A Theoretical and Computational Analysis of Linear Free Energy Relations for the Estimation of Activation Energies

Abstract

We present a theoretical and computational analysis to elucidate the relation of the Brønsted−Evans−Polanyi (BEP) and transition state scaling (TSS) correlations. We find that the TSS correlation is an approximation of the BEP correlation. The BEP correlation allows for the straightforward identification of homologous series via standard statistical tests and has better error properties than the TSS correlations. We find that the unit cell size used in the DFT calculations does not have a significant effect on the correlation parameters; however, the zero point energy correction does have a significant effect on the correlation parameters, especially for (de)hydrogenation reactions. We propose a method for using this information to estimate zeropoint-energy-corrected activation energies without resorting to calculations of the zero point energy correction for every species. Finally, we find that BEP correlations derived for one parent molecule may be applicable to other molecules beyond the training set.

Towards more accurate prediction of activation energies for polyalcohol dehydrogenation on transition metal catalysts in water

“…Considering the satisfying GGAs performance in modeling metallic surfaces, (19,(27)(28)(29) and as a continuation of our previous works (22,24) we used PW91 functional (30) in the current study. The two bottom layers are frozen in a bulk-like geometry, only the two uppermost layers being free to relax.…”

Ethanol Activation on Closed-Packed Surfaces

“…76 The intercept can also be shown to give insights into the inherent reactivity and selectivity of a metal for different chemistries. 65 We begin our analysis by examining trends in the earliness/ lateness of the transition states. Figure 5 and the slopes in Table 5 indicate that the BEP slopes for the different bond types do not change appreciably on the different metals (at least within the uncertainty of the parameters).…”

Building large microkinetic models with first-principles׳ accuracy at reduced computational cost

“…In the FPSEM model, the species free energies were estimated with group additivity. The activation energies were estimated using BEP correlations, which were divided into five homologous series (C-H, O-H, C-C, C-OH, and C-O), in line with our previous findings (Sutton and Vlachos, 2012), excluding the values for ethanol dehydroxylation and CCOH n dehydrogenation, as these were found to deviate significantly from the trends of the remaining points. This model is then refined as described below to generate a hierarchy (a family) of refined microkinetic models.…”

“…The zero-order accurate methods are all semi-empirical correlations (typically regressed from a set of DFT training data): group additivity (GA) (Benson and Buss, 1958;Benson et al, 1969;Chen et al, 2011;Cohen and Benson, 1993;Kua et al, 2000; for estimating the free energies of species from group values, the linear scaling relations (LSR) (Abild-Pedersen et al, 2007;Fernández et al, 2008;Jones et al, 2011;Salciccioli et al, 2010; for transferring previously estimated thermochemistry from one metal to another, and the Brønsted-Evans-Polanyi (BEP) relations (Alcala et al, 2003;Bligaard et al, 2004;Ferrin et al, 2009;Michaelides et al, 2003;Pallassana and Neurock, 2000;Salciccioli et al, 2011b;Sutton and Vlachos, 2012;Van SANTEN et al, 2007) for estimating activation energies from reaction energies. These correlations are all linear, and thus, kinetic parameters are accessible in real time and thereby enable the construction of high throughput microkinetic models for catalyst screening (Ferrin et al, 2009).…”