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Nature Chemistry 1, 37 - 46 (2009)


Towards the computational design of solid catalysts

J. K. Nørskov1, T. Bligaard1, J. Rossmeisl1 & C. H. Christensen2

Over the past decade the theoretical description of surface reactions has undergone a radical development. Advances in density functional theory mean it is now possible to describe catalytic reactions at surfaces with the detail and accuracy required for computational results to compare favourably with experiments. Theoretical methods can be used to describe surface chemical reactions in detail and to understand variations in catalytic activity from one catalyst to another. Here, we review the first steps towards using computational methods to design new catalysts. Examples include screening for catalysts with increased activity and catalysts with improved selectivity. We discuss how, in the future, such methods may be used to engineer the electronic structure of the active surface by changing its composition and structure.

During the past century chemists have developed efficient chemical reactions for converting fossil resources into a broad range of fuels and chemicals, and this can be considered one of the most important and far-reaching scientific developments up to now. Today, essentially all transportation fuels are refined in a number of catalytic processes and most chemicals are also produced using technologies based on catalysis1. A few well-known examples illustrate the impact: about half of all petrol in the world is now produced by fluid catalytic cracking using specially designed zeolite catalysts, and the Haber–Bosch process — featuring an iron catalyst — continues to have a key role in the production of fertilizers. The list of important small- and large-scale processes by which fossil resources are converted into fuels and chemicals is almost endless.

Such catalytic technologies have also resulted in various environmental issues — even the best processes do not allow a complete elimination of undesirable byproducts. Many innovative, catalytic technologies have subsequently been implemented to remedy these new problems; one famous example is the precious-metal-based three-way catalyst installed in most petrol-fuelled passenger cars. Moreover, these developments have contributed to an increased use of fossil resources and thus to the increasing carbon dioxide levels in the atmosphere. Currently, there is a significant drive to relinquish our dependence on fossil fuels and to minimize the emission of carbon dioxide. Clearly, this calls for many new and improved catalytic processes, and for catalytic technologies that focus on prevention rather than on remediation.

Reducing environmental impact will require entirely new catalysts: catalysts for new processes, more active and more selective catalysts and preferably catalysts that are made from earth-abundant elements. This represents a formidable challenge and it will demand an ability to design new catalytic materials well beyond our present capabilities. The ultimate goal is to have enough knowledge of the factors determining catalytic activity to be able to tailor catalysts atom-by-atom. The catalytic properties of a material are in principle determined completely by its electronic structure, so the objective is the engineering of electronic structure by changing composition and physical structure. The approach is illustrated in Fig. 1. Over the past few decades our understanding of why particular materials are good catalysts for given reactions has improved. The challenge is to invert this problem; given that we need to catalyse a certain reaction under a set of specified conditions, which material should we choose?

Figure 1: Tailoring materials.

Figure 1 : Tailoring materials.

Illustration of the way the electronic structure is the link between the structure and composition of a material and its functionality. Changing the functionality can be achieved by engineering the electronic structure through modification of structure and composition. The example shown is a MoS2 sheet, a few atoms wide, where new electronic states at the edges cross the Fermi level and give rise to catalytic activity, for instance in electrochemical hydrogen evolution63.

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The aim of controlling matter at the molecular scale by engineering the electronic structure is not restricted to catalytic materials; it is a general challenge in chemistry, physics and materials science, and there is considerable progress in several areas such as materials for batteries2, hydrogen storage3, optical absorption4 and molecules for homogeneous catalysis5, 6. Catalysis at surfaces is particularly well suited for electronic structure engineering, primarily because the link between the atomic-scale properties and the macroscopic functionality — the kinetics — is well developed. In addition, the theoretical description of surface reactions has been enhanced considerably by the availability of a large number of quantitative experimental surface-science studies of adsorption and reaction phenomena7, 8, 9, 10, 11, 12.

Here, we review some of the first examples of the computer-based design of solid catalysts. We introduce a number of concepts linking catalytic performance to the properties of the catalyst's surface, and in turn discuss how the surface electronic structure determines the catalytic properties. Finally, we discuss some of the challenges ahead.

Trends and descriptors of catalytic activity

The extraordinary progress in density functional theory (DFT) calculations for surface processes is the key development that has created the possibility of computer-based catalyst design13. Current methods are fast enough to allow the treatment of complex, extended systems14, 15. They can also now provide the interaction energies of molecules and atoms with metal surfaces with sufficient accuracy to describe trends in reactivity for transition metals and alloys16.

There are now several cases where the complete kinetics of a catalytic reaction has been evaluated solely on the basis of DFT calculations of reaction barriers, reaction energies and the associated entropies17, 18, 19, 20. Figure 2 shows the comparison between calculated and measured rates for three different reactions and catalytic surfaces. Overall, the agreement between DFT-based kinetic models and experiment is surprisingly good, and they serve to illustrate the accuracy and value of current density functional theory.

Figure 2: Comparison of experimental results for three different catalytic reactions with the results of kinetic models based on DFT calculations.

Figure 2 : Comparison of experimental results for three different catalytic reactions with the results of kinetic models based on DFT calculations.

a, CO oxidation activity over ruthenium oxide at low oxygen pressures. Adapted from ref. 18; © 2004 APS. b, Ammonia synthesis productivity over a ruthenium catalyst at industrial reaction conditions. Based on data from ref. 19. c, Methanol decomposition rate over a platinum catalyst. In each of these three cases the theoretical calculations and the experiments agree semi-quantitatively. Adapted from ref. 20; © 2006 Springer.

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The agreement between theory and experiment is particularly noteworthy in two cases for supported metal catalysts (ruthenium and platinum in Fig. 2) — which are considerably more complex than a well-defined single crystal surface. Here, the theoretical treatment has assumed that the supported metallic nanoparticles can be viewed as crystalline particles with well-defined facets in addition to edges, corners, steps and kinks, and that these surface features can be treated as being independent of each other. Each surface structure will then contribute to the overall rate and the most active one will typically dominate. This is, for instance, the case for ammonia synthesis where step sites dominate19. Several experiments have shown real catalyst particles to have well-defined geometrical features21, 22, 23, 24, 25. The independence of the different types of surface sites on metal particles can be understood by noting that the electrostatic screening by the metallic, freely moving electrons introduces a 'nearsightedness'26, 27 such that a perturbation to the surface is only significant within a screening length — typically a few ångströms. For very small particles, where the electrons are no longer metallic, this picture breaks down — the exact size where this happens is still an open question.

The complete kinetic description of a given system is a quite demanding task. One cannot, at this moment, imagine screening a large number of systems using a procedure that requires such a description for each system considered. Rather, it is instructive to establish which properties at the atomic scale determine the macroscopic kinetics. Such an approach in terms of descriptors is outlined below.

The identification of descriptors is facilitated substantially by the observation that activation energies for elementary surface reactions are strongly correlated with adsorption energies. This is illustrated in Fig. 3 for the methanation reaction (CO + 3H2 right arrow CH4 + H2O). First, it is established computationally that the activation barrier for CO dissociation is forbiddingly high on the most close-packed surface, whereas certain steps (and other similar geometries) have much lower barriers (by approximately 1 eV)28, 29. The active site on the catalyst surface is therefore identified as the steps or edges on the surface of the catalyst material.

Figure 3: Identification of a descriptor for the methanation reaction (CO + 3H2 right arrow CH4 + H2O).

Figure 3 : Identification of a descriptor for the methanation reaction (CO + 3H2 |[rarr]| CH4 + H2O).

a, Calculated energy diagrams for CO methanation over nickel, ruthenium and rhenium. Only the highest of the activation barriers for hydrogenation of C and O are included. b, Brønsted–Evans–Polanyi relation for CO dissociation over transition metal surfaces. The transition state potential energy, Ea, is linearly related to the CO dissociation energy. c, The corresponding measured volcano-relation for the methanation rate33. Parts b and c reprinted from ref. 50; © 2006 Elsevier.

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On comparing a series of different metal surfaces as catalysts for the methanation reaction (Fig. 3a) it is found that the barrier for CO activation, as well as the barriers for CH4 and H2O formation, are closely related to the stability of C and O on the surface. The more stable they are, the lower the barrier for CO dissociation will be, and the higher the barrier becomes for CH4 and H2O formation. In fact, all three activation energies are found to scale essentially linearly with the reaction energy in Brønsted–Evans–Polanyi (BEP)-type relationships (see Fig. 3b for CO dissociation)28, 30, 31, 32. Such correlations lead directly to a volcano relationship between the rate and the dissociative chemisorption energy, Ediss, of CO (ref. 33; see Fig. 3c). The reason is that in the limit of weak coupling (Ediss is only a little negative), the BEP relation gives that the barrier for dissociation of the reactants will be high and the rate low. For strong coupling (Ediss very negative) the activation energy of adsorption is small but now the barrier for forming the products will be large. An optimal interaction strength must exist between these two limits — this is known as the Sabatier principle34. Figure 3 shows that calculations can be used to quantify the interaction strength in such a way that experimental data for the methanation rates can be understood on this basis. Ediss is therefore a good descriptor for the catalytic activity of different catalysts for the methanation reaction, and we can identify its optimum value from Fig. 3.

In general there may be several descriptors, depending on the number of different important surface intermediates. The number of independent variables is limited strongly by the fact that it has been found that adsorption energies for a number of molecules scale with each other35. For the methanation reaction, for instance, the bond energy of adsorbed CH, CH2 and CH3 vary linearly with the bond energy of adsorbed C from one metal surface to the next, and the same is true for OH versus O adsorption energies.

Volcano relations between rates and adsorption energies have been widely identified in heterogeneous catalysis. For many years adsorption energies of intermediates were not readily available and various thermodynamic data, such as heats of oxide formation, were used as descriptors36. With the advent of sufficiently accurate DFT calculations this situation has completely changed, and descriptors of catalytic activity in terms of calculated adsorption energies have been identified for a number of systems33, 37, 38.

The volcano-shaped relationships between total catalytic rates and adsorption energies may explain some of the good agreement between experiments and theory shown in Fig. 2. Close to the top of the volcano the rate depends only weakly on the absolute strength of the adsorption energies. For the methanation reaction, for instance, the window of values of Ediss around the maximum where the rate is within an order of magnitude of the maximum values is on the order of 0.5 eV. This means that for the best catalysts (close to the maximum of the volcano) errors of a few tenths of an eV may still give reasonable values for the rate. As this is the typical error of DFT calculations15, they can give quite accurate rates at least close to the top of the volcano.

The electronic structure factor

The variation in adsorption energy (and hence the catalytic activity) from one metal to the next is determined by the electronic structure of the surface. It turns out that for the transition metals the coupling between the adsorbate valence states and the metal d-states largely describe the variations39, 40, 41, 42, 43, 44 The rule is that the higher in energy the d-states are relative to the highest occupied state — the Fermi energy — of the metal, the stronger the interaction with adsorbate states. The reason is that when the d-states are close to the Fermi energy, antibonding states can be shifted well above it and become empty (or bonding states can be shifted below it and become occupied). This increases the bond strength. Figure 4a establishes how variations in adsorption energy from one metal to the next are correlated with shifts in the energy of the d-states. Figure 4b,c shows a more subtle effect: The electronic structure of a platinum surface can be engineered by inserting another metal (nickel, cobalt, iron and so on) in the second layer and this directly affects the oxygen and hydrogen adsorption energies. It shows how changing the metal ligands of the surface platinum atoms can change its chemical properties substantially.

Figure 4: The d-band model — understanding the electronic origin of variations in surface chemistry.

Figure 4 : The d-band model |[mdash]| understanding the electronic origin of variations in surface chemistry.

a, Variations in the O adsorption energy, DeltaEads(O), on the most close-packed surface of the 4d transition metal series. The results of full DFT calculations are compared with those from a simple Newns–Anderson model98 and to experiments (polycrystalline surfaces)9. Below, the same data are plotted as a function of the average energy of the d-electrons (the d-band centre with respect to the Fermi level), epsilond-epsilonF, on the transition metal. Adapted from ref. 16; © 2000 Elsevier. b, Calculated changes in the dissociative adsorption energy of H2 and O2, DeltaE, versus the average energy of the projected density of states for the surface platinum d-states. c, Local projected densities of states, n(epsilon), for a series of Pt(111) surfaces, where the second layer has been replaced by a layer of a 3d transition metals are shown. Nd is the number of d electron on the surface Pt atoms, which is hardly affected by the subsurface atoms. Parts b and c adapted from ref. 99; © 2004 Elsevier.

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Catalyst design

The first examples of where ideas generated from electronic structure calculations were exploited in the search for new solid catalysts include: the modification of the stability of Ni catalysts for steam reforming by the addition of gold45; the mixing of cobalt and molybdenum in ammonia synthesis catalysts46; new mixed transition metal sulfides for hydro-desulfurization47; new CO-tolerant alloys for fuel-cell anodes48; and near-surface alloys for hydrogen activation49.

The first example of extensive computational screening of surface structures for new catalysts was for the methanation reaction50; this reaction is used extensively in industry to remove trace amounts of CO from hydrogen streams produced by steam-reforming of hydrocarbons51.

The approach taken was as follows. First the CO dissociation energy, Ediss, was identified as a descriptor of catalytic activity as described above, and indicated in Fig. 3. The optimal value was identified by comparison to experimental data for the elemental metals, see Fig. 3c. Then a series of binary alloys (with concentration varying in steps of 25%) were formed from metals (Ni, Pd, Pt, Co, Rh, Ir, Fe, Ru and Re) chosen so that they should be reasonably stable at methanation conditions. For each alloy the catalytic performance descriptor |EdissEdiss(optimal)| was then calculated using a simplified interpolation model. A total of 117 different systems were studied.

In the case of the methanation reaction, there are already elemental metals, ruthenium and cobalt, close to the top of the volcano, see Fig. 3c. These metals are, however, not used industrially because they are quite costly. Instead the cheaper but also inferior catalyst material Ni is used. The cost of the raw materials is therefore an important parameter, and in Fig. 5a all the alloys and elemental metals included in the study are shown in a cost versus catalytic performance plot. NiFe alloys stand out in this plot as having a high catalytic activity as well as a low price. They were therefore chosen for a more detailed theoretical and experimental study. This involved a full DFT calculation of the energetics to make sure that the simple interpolation model was correct. It also involved a series of computational tests of stability of the alloy towards segregation. The result of the experimental test is included in Fig. 5b. A series of catalysts supported on MgAl spinel were prepared and their methanation activities were measured. It can be seen that the NiFe alloys are indeed more active than both pure nickel and iron, as predicted. Subsequently, the concept was converted into a technical catalyst at Haldor Topsøe52.

Figure 5: Computational screening for methanation catalysts.

Figure 5 : Computational screening for methanation catalysts.

a, A price versus catalytic-performance plot for methanation over a range of elemental metals and alloys. The closer the descriptor Ediss (the CO dissociation energy) is to the optimum value (the smaller the value of |Ediss-Ediss(optimal)| is) the better the predicted catalytic activity. The Pareto optimal set of solutions is connected by the solid line, which defines the best compromise between price and catalytic performance for the set of systems investigated theoretically. b, Experimental confirmation that NiFe alloys are more active than pure nickel. The error bars indicate the estimated standard deviation of the measured rate of 10%. Adapted from ref. 50; © 2006 Elsevier.

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An example from electrocatalysis

Electro-catalysis design is currently attracting much attention mainly for energy-conversion purposes. Many future energy transformation processes rely on electro-catalysis. One important example is the evolution of hydrogen in electrolysis and the reverse process where hydrogen is used as a fuel in a fuel cell. In acidic solutions platinum is the preferred catalyst material for both processes. As a hydrogen electrode it is stable and effective, but it is scarce and expensive, and extensive research efforts are directed towards replacing it — or at least reducing the amount needed.

Compared with catalysts for gas-phase reactions, the description of electro-catalysts has additional challenges due to the liquid phase in direct contact with the catalysts surface and due to charging of the surface53, 54, 55, 56, 57, 58. Another very important constraint is the corrosive environment that the catalyst is often exposed to in the electrolyte. Many of the non-precious catalyst materials important in conventional heterogeneous catalysis, for example, iron, cobalt or nickel, will quickly dissolve in acids.

The hydrogen-evolution reaction, where protons and electrons recombine to form molecular H2, is one of the simplest electrochemical reactions, but still no good alternative to the platinum catalyst has been found. The adsorption free-energy of hydrogen, DeltaGH*, is a good descriptor for hydrogen evolution59, 60, 61. This makes sense because no matter what the reaction path is, adsorbed hydrogen is one of the intermediates. If H binds too weakly to the surface, H+ cannot adsorb from the dissolved phase and if it binds too strongly, it will have difficulty leaving the surface for the gas phase. One would expect the optimal rate when hydrogen at the surface is as stable as gas-phase hydrogen — which by definition has the same free energy as solvated protons and electrons at zero potential relative to the normal hydrogen electrode (see Fig. 6a). Plotting the exchange current density versus the binding of hydrogen obtained by DFT indeed shows a volcano with an optimum around zero free energy of adsorption62 (see Fig. 6b).

Figure 6: Screening for hydrogen-evolution catalysts.

Figure 6 : Screening for hydrogen-evolution catalysts.

a, The free energy diagram of hydrogen evolution at zero potential and zero pH for gold, platinum, nickel, molybdenum and PtBi close-packed surfaces, the MoS2 edge, and the active centres in hydrogenase and nitrogenase. The closer the binding free energy of the intermediate — where H atoms are bound to the catalyst — is to zero the higher the activity. Adapted from ref. 63; © 2005 ACS. b, The experimental exchange current, i0, is plotted as a function of the calculated standard free energy of adsorption of hydrogen, DeltaGH*. Experimental data from many different experiments are included, which accounts for the scatter. In one particular set of experiments (marked in blue) platinum and a PtBi surface alloy are compared. Adapted from ref. 71; © 2007 AAAS. c, The stability of different surface alloys is plotted as a function of the binding free energy of hydrogen. In the lower left quadrant are the stable and active surface alloys and the points that limit the set from lower left is the Pareto optimal set. Adapted from ref. 64; © 2006 NPG.

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A computational search for high activity can then be carried out by calculating DeltaGH*. As stability of the catalyst is a major issue, the calculation of descriptors for stability is as important as for activity. A range of surface alloys (alloys only in the first layer) with the optimal combined stability and activity can then be indentified63, 64 (see Fig. 6c). One interesting candidate is a surface alloy of platinum and bismuth. Supported on pure platinum, adsorbed bismuth is known to poison hydrogen evolution65, however, when the surface is annealed, a PtBi surface alloy is formed showing a measured activity slightly higher than that of a reference sample of pure platinum64.

Another strategy for identifying materials that could have promising features as hydrogen-evolution catalysts is by taking inspiration from biology. Hydrogenases66 and nitrogenases67 are known to be good catalysts for hydrogen evolution. The descriptor approach also applies to the active centres of enzymes63, 68 (see Fig. 6a). Both hydrogenases and nitrogenases have catalytic sites containing sulfur atoms bridged between metal atoms. In looking for inorganic analogues to the active centre in the enzymes it was noted that the same arrangement for sulfur is found at the edge of MoS2 slabs or nanoparticles. These structures are well-known as hydro-desulfurization catalysts used in removing sulfur-containing molecules from oil products69, 70. The MoS2 particles supported on carbon and gold have been tested showing that hydrogen evolution is indeed possible on MoS2 (refs 63, 71; see Fig. 6b).

Addressing selectivity

Often selectivity towards specific products is of key interest. Selective processes do not only offer cleaner chemistry and better environmental protection, but also allow for improving the use of resources thus leading to more economic production72.

As selectivity is related to favouring specific reaction pathways among several competing pathways, a prerequisite for the theoretical treatment of selectivity is the accurate treatment of the activity of single reaction pathways. This treatment has to be accomplished at least with sufficient accuracy to address relative changes in the energy barriers between competing pathways.

Ethylene oxide synthesis. Ethylene oxide (EO) is an important chemical with an annual global production of the order of 10 million tons73. It is primarily used in organic synthesis reactions. All large-scale production of ethylene oxide is today done by direct partial oxidation of ethylene over a silver catalyst74. The selectivity of a typical catalytic EO process is 65% to 80% depending on whether the oxidant is air or pure O2 (ref. 73). The side product is mainly the full combustion product, CO2. As the primary expense in the process is the ethylene cost, high selectivity towards EO is important in improving cost-efficiency and minimizing CO2 emissions.

High-resolution electron energy loss spectroscopy (HREELS) experiments and DFT calculations have shown that an oxametallacycle75 species is a key intermediate in the ethylene oxide formation over Ag(111) (ref. 76). This has enabled the construction of a detailed DFT-based kinetic model that agrees well with ethylene oxidation rate experiments over Ag (ref. 77). Two competitive transition states lead to ethylene oxide and acetaldehyde, respectively, see Fig. 7a,b. The acetaldehyde eventually goes to full combustion, whereas EO directly desorbs and is unlikely to react further. The difference in energy between these two transition states thus becomes a good descriptor for the selectivity of an EO catalyst, and catalysts, which favour the transition state going towards EO, can be sought computationally78. In Fig. 7c the difference in the two transition state energies relative to the difference over silver is shown for a few bimetallic Ag catalysts. It is observed that some presence of copper atoms in the silver surface should yield particularly high selectivity towards EO. The calculations were subsequently verified through the synthesis and testing of a number of Cu/Ag-containing surface alloys. The results are shown in Fig. 7d. It is observed that as the bulk contents of copper increases slightly, the selectivity increases by almost 50% compared with a pure silver reference catalyst78.

Figure 7: Computational design of ethylene oxide (EO) synthesis catalysts with improved selectivity.

Figure 7 : Computational design of ethylene oxide (EO) synthesis catalysts with improved selectivity.

a, Competing oxametallacycle pathways. Activation barriers for the two pathways are calculated to be similar over silver. b, Structure of a bimetallic model catalysts. TS is transition state. c, The selectivity descriptor, DeltaDeltaEA = (DeltaETS2(alloy) – DeltaETS1(alloy)) – (DeltaETS2(Ag) – DeltaETS1(Ag)), shown for a number of catalyst compositions. Higher descriptor values means that the bimetallic should be more selective than pure silver. d, The measured selectivity relative to pure silver as a function of bulk copper content. All parts adapted from ref. 78; © 2004 Elsevier.

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Preferential oxidation of CO in hydrogen. Preferential oxidation of CO in hydrogen (PROX) currently attracts significant attention as an alternative to methanation for removing CO from hydrogen, in particular for fuel-cell applications. The PROX reaction is carried out in a large excess of hydrogen, and the reaction can for example be written as:

Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com

specifying that hydrogen is not consumed in the process. It is very difficult in practice to avoid some hydrogen being oxidized into water. A highly selective catalyst is thus desirable to reduce the amount of CO to an adequate level without combusting too much of the valuable hydrogen. This is of particular importance for hydrogen-consuming applications such as hydrogen proton exchange membrane fuel cells, where even a few tens of ppm CO will poison currently used Pt-based electrocatalysts79.

On the basis of DFT studies, core–shell nanoparticles have been proposed as candidates for new catalytic properties different from pure metal surfaces, surface alloys and near-surface alloys80. Detailed computational studies of platinum-covered ruthenium, iridium, rhodium, palladium, gold and platinum were carried out. These studies suggested that Pt-covered ruthenium, so-called Ru@Pt, could present unique features compared with the other core–shell structures and the pure platinum nanoparticles, as the binding of CO molecules were significantly weakened on the Ru@Pt. The effect of the ruthenium underneath the platinum surface on the CO adsorption is the same electronic effect discussed in connection with Fig. 4: the platinum d-states are shifted up in energy due to the ruthenium atoms, and this ligand effect81 changes the CO bond strength. Experiments have shown that the reaction temperature is significantly lower for PROX over Ru@Pt particles than PtRu alloy, as predicted from calculations. Experiments also show that 70% of the CO is already oxidized to CO2 at 30°C over the Ru@Pt (ref. 80).

Selective hydrogenation of acetylene. Large-scale production of ethylene is primarily carried out by steam-cracking of saturated hydrocarbons73 which leads to impurities in the form of acetylene in the ethylene product slate. Much of the ethylene is used in processes where acetylene is undesirable. One process where the acetylene is particularly undesired is the important polymerization of ethylene into polyethylene. The acetylene concentration in the ethylene feed can be reduced by selective hydrogenation to ethylene. A high selectivity is necessary to get the acetylene reduced to the desired low levels of a few ppm without hydrogenating ethylene to ethane. The most commonly used catalyst in industry is a silver-modified palladium catalyst.

Density functional theory calculations for a number of transition-metal surfaces show that acetylene and ethylene adsorption energies scale with methyl adsorption energies82 (Fig. 8a). The slope of the scaling relations in the reactive surface regime is four for C2H2 and two for C2H4. This can be viewed as a manifestation of bond-order conservation for the surface-bonded carbon atoms35. The scaling relations are thus related to bond-order conservation models83. A good acetylene hydrogenation catalyst should present a high stability of adsorbed acetylene and a low stability of ethylene. Strong acetylene binding leads to high acetylene removal rate, whereas weak ethylene adsorption leads to ethylene being desorbed instead of further hydrogenation, and therefore high selectivity. This, together with the scaling relations, leads to a window of simultaneously active and selective catalysts as expressed by using the methyl binding energy as a descriptor (see Fig. 8a).

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