Reaction coordinates transition state theory

The original microscopic rate theory is the transition state theory (TST) [10-12]. This theory is based on two fundamental assumptions about the system dynamics. (1) There is a transition state dividing surface that separates the short-time intrastate dynamics from the long-time interstate dynamics. (2) Once the reactant gains sufficient energy in its reaction coordinate and crosses the transition state the system will lose energy and become deactivated product. That is, the reaction dynamics is activated crossing of the barrier, and every activated state will successfully react to fonn product. 

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... 

We must be able to define the reaction coordinate along which the transition state theory dividing surface is defined. 

Transition state theory assumes an equilibrium energy distribution among all possible quantum states at all points along the reaction coordinate. The probability of finding a molecule in a given quantum state is proportional to which is a Boltzmann... 

According to the transition state theory, the pre-exponential factor A is related to the frequency at which the reactants arrange into an adequate configuration for reaction to occur. For an homolytic bond scission, A is the vibrational frequency of the reacting bond along the reaction coordinates, which is of the order of 1013 to 1014 s 1. In reaction theory, this frequency is diffusion dependent, and therefore, should be inversely proportional to the medium viscosity. Also, since the applied stress deforms the valence geometry and changes the force constants, it is expected... 

Several attempts to relate the rate for bond scission (kc) with the molecular stress ( jr) have been reported over the years, most of them could be formally traced back to de Boer s model of a stressed bond [92] and Eyring s formulation of the transition state theory [94]. Yew and Davidson [99], in their shearing experiment with DNA, considered the hydrodynamic drag contribution to the tensile force exerted on the bond when the reactant molecule enters the activated state. If this force is exerted along the reaction coordinate over a distance 81, the activation energy for bond dissociation would be reduced by the amount ... 

When processes are slow because they involve an activation barrier, the time scale problems can be circumvented by applying (corrected) transition state theory. This is certainly useful for reactive systems (5 ) requiring a quantummechanical approach to define the reaction path in a reduced system of coordinates. The development in these fields is only beginning and a very promising... 

The top of the profile is maximum (saddle point) and is referred as the transition state in the conventional transition state theory. It is called a saddle point because it is maximum along the orthogonal direction (MEP) while it is minimum along diagonal direction of Fig. 9.12. The minimum energy path can be located by starting at the saddle point and mapping out the path of the deepest descent towards the reactants and products. This is called the reaction path or intrinsic reaction coordinate. 

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... 

As in the conventional transition state theory Equation 14.27 does not contain any reference to the mass of the reaction coordinate motion or to the length l of the transition state. While some aspects of the derivation have been skipped, it is hoped that the reader understands that the expression in the numerator for the sum of the vibrational energy levels in the transition state arises from Equation 14.25 which applies to the transition state but not to the excited molecule A. ... 

Phase space theory (PST) has been widely used for estimation of rates and energy partitioning for ion dissociations. It can be considered within the framework of transition-state theory as the limiting case of a loose transition state, in which all product degrees of freedom are statistically fully accessible at the transition state. As such, it is expected to give an upper limit for dissociation rates and to be best suited to barrierless dissociations involving reaction coordinates with simple bond cleavage character. 

The formidable problems that are associated with the interpretation of LP kinetic data for nonstatistical IM reactions can be entirely avoided if the reactions can be studied in the HPL of kinetic behavior. In the HPL, the energy content of the initially formed species, X and Y, in reaction (2) would be very rapidly changed by collisions with the buffer gas so that the altered species, X and Y, would have normal Boltzmann distributions of energy. Furthermore, those Boltzmann energy distributions would be continuously refreshed as the most energetic X and Y within the distributions move forwards or backwards along the reaction coordinate. The interpretation of rate constants measured in the HPL is expected to be relatively straightforward because conventional transition-state theory can then be applied. 

Free energy diagrams for enzymes REACTION COORDINATE DIAGRAM ENZYME ENERGETICS POTENTIAL-ENERGY SURFACES TRANSITION-STATE THEORY ARRHENIUS EQUATION VAN T HOFF RELATIONSHIP... 

---