Elementary reactions energy profiles

Figure 5.52 A schematic reaction energy profile for the bimolecular elementary reaction (5.82).

The relative energies obtained for the optimized structures of reactants, transition states, and products provide the reaction energy profile. Transition states are theoretically determined as a saddle point on the potential energy surface, and are confirmed by frequency analysis as well as IRC (intrinsic reaction coordinate) search then kinetics and thermochemistry of a reaction can be obtained. Since direct experimental evidence of elementary reactions is limited, the theoretical infortnation provides insight for improving the current properties of the catalyst. Studies of many catalytically important reactions have been reviewed recently. " ... 

The effect of the cluster size on the energy profile was calculated by comparing the first elementary steps of the N20 decomposition reaction route considering the two clusters (Z) and (Z0H). In Figures 2i. and 2ii, the calculated energy profiles for the adsorption and dissociation steps (equations 1 and 2), occurring over [Fe (p-0)(p-OH)Fe]+ inserted in part of the zeolite framework Z and Z 0H respectively, are reported. Structures (a), (b) and (d) correspond to local minima on the PES, whereas structure (c) represents the TS for N20 dissociation. 

Scheme 5. Condensed free-energy profile (kcalmol-1) of the complete catalytic cycle of the Ci2-reaction channel of the nickel-catalyzed cyclo-oligomerization of 1,3-butadiene, focused on viable routes for individual elementary steps. The favorable [Ni°(r 2-/r<2fts-butadiene)3] isomer of the active catalyst 1/b was chosen as reference and the activation barriers for individual steps are given relative to the favorable stereoisomer of the respective precursor...

Figure 10.5 Energy profile corresponding to the elementary reaction step transforming the initial reagents Ri +R2 to the products Pi +P2. (From ref. 10.)...

FIGURE 13.24 The ratedetermining step in a reaction is an elementary reaction that governs the rate at which products are formed in a multistep series of reactions. It is like a ferry that cannot handle busy traffic. The reaction profile shows that the slow step has the highest activation energy. 

Potential energy profile for elementary reaction. (From Boudart, M., Kinetics of Chemical Processes, Prentice Hall, Englewood Cliffs, NJ, 1968. With permission.)... 

The question now is how these energy profiles relate to reaction rates. Remember that the reaction rate constant r of an elementary process is described in the Arrhenius form as (5, 106)... 

Kelly E, M Seth, T Ziegler, Calculation of free energy profiles for elementary bimolecular reactions by a initio molecular dynamics Sampling methods and thermostat considerations, J Phys Chem... 

Since our calculations on the Halpern mechanism have been published (2) > will give a brief summary for comparison in a succeeding section. The potential energy profile shown in Figure 1 is constructed from the energetics of the elementary reactions involved in the Halpern mechanism. The optimized structures are shown in Figure 2. 

In this work, we have compared the potential energy profiles of the model catalytic cycle of olefin hydrogenation by the Wilkinson catalyst between the Halpern and the Brown mechanisms. The former is a well-accepted mechanism in which all the intermediates have trans phosphines, while in the latter, proposed very recently, phosphines are located cis to each other to reduce the steric repulsion between bulky olefin and phosphines. Our ab initio calculations on a sterically unhindered model catalytic cycle have shown that the profile for the Halpern mechanism is smooth without too stable intermediates and too high activation barrier. On the other hand, the key cis dihydride intermediate in the cis mechanism is electronically unstable and normally the sequence of elementary reactions would be broken. Possible sequences of reactions can be proposed from our calculation, if one assumes that steric effects of bulky olefin substituents prohibits some intermediates or reactions to be realized. 

Potential energy profiles for the elementary reaction A + B endothermic reaction and (b) an exothermic reaction. 

The difference in energies of the reactants and products is related to the heat of reaction—a thermodynamic quantity. Figure 2.3.1 shows potential energy profiles for endothermic and exothermic elementary reactions. 

Figure 2. Comparison between component potential-energy surfaces for elementary electrochemical exchange reaction for which the reaction entropy AS is positive (A) and resultant free-energy profile (B), plotted against the nuclear-reaction coordinate.

Obviously, linear Gibbs energy relationships are quite useful because of their predictive power. However, it must be remembered that they are based on fundamental concepts which originate in the theory of elementary reactions. Thus, the experimental study of these relationships has helped elucidate the energy profiles involved in the basic processes which occur in solutions. 

If we now turn to a macroscopic interpretation of the energy profile in Figure 2.1 then we can still retain the ideas of a transition state and an activated complex. The energy barrier to reaction is now a very complex average over many molecular events but, as we shall see later, it can still be related to a quantity that is measured experimentally. From a thermodynamic viewpoint, the energy difference between the products and reactants can be taken — to a good approximation — to be equal to the enthalpy change for the elementary reaction. 

Given that the elementary reaction in Equation 2.5 is endothermic, sketch and label an energy profile. What can you deduce about the magnitude of the energy barrier to reaction from this energy profile ... 

It is also possible to draw a schematic energy profile for a composite reaction this will consist of the energy profiles for the individual elementary steps. For a two-step mechanism, such as that represented by Reactions 2.5 and 2.6, a possible energy profile would be as shown in Figure 2.2. Note that the horizontal axis is still labelled reaction coordinate , although this should not be taken to imply that the second step occurs immediately on completion of the first. The intermediate carbocation may undergo many, many collisions with various species before finally experiencing a successful collision with an OH ion as represented by Equation 2.6. 

Any elementary reaction can be represented by a schematic energy profile which can be interpreted at the molecular level or on a macroscopic scale. 

J In Section 2.1 we introduced the idea of drawing an energy profile for an elementary reaction. Sketch such a profile for an exothermic bimolecular reaction and indicate on the profile the activation energy for the reaction. 

Since the Arrhenius equation applies equally well to composite reactions, it is sometimes the case that an energy profile such as that in Figure 7.4 is also used to represent these reactions. Strictly this is not correct, although it can be useful as a shorthand representation. A composite reaction consists of a sequence of elementary steps each of which will have its own energy profile and activation energy. The... 

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