Transition-state complex, activation energy

Collision theory explains some important features of a reaction, but it is limited in that it does not explain the role of activation energy. Transition-state theory explains the reaction resulting from the collision of two molecules in terms of an activated complex. An activated complex (transition state) is an unstable grouping of atoms that can break up to form products. We can represent the formation of the activated complex this way ... 

Efficiency and selectivity are the two keywords that better outline the outstanding performances of enzymes. However, in some cases unsatisfactory stereoselectivity of enzymes can be found and, in these cases, the enantiomeric excesses of products are too low for synthetic purposes. In order to overcome this limitation, a number of techniques have been proposed to enhance the selectivity of a given biocatalyst. The net effect pursued by all these protocols is the increase of the difference in activation energy (AAG ) of the two competing diastereomeric enzyme-substrate transition state complexes (Figure 1.1). 

This reduction in activation energy will occur only when the structure of the transition state complex fits well in the zeoHte cavity. This is the case for the protonated toluene example in the zeoHte mordenite channel. The structure of the transition state complex in the cluster simulation and zeoHte can be observed to be very similar to the one in Figure 1.10. 

The activation energy will be strongly increased when there is a mismatch between transition-state-complex shape and cavity. The rate constant then typically behaves as indicated in the following equation ... 

Figure 8.23 During a reaction, the participating species approach, collide and then interact. A seamless transition exists between pure reactants and pure products. The rearrangement of electrons requires large amounts of energy, which is lost as product forms. The highest energy on the activation energy graph corresponds to the formation of the transition-state complex. The relative magnitudes of the bond orders are indicated by the heaviness of the lines...

The activation energy Ea is always positive, so the formation of a transition-state complex is always endothermic. 

All reactions proceed via a transition-state complex, and with an activation energy Ea. The values of Ea vary tremendously, from effectively zero (for a so-called diffusion-controlled reaction, as below) to several hundreds of kilojoules per mole (for reactions that do not proceed at all at room temperature). The rate constant of a reaction is relatively insensitive to temperature if Ea is small. 

Next, we recall, from the second law of thermodynamics, that AGe = AH — T AS . By direct analogy, AG = AHt — TAY, where A// is the enthalpy of forming the transition-state complex (akin to the activation energy E ). AY is the entropy of forming the transition-state complex. 

Figure 2 AAHS P + + Px) is the difference between the solvation energy of (Pn+ + Px) in hydrocarbon solvent and in a polar solvent, and AAHS is the corresponding difference for the Transition State Complex (TrStC). Since AAHS(P+ + Px) > AAPf, the activation energy AH2 in the polar solvent is greater than that (AHX) in hydrocarbon solvent...

Thus, Marcus theory ascribes the free energy of activation to three factors electrostatic interactions between reactants in the transition state, bond distortion to the nuclear configuration of the transition state, and rearrangement of the solvent sphere around the transition state complex. 

In summary, our photophysical studies indicate that the thermally activated relaxation pathways of (2E)Cr(III) very likely involve 2E-to- (intermediate) surface crossing. These (intermediates) can be associated with some, not necessarily the lowest energy, transition state (or transition states) for ground state substitution. The Arrhenius activation barriers for thermally activated relaxation are remarkably similar from complex to complex, but they can be altered in systems with highly strained ligands. Some of this work indicates that the steric and electronic perturbations of the ligands dictate the choice among possible relaxation channels. 

As with carbonic anhydrase the metal is in a cleft that exposes the active site. Interestingly the metal-free enzyme is inactive but the cobalt and nickel analogues are more active. It appears that the transition state complex, where the terminal amino acid side chain is held in place while the peptide bond is hydrolysed, requires six-fold co-ordination. The activation energy required to change from the tetrahedral to octahedral geometries is higher for zinc than the other metals. 

Schematic change in Gibbs free energy as a function of the "reaction coordinate" x. R denotes the reagent(s), P represents the product(s) 77 is the transition state (also known as the activated complex), 11 is the reaction intermediate (if it exists). 72 denotes the lower-energy transition state (or activated complex) for the catalyzed reaction.

Calculate the rate enhancement that would be achieved if the activation energy of the transition-state complex of an enzyme with its substrate were halved. 

Deutsch and coworkers have used a simple harmonic oscillator model to relate the kinetic effects (as measured by activation enthalpies) to the energy necessary to stretch the trans N bond, AH S(0)2R- - AHt(SOj = k US - /- S Rf )2 - (r - r(SO )2, which gives rx = 320pm for the transition-state complex.426 This represents a stretching of some 120 pm. This value may be used to estimate AH for other (perhaps hypothetical) dissociation processes. More general articles on the trans effect emphasizing its structural and electronic aspects are available.1102"1104... 

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