Evans Polanyi Relationship Research Articles

Analytical approach for estimating kinetics of elementary steps on transition metals: Tunneling, trends and Brönsted–Evans–Polanyi relation

An overall formulation of an adiabatic approach, which combines adsorption characteristics of reactants and products with an analytical method of searching for the saddle point (SP) on semi-empirical adiabatic potential energy surface (APES), is presented for studying surface reactions kinetics. The following cases are analyzed: (i and ii) breaking or formation of a chemical bond, (iii) diffusion hopping of a molecule on a metal surface, and (iv) subsurface penetration of a metal surface. Numerical results for the activation energies and rate constants of elementary steps of CO oxidation, oxygen dissociative adsorption and water dissociation on transition metals (Pt, Pd, etc.) at the zero-coverage limit are presented. Specifically, the reaction energy dependencies of the kinetic characteristics like activation energy are presented as Brönsted–Evans–Polanyi relation. Moreover, the effect of tunneling along reaction coordinate is shown to be significant for several steps. The calculated diffusitivities of CO on (111) surfaces of several metals are correlated with the corresponding adsorption energies. The mechanism of subsurface oxygen penetration in a cluster resembling a (111) palladium surface is investigated. Approximate dependence of the activation energy of the oxygen subsurface diffusion on surface coverage is suggested.

Temperature-programmed reduction of unpromoted MoS 2-based hydrodesulfurization catalysts: First-principles kinetic Monte Carlo simulations and comparison with experiments

We present the first kinetic Monte Carlo (kMC) simulations of elementary processes corresponding to temperature-programmed reduction (TPR) experiments of unpromoted MoS 2-based γ-Al 2O 3-supported hydrodesulfurization catalysts. The active Mo-edge surfaces in interaction with the gas phase are represented by a one-dimensional periodic array of alternating “top” and “bridge” sites covered by surface species involved in the pathways connecting dissociative adsorption of dihydrogen and associative desorption of hydrogen sulfide. The simulations are monitored by setting partial pressures of H 2 and H 2S, and temperature or rate of temperature increase. Configuration energies and transition barriers computed by DFT were supplemented by a semi-empirical bond-counting scheme and Brönsted–Evans–Polanyi relationships. Simulated TPR spectra closely match the experimental results.

Interplay between carbon monoxide, hydrides, and carbides in selective alkyne hydrogenation on palladium

Alkyne hydrogenation, a widely used process in industry to purify olefin streams, comprises a prototype reaction to understand selectivity in heterogeneously catalyzed reactions. The selectivity of the reaction on palladium catalysts to the alkene, alkane, or oligomers strongly depends on the state of the (sub)surface; i.e., the occurrence of complex carbide/hydride phases. In practice, hydrogenation reactors in C2 and C3 cuts of steam crackers require continuous CO feeding in order to enhance the alkene selectivity of palladium-supported catalysts. In the present work, we have studied the impact of carbon monoxide on the formation of carbide and hydride phases as a standpoint to derive structure–performance relationships under realistic process conditions. For this purpose, catalytic tests on a standard 1 wt.% Pd/Al 2O 3 and Density Functional Theory on Pd(1 1 1) were combined. The influence of: (i) the alkyne (ethyne and propyne), (ii) the hydrogen:alkyne ratio (1–10), (iii) the carbon monoxide:hydrogen ratio (0–0.2), and (iv) the catalyst pretreatment on the product distribution was assessed in a continuous flow fixed-bed reactor at ambient pressure. In absence of CO, subtle changes in the hydrogen:alkyne ratio generate undesired products. Carbon monoxide enables the external control of the catalyst state by suppressing the formation of subsurface hydride and carbide phases, thereby stabilizing a high alkene yield in a broad range of feed hydrogen:alkyne ratios. This scenario contrasts with the more fragile regime of the hydride–carbide phases under CO-free conditions. DFT calculations obtained a single Brønsted–Evans–Polanyi relationship independently of the state of the catalyst (carbide, hydride, CO-covered) and the alkyne–alkene–alkane set (C2, C3).

Intramolecular Hydrogen Migration in Alkylperoxy and Hydroperoxyalkylperoxy Radicals: Accurate Treatment of Hindered Rotors

We have calculated the thermochemistry and rate coefficients for stable molecules and reactions in the title reaction families using CBS-QB3 and B3LYP/CBSB7 methods. The accurate treatment of hindered rotors for molecules having multiple internal rotors with potentials that are not independent of each other can be problematic, and a simplified scheme is suggested to treat them. This is particularly important for hydroperoxyalkylperoxy radicals (HOOQOO). Two new thermochemical group values are suggested in this paper, and with these values, the group additivity method for calculation of enthalpy as implemented in reaction mechanism generator (RMG) gives good agreement with CBS-QB3 predictions. The barrier heights follow the Evans-Polanyi relationship for each type of intramolecular hydrogen migration reaction studied.

Theoretical Prediction and Experimental Verification of Stability of Pt–3d–Pt Subsurface Bimetallic Structures: From Single Crystal Surfaces to Polycrystalline Films

In this paper we will provide a review of our recent studies on the general stability of the Pt–3d–Pt (3d = Ti, V, Cr, Mn, Fe, Co and Ni) subsurface structures, which are the desirable structural configurations in several applications in heterogeneous catalysis and electrocatalysis. We will first provide a review of density functional theory (DFT) predictions of the thermodynamic stability of Pt–3d–Pt(111) and Pt–3d–Pt(100) in vacuum and with adsorbed hydrogen and oxygen. The DFT results predict that the Pt–3d–Pt subsurface structures are stable in vacuum and with adsorbed hydrogen, while with adsorbed oxygen the 3d atoms should segregate to the surface to produce the 3d–Pt–Pt surface structures. The DFT predictions are verified experimentally on selected Pt–3d–Pt(111) systems. The experimental efforts are further expanded by bridging the materials gap form single crystal Pt(111) to polycrystalline Pt to incorporate multiple crystal facets and to determine their effects on the kinetic barriers for the segregation of the subsurface 3d atoms. In order to further correlate DFT calculations with experimental results, a Bronsted–Evans–Polanyi relationship is derived to correlate thermodynamic stability from DFT calculations with kinetic barriers from experimental measurements for the Pt–3d–Pt systems. Finally, empirical equations have been developed for predicting the thermodynamic stability of other bimetallic systems both in vacuum and with adsorbed hydrogen and oxygen.

Cover Picture: Fast Prediction of Selectivity in Heterogeneous Catalysis from Extended Brønsted–Evans–Polanyi Relations: A Theoretical Insight (Angew. Chem. Int. Ed. 47/2009)

Brønsted–Evans–Polanyi relations are famous in heterogeneous catalysis for their fast prediction of activation barriers with the sole knowledge of the reaction enthalpies. This model has now been extended by D. Loffreda et al. to the hydrogenation of unsaturated aldehydes on platinum. In their Communication on page 8978 ff., they describe on the basis of density functional theory calculations a linear relation connecting the activation barrier with the stability of the initial precursor state.

Fast Prediction of Selectivity in Heterogeneous Catalysis from Extended Brønsted–Evans–Polanyi Relations: A Theoretical Insight

Fast Prediction of Selectivity in Heterogeneous Catalysis from Extended Brønsted–Evans–Polanyi Relations: A Theoretical Insight

Influence of step sites in the molecular mechanism of the water gas shift reaction catalyzed by copper

The role of the step sites in the water gas shift reaction catalyzed by Cu surfaces has been studied by using the Cu(3 2 1)-stepped surface as a representative model and periodic density functional theory within a supercell approach. Several reaction pathways were considered and the corresponding transition states for the elementary steps on each pathway were located and characterized. It was found that the presence of steps favors the associative route through the carboxyl intermediate assisted by co-adsorbed OH. The presence of step sites decreases the activation energy barriers for the rate-limiting steps, compared to the perfect Cu(1 1 1) surface. Reaction rate constants for the different pathways involved in the two molecular mechanisms, obtained from transition state theory, are reported. Finally comparison to previous work allows one to propose a useful Brønsted–Evans–Polanyi relationship.

Automated mechanism generation. Part 1: mechanism development and rate constant estimation for VOC chemistry in the atmosphere

A framework for automated mechanism generation for modeling atmospheric chemistry at the mechanistic level was developed. In part 1, categorization of reactions into reaction families and determination of rate coefficients using a hierarchical approach that uses experimental data and kinetic correlations are described. The main focus was to develop kinetic correlations for estimating rate coefficients that are not available experimentally, and the main correlation used was the Evans–Polanyi relationship that relates the activation energy to the heat of reaction. A hierarchical scheme for calculating heats of reaction and other thermodynamic properties was developed. The rate constants calculated using the proposed correlations are in most cases within an order of magnitude of available experimental values, and 82% are within a factor of five.

Theoretical elucidation of the selectivity changes for the hydrogenation of unsaturated aldehydes on Pt(1 1 1)

On the basis of density functional theory calculations and an original use of a generalized Brönsted–Evans–Polanyi relationship, the key question of the change of selectivity has been solved for hydrogenation of three unsaturated aldehydes (acrolein, crotonaldehyde and prenal) on a Pt(1 1 1) surface. This study supports the idea that the selectivity in favor of the unsaturated alcohol (UOL) is controlled by adsorption thermodynamics of this partially hydrogenated product while the selectivity in favor of the other compound in competition (saturated aldehyde, SAL) obeys a more subtle kinetic control. The present work demonstrates the efficiency and the potentiality of the exposed correlation.

Reaction of Phenols with the 2,2-Diphenyl-1-picrylhydrazyl Radical. Kinetics and DFT Calculations Applied To Determine ArO-H Bond Dissociation Enthalpies and Reaction Mechanism

The formal H-atom abstraction by the 2,2-diphenyl-1-picrylhydrazyl (dpph(*)) radical from 27 phenols and two unsaturated hydrocarbons has been investigated by a combination of kinetic measurements in apolar solvents and density functional theory (DFT). The computed minimum energy structure of dpph(*) shows that the access to its divalent N is strongly hindered by an ortho H atom on each of the phenyl rings and by the o-NO(2) groups of the picryl ring. Remarkably small Arrhenius pre-exponential factors for the phenols [range (1.3-19) x 10(5) M(-1) s(-1)] are attributed to steric effects. Indeed, the entropy barrier accounts for up to ca. 70% of the free-energy barrier to reaction. Nevertheless, rate differences for different phenols are largely due to differences in the activation energy, E(a,1) (range 2 to 10 kcal/mol). In phenols, electronic effects of the substituents and intramolecular H-bonds have a large influence on the activation energies and on the ArO-H BDEs. There is a linear Evans-Polanyi relationship between E(a,1) and the ArO-H BDEs: E(a,1)/kcal x mol(-1) = 0.918 BDE(ArO-H)/kcal x mol(-1) - 70.273. The proportionality constant, 0.918, is large and implies a "late" or "product-like" transition state (TS), a conclusion that is congruent with the small deuterium kinetic isotope effects (range 1.3-3.3). This Evans-Polanyi relationship, though questionable on theoretical grounds, has profitably been used to estimate several ArO-H BDEs. Experimental ArO-H BDEs are generally in good agreement with the DFT calculations. Significant deviations between experimental and DFT calculated ArO-H BDEs were found, however, when an intramolecular H-bond to the O(*) center was present in the phenoxyl radical, e.g., in ortho semiquinone radicals. In these cases, the coupled cluster with single and double excitations correlated wave function technique with complete basis set extrapolation gave excellent results. The TSs for the reactions of dpph(*) with phenol, 3- and 4-methoxyphenol, and 1,4-cyclohexadiene were also computed. Surprisingly, these TS structures for the phenols show that the reactions cannot be described as occurring exclusively by either a HAT or a PCET mechanism, while with 1,4-cyclohexadiene the PCET character in the reaction coordinate is much better defined and shows a strong pi-pi stacking interaction between the incipient cyclohexadienyl radical and a phenyl ring of the dpph(*) radical.

Thermodynamics and kinetics of oxygen-induced segregation of 3d metals in Pt–3d–Pt(111) and Pt–3d–Pt(100) bimetallic structures

The stability of subsurface 3d transition metals (3d represents Ni, Co, Fe, Mn, Cr, V, and Ti) in Pt(111) and Pt(100) was examined in vacuum and with 0.5 ML atomic oxygen by a combined experimental and density functional theory (DFT) approach. DFT was used to predict the trends in the binding energy of oxygen and in the stability of 3d metals to remain in the subsurface layer. DFT calculations predicted that for both (111) and (100) crystal planes the subsurface Pt-3d-Pt configurations were thermodynamically preferred in vacuum and that the surface 3d-Pt-Pt configurations were preferred with the adsorption of 0.5 ML atomic oxygen. Experimentally, the DFT predictions were verified by using Auger electron spectroscopy to monitor the segregation of Ni and Co in Pt-3d-Pt structures on polycrystalline Pt foil, composed of mainly (111) and (100) facets. The activation barrier for the oxygen-induced segregation of Ni was found to be 17+/-1 kcal/mol attributed to the Pt(111) areas and 27+/-1 kcal/mol attributed to the Pt(100) areas of the Pt foil. For Pt-Co-Pt, the activation barrier was found to be 10+/-1 kcal/mol and was attributed to the Pt(111) areas of the Pt foil. The Bronsted-Evans-Polanyi relationship was utilized to predict the activation barriers for segregation of the other Pt-3d-Pt(111) and Pt-3d-Pt(100) systems. These results are further discussed in connection to the activity and stability for cathode bimetallic electrocatalysts for proton exchange membrane fuel cells.

Dissociative Adsorption of O2 on Clean and CO-Precovered Pt Surfaces

ABSTRACTIt is generally accepted that CO oxidation on transition metals follows a Langmuir-Hinshelwood mechanism. The oxidation reaction takes place in two sequential steps where the oxygen molecule first dissociates into atomic oxygen and then reacts with an adsorbed CO to form CO2. One critical question concerning the reaction kinetics under high pressure is the probability of oxygen dissociation on a highly CO covered surface. On bare transition metal surfaces, molecularly adsorbed oxygen readily dissociates with little or no apparent activation barrier. In industrial diesel engine catalysis, the metal surface is initially packed with CO. Subsequent reactions such as oxygen dissociation must take place on a CO covered surface. In this paper, we performed density functional theory (DFT) calculations for O2 dissociation on Pt(111) in the presence of different CO adsorption environments. While several stable O2 molecular precursor states (top-bridge-top, top-fcc-bridge, and top-hcp-bridge) exist on a clean Pt(111) surface, these precursors become endothermic beyond a critical CO coverage of ∼0.44 ML. Furthermore, the reaction path for CO oxidation via dissociated atomic oxygen becomes less favorable at higher CO coverage, primarily due to competitive adsorption and lateral repulsion. It was found that the oxygen dissociation barrier and the binding energies of atomic oxygen are well correlated via the Evans-Polanyi relationship.

Microkinetic interpretation of HDS/HYDO selectivity of the transformation of a model FCC gasoline over transition metal sulfides

The conversion of a model FCC gasoline (composed of 2-methylthiophene (2MT), 2,3-dimethylbut-2-ene (23DMDB2N) and orthoxylene in n-heptane) under realistic hydrodesulfurization (HDS) conditions was investigated over a serie transition monometallic sulfides (Ni 3S 2, PdS, Co 9S 8, Rh 2S 3, RuS 2, PtS and MoS 2) and unsupported transition bimetallic sulfide catalysts (NiMoS and CoMoS). The results reveal for the first time that a volcano curve relationship exists between the ab initio calculated sulfur–metal bond energy, E(MS), descriptor of bulk TMS and their activities in olefin hydrogenation and in alkylthiophene desulfurization measured simultaneously. In particular, Rh 2S 3 with an intermediate sulfur–metal bond energy of 119 kJ/mol is the most active catalyst in both case hydrogenation of the olefin and in HDS of a sulfur compound. Furthermore, the HDS/HYDO selectivity which is the most important parameter in the deep HDS of gasoline, presents a maximum for the NiMoS catalyst with E(MS) of 128 kJ/mol. A microkinetic model based on Brønsted–Evans–Polanyi relationships and the competitive adsorption of the sulfur molecule and alkene on the catalytic site is proposed to give a rational interpretation of the experimental catalytic results.

High ethane dehydrogenation activity of [GaH] 2+[sbnd]Al pair sites in Ga/H-[Al]ZSM-5: A DFT thermochemical analysis of the catalytic sites under reaction conditions

Through a full thermochemical analysis at reaction conditions, we studied ethane dehydrogenation activity of extra-framework [GaH] 2+ species in Ga/H-[Al]ZSM-5 at the 6–31g(d,p)/B3LYP level. We provide a theoretical evidence to support the proposition of [GaH] + near-pair framework–Al sites as being the active catalytic sites for ethane dehydrogenation. Dehydrogenation activity is governed by the reducibility of [GaH] 2+Z 2− d site in the presence of H 2, which is largely dependent on a zeolite ring structure consisting of two framework Al atoms. The optimum sites are defined by the intersection of linear Brønsted–Evans–Polanyi relations between the activation energy of the structure sensitive steps and enthalpy of reduction for the catalytic site. A comparison of the carbenium and alkyl activation mechanism indicates that the activity of the alkyl activation mechanism will be limited by the removal of highly activated ( Δ E act ∼ 55 – 60 kcal / mol ) ethene from [HGaC 2H 5] + species. Our thermochemical analysis also indicates that at higher temperatures, the pair Al sites with larger Al Al distances become more prevalent, increasing the number of optimum catalytic sites. This work suggests a potential optimal Si/Al ratio for a given Ga loading.

Study of dissociation barriers of [formula omitted] on [formula omitted] and [formula omitted

The minimum energy paths (MEP) of H 2 dissociation on Ni ( 1 1 1 ) and Ni 3 Fe ( 1 1 1 ) are calculated using density functional theory. The dissociation barrier on Ni 3 Fe ( 1 1 1 ) is lower by 0.09 eV with respect to the barrier of 0.1 eV on Ni ( 1 1 1 ) . A formula to approximate MEP is proposed and fits well the calculated MEP of H 2 dissociation on Ni ( 1 1 1 ) . By this formula, the difference in the dissociation barriers can be semi-quantitatively related with the space-independent difference in atomic chemisorption energies, providing a new way to understand the Brønsted–Evans–Polanyi relationship.

Rate constants for the H abstraction from alkanes (R–H) by [formula omitted] radicals: A systematic study on the impact of R and R′

A possible source of chain-branching in low temperature combustion is thermal decomposition of alkyl hydroperoxides (R′OOH). One way these species can be produced is via H atom abstraction reactions from alkanes (RH) by alkylperoxy radicals R ′ O 2 .An earlier study focussing on the abstraction from ethane by HO 2 , CH 3 O 2 and C 2 H 5 O 2 revealed that these reactions have a noticeable impact on calculated ignition times of ethane/O 2 mixtures.Another outcome was that the abstraction rate constants for CH 3 O 2 and C 2 H 5 O 2 are virtually identical but smaller than that for HO 2 .The associated activation energies followed an Evans–Polanyi relationship while a common A-factor could be used to describe the kinetics of all three reactions within a factor of about 2–3.In this current study, we extend the investigation by (1) considering a set of alkanes(RH = CH 4, C 2H 6, C 3H 8, C 4H 10) and (2) by including additional peroxy species ( R ′ O 2 with R′ = H, CH 3, C 2H 5, C 3H 7, C 4H 9, HC O, and CH 3C O). We present rate constants for a total of 32 reactions and analyze the data with respect to systematic trends in the reactivity. The results reveal that the rate constants decrease in the order acylperoxy > HO 2 > alkylperoxy. The reactivity of different C–H bonds follows the bond strengths. Overall the heat of reaction is found to be the dominant but not the only rate constant controlling parameter. The accuracy of the calculations and implications of the results are discussed.

Energetics of methane dissociative adsorption on Rh{111} from DFT calculations

We present DFT calculations of methane activation and CH x ( x = 0 – 3 ) adsorption at a Rh{111} surface and compare our results with data for other elements. The activation mechanism has similar energetics as found for other transition metal surfaces, where the first and last steps are the most difficult. On Rh{111}, the CH dehydrogenation barrier is the highest. The CH radical is also the most stable fragment. The barrier that we find for the first methane activation step on Rh{111} is relatively low, lower than expected from comparing it with that step on Ru{0001} [I.M. Ciobîcă, F. Frechard, R.A. van Santen, A.W. Kleyn, J.P.J. Hafner, J. Phys. Chem. B 104 (14) (2000) 3364–3369] or Ni{111} [R.M. Watwe, H.S. Bengaard, J.R. Rostrup-Nielsen, J.A. Dumesic, J.K. Nørkov, J. Catal. 189 (1) (2000) 16–30] in terms of the Brønsted–Evans–Polanyi relation. Therefore, methane is likely more easily activated on Rh{111} than on Ru{0001} or Ni{111}. Adsorption on Rh{111} in general favors hollow sites, but the energy differences between sites are often < 10 kJ mol −1 .

Modelling of ethanol decomposition on Pt(111): a comparison with experiment and densityfunctional theory

Ethanol decomposition on the clean Pt(111) surface has been studied in the zero-coveragelimit within the framework of the unity bond index-quadratic exponent potential(UBI-QEP) model. Previous work, both experimental and theoretical, was already availablein the literature on this reaction. The system has therefore been used as a benchmark forevaluating the accuracy of the simple phenomenological UBI-QEP model. The latter allowsthe estimation of key reaction parameters such as adsorption energies and reaction barriers.The stability of possible dissociation intermediates has been investigated andthe most probable decomposition pathway has been simulated by integration ofthe related rate equations. We find that the model provides good estimates foradsorption energies of mono-coordinated molecules with long bond distances and givesrealistic values for dehydrogenation barriers. Poor agreement with density functionaltheory (DFT) is found in the estimates of C–C and C–O bond cleavage barriers,even though the results obtained are in line with the experiments. It is foundthat transition and final state energies obtained from the model satisfy the linearBrønsted–Evans–Polanyi relation. Temperature programmed desorption spectra and surfacecoverage of the adspecies as a function of the temperature have been simulated inorder to provide a direct comparison with previous experimental data. A possiblepathway for ethanol decomposition on Pt(111) is finally proposed on the basis ofthe present calculations, conciliating previous DFT and experimental results.

Transition structures and reaction barriers in the styrene–acrylonitrile copolymerization system according to quantum mechanical calculations

AbstractThe geometries and electronic properties of substrates, transition structures (TS), and product radicals in modeled elementary propagation reactions were studied for the styrene–acrylonitrile monomer system by use of quantum‐mechanical calculations: (DFT/B3‐LYP/6–31G(d), ROMP2/6–311+G(3df,2p)//DFT/B3‐LYP/6–31G(d), and DFT/B3‐LYP/6–311+G(3df,2p)//DFT/B3‐LYP/6–31G(d)) and for some parameters, the high‐level composite method G3 (Gaussian‐3, G3/MP2). Activation enthalpies (ΔHact) and reaction enthalpies (ΔHr) for modeled propagation reactions at 298.15 K were evaluated. The enthalpy of activation energy (ΔHact, kJ/mol) for the investigated elementary reactions rises for the B3‐LYP calculation in the following order: (CH3A•+S) &lt; (CH3A•+A) &lt; (CH3S•+A) &lt; (CH3S•+S). For three propagation reactions, (CH3A•+A), (CH3A•+S), and (CH3S•+A), correlation between reaction enthalpy and enthalpy of activation suggests weak or negligible polar effects reflecting the Evans–Polanyi relation. However, from the electron affinities and ionization energies values data, it is not excluded that at least for [CH3A•+S[b]] and [CH3S•+A[b]] reactions, nucleophilic and electrophilic polar effects, respectively, can also be expected. The dependencies between TS geometries, electronic parameters, and enthalpic effects suggest the presence of a steric factor in all TS, including its exceptionally high contribution to the activation enthalpy for the CH3S•+S addition. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1827–1844, 2005