The Potential Energy Diagram

The central theme in catalysis is the effect of the catalyst on the rate of a chemical reaction or on the product distribution, which is given by the relative rates of different reaction pathways. You can say that catalysis is all about what determines the chemical kinetics. A good catalyst is typically one that gives a high rate and a high selectivity toward the desired product. The reaction rate constant, k, for an elementary reaction is often written as an Arrhenius expression in terms of a prefactor, v, and an activation energy, E.  

Fundamental Concepts in Heterogeneous Catalysis, First Edition. Jens K. N0rskov, Felix Studt, Frank Abild-Pedersen and Thomas Bligaard. 

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Section 4 9 The potential energy diagrams for separate elementary steps can be merged into a diagram for the overall process The diagram for the reac tion of a secondary or tertiary alcohol with a hydrogen halide is charac terized by two intermediates and three transition states The reaction is classified as a ummolecular nucleophilic substitution, abbreviated as SnI... 

The concept of ion pairs in nucleophilic substitution is now generally accepted. Presumably, the barriers separating the intimate, solvent-separated, and dissociated ion pairs are quite small. The potential energy diagram in Fig. 5.4 depicts the three ion-pair species as being roughly equivalent in energy and separated by small barriers. 

The potential energy diagram for these channels is quite similar to those in CH2O, and is shown in Fig. 9. 

To see how the catalyst accelerates the reaction, we need to look at the potential energy diagram in Fig. 1.2, which compares the non-catalytic and the catalytic reaction. For the non-catalytic reaction, the figure is simply the familiar way to visualize the Arrhenius equation the reaction proceeds when A and B collide with sufficient energy to overcome the activation barrier in Fig. 1.2. The change in Gibbs free energy between the reactants, A -r B, and the product P is AG. 

Neurock and coworkers [M. Neurock, V. Pallassana and R.A. van Santen, J. Am. Chem. Soc. 122 (2000) 1150] performed density functional calculations for this reaction scheme up to the formation of the ethyl fragment, for a palladium(lll) surface. Figure 6.38(a) shows the potential energy diagram, starting from point at which H atoms are already at the surface. As the diagram shows, ethylene adsorbs in the Jt-bonded mode with a heat adsorption of 30 kj mol and conversion of the latter into the di-a bonded mode stabilizes the molecule by a further 32 kJ mol . ... 

Fran the one dimensional representation of the potential energy diagram one cannot decide vhether the dissociative adsorption takes place throu intermediate tr plng in the molecular state or throu ... 

Figure 2-10. Fully optimized ONIOM QM MM transition states for the enzymatic reaction in glutathione peroxidase. Labels (TS-II-III and TS-III-IV) correspond to labels in the potential energy diagram in Fig. 3-7. Numbers show important bond distances in A. (Adapted from Prabhakar et al. [28]. Reprinted with permission. Copyright 2006 American Chemical Society.)...

These reactions, while not very important for high-energy donors in the absence of azulene, do help define what the potential energy diagrams should look like, that is, the fram-stilbene triplet is a discrete intermediate while the cij-stilbene triplet is a high vibrational form of the phantom triplet. Herkstroeter and McClure(13> have been able to observe the fro/w-stilbene triplet via flash photolysis using low-temperature glasses however, no similar triplet was observed for cfr-stilbene. Only when they studied cfr-stilbene-like... 

This means that energy is released in this reaction. The potential energy diagram for the reaction is ... 

This entirely quantum mechanical phenomenon is called field emission. Expression (7-1) indicates that the current increases with increasing electric field and decreasing work function, in agreement with the potential energy diagram of Fig. 7.9. 

Starting from a concerted mechanism, it is clear from the potential energy diagrams of Figure 3.12 that an increase in the driving force offered to the reaction makes the mechanism pass from a concerted to a stepwise mechanism. The change of mechanism is accompanied by a change of... 

Look carefully at the potential energy diagram. Check that you have labelled it completely. Since the forward reaction is exothermic, the reactants should be at a higher energy level than the products, and they are. The value of afrev) is reasonable. 

Fig. 10. The potential energy diagram for C-C bond rotation in o-chlorophenylmalonic acid calculated with the HF/3-21G method...

The potential energy diagram of the Michaelis Menten mechanism, drawn... 

According to the potential energy diagram on the previous page, the overall process actually occurs in two steps, with a twist-boat structure as a midway point (an intermediate ). The two (equivalent) transition states leading to this intermediate adopt structures in which five of the ring carbons lie (approximately) in one plane. 

Here, Eproducts and Ereactants are the energies of products and reactants on the potential energy diagram, T is the temperature (in Kelvin) and k is the Boltzmann constant. The Boltzmann equation tells us exactly the relative amounts of products and reactants, [products]/[reactants], at infinite time. 

Reactants, products and transition state are all stationary points on the potential energy diagram. In the one-dimensional case (a reaction coordinate diagram ), this means that the derivative of the energy with respect to the reaction coordinate is zero. 

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