proton to the carbanionic centre of a zwitteri-onic intermediate is strongly kinetically unfavourable and that an external proton-donor source is essential to complete quaternization. The proton transfer remained rate determining when a molecular cluster of the intermediate with one molecule of water was modelled for the intermolecular reaction pathway. 

A new ab initio semi-classical technique for the calculation of tunnelling effects has been demonstrated for the case of the interconversion of the (degenerate) enols of malonaldehyde via intramolecular proton transfer the method incorporates tunnelling into first principles molecular dynamics. The use of density functional theory to model transition states in this reaction has also been described even the most advanced levels of theory meet substantial difficulties in such systems. 

Iftimie, R. and Schofield,). (2001) Reaction mechanism and isotope effects derived from centroid transition state theory in intramolecular proton transfer reactions. J. Chem. Phys., 115 (13), 5891-5902. 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

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