Theory in Surface Science and Heterogeneous Catalysis

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high-temperature operation. Next, we will discuss how an understanding of the variations in catalytic activity from one material to the next is beginning to emerge, and, Density Functional finally, we will show how progress in the theoretical description of surface reactions has an impact on catalyst development in Theory in Surface industry. Thermodynamic and Kinetic Modeling: General Concepts Science and This section discusses how atoms or molecules from an environment—for example, an oxygen (O2) gas phase—at tech- nically relevant temperature and pressure Heterogeneous will interact with the surfaces of metals and metal oxides. This implies that the material changes significantly; metals cor- rode (i.e., their surfaces become covered Catalysis by metal oxides), and metal oxides assume a composition and structure at the J.K. Nørskov, M. Scheffler, and H. Toulhoat surface that can be very different from what is known from ultrahigh-vacuum surface science studies. These oxides may be restricted to a thin film at the surface Abstract because of slow kinetics, but surface ox- Solid surfaces are used extensively as catalysts throughout the chemical industry, in ides may exist already as thermodynami- the energy sector, and in environmental protection. Recently, density functional theory cally stable phases at conditions where the has started providing new insight into the atomic-scale mechanisms of heterogeneous bulk oxide is not yet stable. This has re- catalysis, helping to interpret the large amount of experimental data gathered during the cently been shown by DFT calculations.4,5 last decades. This article shows how density functional theory can be used to describe Surface oxide formation also plays a the state of the surface during reactions and the rate of catalytic reactions. It will also role under the conditions of catalysis show how we are beginning to understand the variation in catalytic activity from one when, in addition to O2, reducing agents 6 transition metal to the next. Finally, the prospects of using calculations to guide the (e.g., carbon monoxide) are also present. development of new catalysts in industry will be discussed. However, then the surface may be more or less far from thermodynamic equilibrium. Keywords: catalytic, simulation, surface reaction. Obviously, the chemical and physical properties of oxides (or surface oxides) are very different than those of metals, and whether they are stable or in a (frustrated) Introduction metastable configuration, they will affect A catalyst is a substance that can facili- of parallel synthesis and screening the catalysis. Although this section uses tate a chemical reaction; catalytic technol- methods.3 oxidation catalysis as an example, analogies ogy provides a range of products, from There are new developments which are expected for other situations (e.g., the fuels and fertilizers to plastics and phar- show that progress is being made toward formation of surface nitrides or hydrides). maceuticals. Catalysis is also used to clean a new, molecular-scale picture of the way One main example, ruthenium (the sta- emissions from cars, power plants, and in- solids work as catalysts. One very impor- ble bulk oxide is RuO2) is used here to dustrial production. The importance of tant development is that electronic- address the basic concepts of ab initio catalysis to society is reflected by estimates structure calculations based primarily on atomistic thermodynamics, constrained suggesting that more than 20% of manu- density functional theory (DFT) are begin- thermodynamics, the stability of bulk and facturing in the industrialized world is de- ning to provide information that is hard to surface oxides, and ab initio statistical pendent on catalysis.1 Most catalysts used obtain by experimental methods. The cal- mechanics of adsorption and reaction dy- in industry are solids, and the catalysis culations can illuminate the nature of the namics to surfaces. Generalization to other typically takes place on the surface of transition states of molecules undergoing late transition metals is briefly addressed nanoparticles of the active material. We chemical transformation at the surface of a as well. Only the basic theory is provided are rapidly approaching the 100th an- solid. In doing so, trends in reactivity and here; for details, see Reference 7 and the niversary of the first large-scale industrial conceptual models of the way solids act as references therein. catalytic process, ammonia synthesis, in- catalysts can be developed. troduced by Haber and Bosch.2 Since then, In this article, we will briefly review Ab Initio Atomistic the understanding of the way solid sur- some of the developments that have made Thermodynamics faces can interact with gas-phase mole- it possible to understand how surface- Although catalysis is not a thermody- cules, break them down, and form new catalyzed reactions proceed. First, we will namic equilibrium situation, knowledge of products has increased enormously, and discuss how DFT calculations can be thermodynamic phases that may exist at recently, catalyst development has been used to describe the working state of a or close to temperature and pressure refined substantially by the introduction catalyst under realistic high-pressure and (T, p) conditions of optimum catalyst

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performance is important for any deeper individually assumed to be in equilibrium Stability of Bulk and Surface Oxides analysis. When a material is in contact with the surface.11,12 At the end of the 1990s, it became clear with a one-component gas or liquid What is the value of such an approach? that the high catalytic activity of the Ru phase, the environment can be described The lower regions of Figure 1, from the catalyst cannot be understood in terms of in terms of a reservoir uniquely character- Obr/− structure (bottom left, dark gray) to dissociation, adsorption, and reactions on br cus ized by its chemical potential. For an O2 the O /O structure (bottom right, black), the (pristine) Ru metal, but that the oxy- gas environment, used here as the ex- reflect thermodynamically stable phases gen content in the surface region is signif- ample, we have that exist when the CO concentration is icant.4–6 When the Ru catalyst is in its negligible (the superscripts “br” and highly active state, the surface is covered μ total μ 0 O(T, p) 1/2[EO2 O2(T, p ) “cus”refer to the two important adsorp- by RuO2. In retrospect, this result is not 1/kT ln (p/p0)]. (1) tion sites that exist on the surface, the surprising, because under the (T, p) condi- “bridge” site and the “coordinatively un- tions of catalysis, the Ru bulk oxide is in This is the ideal gas equation, where the saturated site,” respectively). However, fact the stable phase.13 As an example for br cus internal degrees of freedom of the O2 the light-gray region (O /CO ) does not other transition metals (from Ru to Ag), molecule (vibrations and rotations) are represent a stable phase, because ad- Figure 2 shows the results for the O- μ 0 sorbed Obr and adsorbed COcus will react Ag(111) system.4,5,14 Whereas silver oxide contained in the O2 (T, p ) chemical potential term, as is the ideal gas entropy at the to form CO2. As O2 has been dissociated was considered previously to be unstable 0෇ μ 0 already at the surface, the reactions will under catalytic conditions (T Ϸ 450 K), this reference pressure p 1 atm. The O2 (T, p ) total happen at a higher rate than in vacuo. A theoretical work demonstrated that al- term and EO2 , the total energy of the iso- lated molecule, can be computed by DFT. particularly interesting region is that be- though bulk oxides cannot be formed, sur- For details, see Reference 7. tween constrained phases. Here, not only face oxides may be present and active. In A surface that is in contact with such a Obr and COcus but also Ocus and COcus may fact, for Ag(111), DFT calculations predict reservoir attempts to assume the lowest react, and because pronounced fluctua- a variety of different surface oxides with free energy by adsorbing oxygen or by tions are to be expected, other reactions, nearly degenerate energies.15 For other br br transforming into an oxide. Alternatively, namely, CO2 formation via O CO and transition metals, the situation is analo- cus cus the system may transfer oxygen from the O CO , may also become possible. gous: when the transition metals are in surface into the gas phase. Thus, plots of What really happens at such border re- contact with an O2 atmosphere, they may the free energies (calculated by DFT) of all gions requires a careful analysis of the sta- develop thin surface oxides.4,5,15 Experi- plausible structures and stoichiometries as tistical mechanics, which is addressed mental studies for rhodium (Rh) and pal- μ a function of O(T, p) reveal the thermo- later in the section on “Ab Initio Statistical ladium (Pd) confirmed these findings but μ dynamically stable phases. Obviously, O Mechanics.” also showed that the formation of surface can be easily translated into a pressure (or oxides is slow, and under the experimen- ln p) axis for any given T or into a T axis tal (surface science) conditions, thermo- for any given p.7 Because the approach dynamic equilibrium could not always merges first-principles calculations of the be reached (see Reference 16 and refer- atomic (and electronic) structure with con- ences therein). cepts of thermodynamics, it was termed Reuter and Scheffler13 studied the stabil- ෇ ab initio atomistic thermodynamics. It has ity of the bulk oxides MxOy (with M Ru, been used to study defects in semiconduc- Rh, Pd, and Ag) under situations where tors and semiconductor surfaces and in- terfaces for a long time,8,9 and since 199810 it has been widely employed to identify and analyze stable and metastable thermodynamic phases at metal and oxide surfaces. Constrained Thermodynamics For situations where the environment contains more than one component (e.g., O2 as well as CO), the ab initio atomistic thermodynamics approach has been gen- Figure 1. The atomic terminations of eralized.11,12 Obviously, a full thermody- RuO2(110) as obtained by constrained namic description is useless, as then O2 ab initio atomistic thermodynamics. The and CO would not coexist but would form superscripts “br” and “cus” refer to the carbon dioxide (CO2) with a significant two important adsorption sites that exist energy gain (about 3 eV per CO2 mole- on the surface, the “bridge” site and the cule). It is well known that this reaction “coordinatively unsaturated site,” does not happen on sensible time scales, respectively. Each can be occupied by Figure 2. Calculated ( T, p) phase because it is hindered by a significant free- O or by CO. In the upper-left region, diagram for the O-Ag(111) system, above the black dotted line, bulk RuO2 showing the stable structures. Note that energy barrier. Thus, it has been suggested is not stable but will reduce to the at conditions of catalysis, i.e., T Ϸ 450 K to ignore CO2 formation in a first theoreti- Ru metal. The left and bottom axes and log(p/ p0) Ϸ 0, the bulk silver oxide cal attempt and consider two separate, in- note the chemical potentials, and the is not stable. However, surface oxides dependent reservoirs for O2 and CO. top and right axes provide two of various stoichiometry may develop. Whereas the components are therefore not examples ( T ෇ 300 K and T ෇ 600 K) ML stands for monolayer and 4 4 in equilibrium with each other, they are for the corresponding pressures. denotes the periodicity.

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not just O2 but also the strongly reducing Studies of this kind have been employed by the energy barrier for dissociation, Ea, CO is present in the gas phase. Obviously, to compute the composition, structure, and the formation rate of the products will at high CO pressure, oxides are reduced to and activity of the catalyst surface in reac- be given by the adsorption energy, ΔE, of the clean metal. Under catalytic conditions, tive environments ranging from ultrahigh the atomically adsorbed intermediates on bulk Ru oxide was still found to be stable, vacuum to technologically relevant condi- the surface. The stronger the adsorbate– but this is not the case for the other transi- tions (see References 7 and 17 and refer- surface bond (the more negative ΔE is), the tion metals. Minute concentrations of CO ences therein). These studies also provide higher the energy barrier for formation of may be sufficient to prevent the formation a visualization of what happens under the product will be. A good catalyst should 13 of bulk oxides for these systems. Still, catalytic conditions at the atomic scale. have a small Ea and a small numerical even in the presence of CO, surface oxides Several aspects of these statistical mechan- value of ΔE. Unfortunately, calculations are close to forming, and this indetermi- ics results for the steady state of catalysis have shown that the two are strongly cor- nate state may be important for the cat- were surprising. For example, while related for a number of molecules20,21 (see alytic function. under thermodynamic conditions all Figure 3). A small barrier is therefore typi- bridge sites of the RuO2(110) surface are cally associated with a strong adsorbate– Ab Initio Statistical Mechanics occupied by oxygen atoms (the number surface bond. First-principles statistical mechanics of vacancies is far less than 1%), at the starts with elaborate electronic-structure steady state of catalysis, the Obr occupa- calculations to analyze all possibly rele- tion is only 90%. Note that the “steady vant molecular processes, such as adsorp- state” is not a thermodynamic equilib- tion, desorption, diffusion of reactants, rium. It refers to a thermodynamic open and surface chemical reactions. So far, our system and the steady production of CO2 knowledge about these processes is still from incoming CO and O2 molecules. shallow, and a careful study, employing Another interesting point is that an un- ab initio molecular dynamics (MD), is expected short-range order builds up and mandatory. Ab initio MD evaluates the suppresses reaction channels that, when forces on all the atoms using DFT and just looking at energy barriers, would be then feeds them into Newton’s equation assumed to be the most important.17 The of motion to evaluate the dynamics of the highest reactivity by far is found at the atoms. In principle, that is all that is phase boundary (see the previous discus- needed if the relevant time and length sion of Figure 1), and the obtained value scales are covered. However, this is not the for the turnover frequency (CO2 pro- case: with ab initio MD, at most about 10 ps duction) of 1018 cm–2 s–1 is in agreement can be modeled, even on the most power- with experimental work by Peden and ful supercomputer. For analyzing the Goodman.18 function of materials, time spans that are 9–12 orders of magnitude longer are Understanding Trends in needed. Corrosion, for example, typically Reactivity proceeds at a speed of about 1 atomic There are now a few reactions that are layer per minute. understood in some detail.17,19 Such com- To overcome these limitations, a sys- binations of DFT calculations and kinetics tematic coarse-graining has been devel- are extremely demanding, and there is a oped. The ab initio MD information is strong need to develop concepts that as- Figure 3. Calculated activation energies compressed into probabilities at which the sist in understanding trends in reactivity (transition-state potential energies) for various processes happen, and then the from one metal to the next without going N2, CO, NO, and O2 dissociation on a statistical mechanics of the many-atoms into all the details. DFT calculations are number of different metals, plotted as a dynamics is solved using an extended also extremely important in this respect, function of the calculated dissociative kinetic Monte Carlo (kMC) approach (see and some simple models by which we are chemisorption potential energy for the Reference 17 and references therein). In beginning to understand the overall dissociation products. Results for simple words, this may be called “coarse- trends are discussed here. (a) close-packed (flat) surfaces and grained MD,” and when done properly, Grossly speaking, a surface reaction (b) steps, showing the same trends but grouping along two different straight no significant information is lost. An im- takes place in two overall steps. First, the lines. The steps are more reactive portant aspect of an extended kMC reactants adsorb on the surface, typically than the terraces for these reactions. scheme, considering well-defined atom- by dissociating. If we take ammonia syn- The linear relationship for N + → 2 istic processes, is that it also enables so- thesis (N2 3H2 2NH3) over a transition- dissociation on the most reactive step called reverse-mapping. Thus, the ab initio metal surface as the example, both N2 and sites [red points in (b)] has been used as extended kMC scheme enables access to H2 need to dissociate. The second step is input into a kinetic model for the time scales of the order of seconds or the reaction of the surface species to form ammonia synthesis reaction. (c) The longer, even for mesoscopically sized sys- the product molecules. In the case of am- calculated reactivity per site per second tems, while retaining the full atomistic in- monia synthesis, these are the steps where (the turnover frequency, TOF), normalized to give the same maximum formation. It is then possible to identify adsorbed nitrogen is successively hydro- value, is shown for three different which aspects of the electronic structure genated to form NH3, which desorbs into reaction conditions (red Gaussian and which atomistic processes are actuat- the gas phase. A good catalyst must facili- peaks). (From Reference 20.) The ing the catalytic function. For details of the tate both the activation of the reactants vertical bar in (b) and (c) indicates the method and its approximations, see Refer- and the formation of the products. The ac- range of near-optimal dissociative ences 7 and 17. tivation rate of the reactants will be given chemisorption energies.

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The reason for the linear correlation be- For O2 activation, none of the metals we tween the dissociation barrier and the ad- considered are in the optimum range, but sorption energy is found by studying the the closest are Ag (−0.65 eV), Pd (−1.56 eV), nature of the transition states. Typically, and Pt (−2.2 eV).20 In all cases, these are they correspond to quite stretched mole- metals known as some of the best cata- cules (see Figure 4), making the transition lysts for these reactions. The principle of states seem as final-state, hence the corre- an optimum adsorption energy is there- lation between the transition- and final- fore in excellent agreement with experi- state energies. mental observations, suggesting that the The linear Brønsted–Evans–Polanyi BEP relationships are the core ingredient (BEP)-type relationships between Ea and in rationalizing a large number of empiri- ΔE mean that the best catalyst must be a cal data. It should be noted that the con- compromise with an intermediate value cepts of BEP relations, “volcanos,” and the of the adsorption energy. This is a mani- Sabatier principle are not restricted to metal festation of the so-called Sabatier princi- surfaces. The same general principles apply Figure 5. Calculated dissociative N2, ple.22 It is illustrated further in Figure 3, to oxides, sulfides, nitrides, and carbides. CO, and O2 chemisorption energies where the rate of reaction for ammonia According to Figure 3, it is the varia- over different 3d transition metals plotted as a function of the center of the synthesis is plotted as a function of ΔE, as- tions in the dissociative adsorption energy transition-metal d-bands. The term εd is suming the linear relationship with Ea. of the reactants that control the trends in the energy of the center of the d-band, The “volcano” shape of the rate indicates catalytic activity from one transition metal while εF is the Fermi-level energy. (From that the optimum catalyst has a particular to the next. The calculations also enable an Reference 23.) Filled circles represent bond strength to the dissociated reactants. analysis of the electronic factors control- N2, open squares CO, and open The fact that calculations can give a con- ling these variations. Figure 5 shows how triangles O2. sistent set of activation energies and ad- one particular property of the surface elec- sorption energies has paved the way for a tronic structure, the average energy of semiquantitative analysis of the optimum the transition-metal d-states relative to the heterogeneous catalysis. This section illus- bond strength for a given reaction. Fermi level, is largely responsible. The trates how insight provided by DFT calcu- Since different diatomic molecules have value of the d-band center projected onto lations has already been used in the the same BEP relation, they would be ex- the surface atoms involved in bonding development of new catalysts in industry pected to obey roughly the same general turns out to not only explain variations by concentrating on the catalytic processes dependence of the reaction rate on the in- in the adsorption energy from one metal employed to remove sulfur-containing teraction strength. If ammonia kinetics is to the next but also the effect of steps and molecules from fossil fuels. The societal taken as a guideline, the optimum catalyst other defects, strain, alloying, and adsor- demand for ultraclean fuels, with a maxi- should be one with an adsorbate binding bate–adsorbate interactions.24–29 mum of 50 ppm sulfur currently, required energy in the range of –1.1 ± 0.3 eV (Fig- catalyst manufacturers to double the ure 3c). For ammonia synthesis (N2 activa- Applications in Industry: activity per unit volume of hydrodesul- tion), both Ru and Fe lie within this range. Improved Catalysts for Producing furization (HDS) catalysts in less than For CO activation (Fischer–Tropsch syn- Ultralow-Sulfur Fuels 10 years.30 This has been possible through thesis), the same is true for Rh, Co, Ni, and As mentioned in the Introduction, large a tremendous research effort, to which Ru, and for NO activation it is Pd and Pt. sectors of industry are dependent on DFT contributed much. Industrial HDS catalysts in their active state may be described as nanoparticles of ternary transition-metal sulfides (TMSs) associating Co or Ni to Mo or W, supported over nanoparticles of cubic γ-alumina. The active nanoparticles look like the image in Figure 6, which is a roughly hexagonal patch cut off a single layer of MoS2 (WS2 is isostructural). The basal planes are capped by tri-coordinated S and inert. Active sites are on the edges, where undercoordinated metal ions appear. The promoter atoms, Co or Ni, substitute Mo or W at the edges. Early ideas of this particular self- organization31,32 were recently supported by detailed DFT investigations33,34 that showed the substitutional position to be energetically favored and led to the best match of local structures with available experimental data (e.g., Co-S, Mo-S, and Co-Mo distances and numbers of average first-and second-neighbors from extended Figure 4. Calculated transition-state structures for N2, NO, O2, and CO dissociation on different transition-metal surfaces. Results for close-packed surfaces are shown in the upper x-ray absorption fine structure). Scanning row and for stepped surfaces in the lower row. N is shown in blue, O in red, and C in gray. tunneling microscopy (STM) studies (From Reference 20.) of gold-supported preparations of such

672 MRS BULLETIN • VOLUME 31 • SEPTEMBER 2006 Density Functional Theory in Surface Science and Heterogeneous Catalysis

morphology inherited from boehmite were described according to experimental conditions.45 O–H bond-stretching vibra- tion frequencies were determined on the basis of the DFT potential energy surfaces and compared to the experimental Fourier γ transform infrared spectra of -Al2O3 available as a function of pretreatment conditions. A striking agreement allowed a complete reassignment of these spectra in terms of precise local coordination of hy- droxyls and the particular facets involved. A detailed analysis of Lewis and Brønsted γ acid–basic properties of -Al2O3 surfaces was also provided.44 Determining the stable surface terminations in the presence of Figure 6. Model in perspective view of an active CoMoS nanoparticle in interaction with 46 both water and H2S was a prerequisite dibenzothiophene on a S-edge and acridine on a Mo-edge. (H, white; C, gray; S, yellow; for the direct DFT simulation of (smaller) N, blue; Co, green; and Mo, pink). (Courtesy of P. Raybaud, Institut Français du Pétrole.) MoS2 aggregates interacting with the different alumina surfaces, so as to determine particles35,36 provided magnificent direct The precise nature of the interaction the stable configurations in operando.47 observations of these structures. DFT cal- of the TMS active nanoparticles with Similar studies are ongoing for the pro- culations provided the necessary clues for γ-alumina nanoparticles is a very chal- moted systems, revealing generally weaker a precise interpretation of images37,38 in lenging question. The formerly controver- interactions under the same conditions γ 48 terms of the underlying geometrical and sial -Al2O3 structure is produced by (Figure 7). electronic structures, and through ab initio controlled topotactic dehydration of Experimental activities of binary TMS49 atomistic thermodynamics (as described ultrafine (e.g., nanoparticular) boehmite follow nicely a “volcano” curve when earlier), they also provide the link be- (AlOOH), a layered mineral.42 It was pos- plotted against a DFT-computed estimate tween the observations under ultrahigh- sible to find a reasonable pathway for this of the metal–sulfur bond strength EMS vacuum conditions and the active state of solid–solid reaction, along which the free- within the bulk material (Figure 8).50,51 the catalyst under reaction conditions. energy profile was evaluated by DFT.43 A This is another illustration of the Sabatier + The influence of the gas-phase (H2 H2S) model bulk structure resulted, the com- principle, analogous to that shown in Fig- composition and temperature on the equi- puted properties of which match nicely ure 3; therefore, this principle explains the γ 44 librium shape of the nanoparticles has the known characteristics of -Al2O3. synergetic effect in ternaries used industri- been among the most remarkable of the Again, using ab initio atomistic thermody- ally. EMS should then provide a relevant insights brought by DFT and confirmed namics, the nature and density of the var- descriptor when more complex TMS by STM. Making use of ab initio atomistic ious hydroxyl groups terminating the low structures are screened for potentially thermodynamics,7 all surface energies Miller index surfaces dominating the HDS-active materials. In such a search were evaluated by DFT as functions of controlling chemical potentials, so that surface phase diagrams and morphology diagrams could be constructed. Basal (0001) planes have negligible surface energies, compared with the two crystal- lographically unequivalent S-edge and (1010)¯ Mo-edge (10¯10) planes. At usual operating conditions for HDS processes, the surface tensions for the two edges are comparable, and morphologies are thus approximately hexagonal. Subtle differ- ences remain, however, between the CoMoS and NiMoS systems;39 for in- stance, at HDS conditions, Co prefers to sit at S-edges, whereas Ni decorates both edges. Major steps have thus been achieved toward an atomistic description of active sites in operando for these important systems. Important new insight into the active site for HDS was obtained by the com- Figure 7. DFT-optimized model of minimal CoMoS aggregate in interaction with the (110) bined DFT and STM discovery that surface of γ-Al2O3 under hydrodesulfurization conditions. It is predicted that one strong around the edge of the nanoparticles, the iono-covalent Mo–O bond binds the active aggregate to the support, while the promoter otherwise insulating MoS2 becomes metal- Co atom remains in the same coordination as in the standalone aggregate. (H, white; O, lic35,36,40 and that these metallic “brims” are green; Al, black; S, yellow; Co, blue; and Mo, red). (Courtesy of D. Costa, Institut Français important for the catalytic chemistry.41 du Pétrole.)

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an era where DFT calculations contribute a 25. M. Mavrikakis, B. Hammer, and J.K. new perspective to the many important Nørskov, Phys. Rev. Lett. 81 (1998) p. 2819. experimental tools that have been devel- 26. V. Pallassana and M. Neurock, J. Catal. 191 oped to understand surface reactivity. (2000) p. 301. 27. O.M. Lovvik, R.A. Olsen, J. Chem. Phys. 118 (2003) p. 3268. References 28. A. Roudgar and A. Gross, Phys. Rev. B 67 1. I. Maxwell, Stud. Surf. Sci. Catal. 101 (1996) p. 1. 033409 (2003). 2. F. Haber, Nobel Prize Lecture (1919); C. 29. M. Gajdos, A. Eichler, and J. Hafner, J. Phys.: Bosch, Nobel Prize Lecture (1932). Cond. Matt. 16 (2004) p. 1141. 3. P. Cong, R.D. Doolen, Q. Fan, D.M. Gi- 30. See Axens IFP Group Technologies Web aquinta, S. Guan, E.W. McFarland, D.M. Poojary, site, www.axens.fr, and Haldor Topsoe Web K. Self, H.W. Turner, and W.H. Weinberg, site, www.topsoe.com (accessed August 2006). Angew. Chem. Int. Ed. 38 (1999) p. 484. 31. H. Topsoe, B.S. Clausen, R. Candia, 4. W.-X. Li, C. Stampfl, and M. Scheffler, Phys. C. Wivel, and S. Morup, J. Catal. 68 (1981) p. 433. Figure 8. The Sabatier principle applied Rev. Lett. 90 256102 (2003). 32. S. Kasztelan, H. Toulhoat, J. Grimblot, and to the catalysis of hydrodesulfurization 5. W.-X. Li, C. Stampfl, and M. Scheffler, Phys. J.P. Bonnelle, Appl. Catal. 13 (1984) p. 127. (HDS) by transition-metal sulfides. Solid Rev. B 67 045408 (2003). dots: experimental catalytic activity data 6. C. Stampfl, M.V. Ganduglia-Pirovano, K. 33. L. Byskov, J.K. Nørskov, B.S. Clausen, and for HDS of dibenzothiophene (DBT) Reuter, and M. Scheffler, Surf. Sci. 500 (2002) H. Topsøe, J. Catal. 187 (1999) p. 109. from Reference 49 in ordinates, and p. 368. 34. P. Raybaud, J. Hafner, G. Kresse, S. Kasztelan, DFT-calculated metal–sulfur bond 7. K. Reuter, C. Stampfl, and M. Scheffler, and H. Toulhoat, J. Catal. 190 (2000) p. 128. energies in abscissa. Open dots: Handbook of Materials Modeling, Vol. 1, edited by 35. S. Helveg, J.V. Lauritsen, E. Lægsgaard, predicted activities for mixed sulfides in S. Yip (Springer, Berlin, 2005) p. 149. I. Stensgaard, B.S. Clausen, H. Topsøe, and ordinates, DFT-calculated strength of 8. C.M. Weinert and M. Scheffler, in Defects in F. Besenbacher, Phys. Rev. Lett. 84 (2000) p. 951.

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