Evans-Polanyi relation for

The discrepancies highlighted by Figs. 17.7 and 17.8 may be due to a breakdown of the Evans-Polanyi relation for a HAT reaction or alternatively the contribution of asynchronous PCET induced by the site-differentiation inherent to the metal oxidations as presented in Fig. 17.4. Studies that comprehensively treat the IE vs. 

Voj vodic A, Calle-Vallejo F, Guo W, Wang S, Toftelund A, Studt F, Shen J, Man IC, Rossmeisl J, Bligaard T, Nprskov JK, Abild-Pedersen F. On the behavior of Brpnsted-Evans-Polanyi relations for transition metal oxides. J Chem Phys 2011 134 244509. 

Wang SG, Temel B, Shen JA, Jones G, Grabow LC, Studt F, Bligaard T, Abild-Pedersen F, Christensen CH, Nprskov JK. Universal Brpnsted-Evans-Polanyi relations for C-C, C-O, C-N, N-O, N-N, and 0-0 dissociation reactions. Catal Lett 2011 141 370-373. 

Linear relations between the activation energies and heats of adsorption or heats of reaction have long been assumed to be valid. Such relations are called Bronsted-Evans-Polanyi relations [N. Bronsted, Chem. Rev. 5 (1928) 231 M.G. Evans and M. Polanyi, Trans. Faraday Soc. 34 (1938) 11]. In catalysis such relations have recently been found to hold for the dissociation reactions summarized in Pig. 6.42, and also for a number of reactions involving small hydrocarbon fragments such as the hydro-... 

The fact that universal Brondsted-Evans-Polanyi relations appear to exist for these dissociation reactions raises the following questions. Why is the relationship between the activation energy and the adsorption energy of the dissociation products linear Why does it depend on structure Why is it independent of the adsorbates ... 

Explain the Bronsted-Evans-Polanyi relation in a simple potential energy scheme for an elementary reaction step. 

Logadottir A, Rod TH, N0rskov JK, Hammer B, Dahl S, Jacobsen CJH. 2001. The Br0nsted-Evans-Polanyi relation and the volcano plot for ammonia synthesis over transition metal catalysts. J Catal 197 229. 

In the present chapter, we have attempted to illustrate how surface bonding and catalytic activity are closely related. One of the main conclusions is that adsorption energies of the main intermediates in a surface catalyzed reaction is often a very good descriptor of the catalytic activity. The underlying reason is that we find correlations, Brpnsted-Evans-Polanyi relations, between activation barriers and reaction energies for a number of surface reactions. When combined with simple kinetic models such correlations lead to volcano-shaped relationships between catalytic activity and adsorption energies. 

For the reaction of H02 with H2 the Evans-Polanyi relation predicts E7 = 25 kcal. per mole. This in excellent agreement with Baldwins value (9) but not in very good agreement with the more reasonable value of E7 = 20 kcal. per mole required to bring the A factor down to a reasonable level. It could, however, be argued that H02 is somewhat more reactive than R02 and that a lower activation energy is in order 20 kcal. per mole is still about 6 kcal. per mole more than the endothermicity of the reaction. 

For analyzing more deeply the origin of free-radical persistence and the eventual activation barrier of their dimerization reactions, we have wondered whether the latter obey the Evans-Polanyi relation ... 

Figure 7.6. Volcano curve for CO methanation (T. Bligaard, J.K. Norskov, S. Dahl, J. Matthiesen, C.H. Christensen, J. Sehested, The Bronsted-Evans Polanyi relation and the volcano curve in heterogeneous catalysis, Journal of Catalysis 224 (2004) 206).

As long as the structures of ttansition state and dissociated state are close, changes in metal-atom interactions will lead to the Bronsted-Evans-Polanyi relation between activation energy and reaction energy of a surface elementary reaction. Interestingly, microscopic reversibility imphes that the Bronsted-Evans-Polanyi proportionality constant for recombination is typically 0.1. This implies that the ratio of the energy of the surface fragments in the transition state compared to the dissociated state is a constant and on the order of 90%. 

The large value of a in these Brpnsted-Evans-Polanyi relations is consistent with a late transition state for the dissociation reactions as discussed in Chapter 2. The only parameter in the universal relations is the reaction energy Er, which can be easily calculated. 

The foregoing discussion deals with the stmcture effect on A (or entropy change). The stmcture effect on the activation energy (or reaction enthalpy change) is described by the Evans-Polanyi relation, with just two parameters Eo and a) for each single event type, which generally are obtained from model-compound experiments. 

Reactions involving simple reactants and products often offer simple descriptions of activity or selectivity. The Bronsted-Evans-Polanyi (BEP) relation, for instance, states that the activation barrier, Ea, and the heat of reaction, AE, of elementary dissociation reactions are often linearly correlated (Fig. 1). Extensive DFT calculations have supported this empirical relation for a large number of elementary dissociation reactions and suggest that it is due to the structural similarities between the transition state and the product states. When such a dissociation step is rate-limiting, knowing AE is sufficient to capture the activity of the overall reaction, which exhibits volcano-shaped... 

Equation (82) predicts that for reactions with zero free energy change a = 0.5, while for exothermic reactions, a < 0.5 and for endothermic reactions, a > 0.5. Since according to both Marcus theory and the Bell— Evans-Polanyi model early transition states are related to exothermic reactions and late transition states to endothermic reactions, a may be interpreted as a relative measure of transition state geometry. However, in our view even this interpretation should be treated with a measure of healthy scepticism. Even if one accepts Marcus theory without reservation, the a... 

These simple considerations yield several corollaries, sometimes known together as the Bell-Evans-Polanyi (BEP) principle [14]. First, there is an approximately linear relation between the barrier height and the reaction energy this is the basis of the Bronsted relation (and other LFERs). Second, the proportionality constant a in Eq. (19.2) tends to be smaller for exothermic reactions (but larger for endothermic reactions). Third, the position of the crossing point between the curves lies closer to the reactants for more exothermic reactions this is the basis of the Hammond postulate, that the TS for a more exothermic reaction more closely resembles the reactants (and that for a more endothermic reaction more closely resembles the products). 

The Bell-Evans-Polanyi relationship, Hammond s postulate, and the Marcus equation are all approaches to analyzing, understanding, and predicting relationships between the thermodynamics and kinetics of a series of closely related reactions. This is an important issue in organic chemistry, where series of reactions differing only in peripheral substituents are common. Each of these approaches provides a sound basis for the intuitive expectation that substituents that favor a reaction in a thermodynamic... 

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