Potential energy profiles elementary reactions, 57

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

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. 

A concerted reaction is one in which the conversion of reactants (R) into the products (P) occurs directly by way of a single transition state (T.S.). An exothermic concerted reaction is represented by the potential energy profile of Fig. 3.1(a). When the conversion of reactants into products proceeds by way of more than one transition state, such that one or more intermediates (I) are formed, the processes are accordingly non-concerted. A two-step process involving one (metastable) intermediate is represented by Fig. 3.1(b). However, since each elementary step of any chemical reaction must be concerted, by definition, then case (b) may be divided into the two concerted sequences ... 

The calculation of reaction profiles is one of the main subjects of the static approach (see later) the relevance of reaction profiles in representing the potential energy determining the course of elementary processes is given by the adequacy of expansion Eq. (36) and of neglecting the second-order term. It is obvious that expansion Eq. (36) tends to be more adequate when the kinetic energy content in the evolving polyatomic system is small. 

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.

A schematic energy profile for the endothermic elementary reaction in Equation 2.5 is given in Figure Q.l. The difference in potential energy between products and reactants is positive, which is consistent with the endothermic nature of the reaction. 

Figure 6-6. Reaction path profile (potential energy curve) for the elementary process of NO synthesis O + N2 — NO + N, showing adiabatic and non-adiabatic reaction channels.

Many reactions involve a sequence of elementary steps, with the rate expression being determined by the nature of the rate-determining step (RDS). Only those species involved in this step are included in the rate expression for that reaction. The sequence of steps is referred to as the reaction mechanism. It is possible to link the ideas involved here with transition-state theory and develop potential energy level profiles that reflect the sequence of steps involved. Consider the reaction... 

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. " ... 

Figure 3.3.10 (A) The electrode potential dependence of the Gibbs free energy reaction pathway of the ORR. While the overall reaction has elementary steps that are energetically uphill at +1.23 V (red pathway), all elementary steps become downhill at +0.81 V (yellow pathway) (i.e. at an overpotential of approximately -0.42 V. At this point, the reaction is not limited by kinetics anymore. (B) The experimentally observed current-potential (j-E) relation of the ORR is consistent with the computational conclusions from (A) between +1.23 V and +0.81 V the j-E curve shows an exponential behavior, while at electrode potentials below +0.81 V, the ORR reaction rate becomes oxygen mass-transport limited, which is reflected by a flat ( j-E) profile. Figure adapted with permission from [19]. 

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