www.mrs.org/bulletin high-temperature operation. Next, we will discuss how an understanding of the vari- ations in catalytic activity from one mate- rial 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 ex- ample, 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 as- sume 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 MRS BULLETIN • VOLUME 31 • SEPTEMBER 2006 669 Density Functional Theory in Surface Science and Heterogeneous Catalysis 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 ϩμ 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 ϩ1/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 poten- tial 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 ϩ br transforming into an oxide. Alternatively, namely, CO2 formation via O CO and transition metals, the situation is analo- cus ϩ 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.