The paper discusses the hierarchy of model studies with increasing complexity towards an understanding of industrial catalysts under reaction conditions. We use three case studies to document the progress in systems complexity as well as the development of instruments that allow us to approach the study of acting catalysts: magnesium oxide clusters in the gas phase, gold nanoparticles on metal oxide surfaces, and palladium nanoparticles compared to crystal surfaces. While the examples are from the field of heterogeneous catalysis, we discuss the relation to homogeneous and enzymatic catalysis.
KeywordsModel systems Heterogeneous catalysis Catalysis Computational chemistry Theory Surface science Electron transfer
In a philosophical sense, a model is a restricted representation of reality. In some contexts, such as architecture, models are miniature replicas of what the finished building will look like and how it will integrate in its surroundings. In other contexts, such as economy, models are highly idealized descriptions of phenomena that do not exist in nature. In physics, for example, gases are modeled by infinitesimally small molecules, which exhibit no forces acting between them. However, in fact, we know that molecules have a finite size and forces act between them. These types of models share a common feature: although models neglect certain features to stress essential aspects, we know how to add corrections to the model to bring it closer to reality.
So, what do we mean by models in catalysis? Here we have to look at the phenomenon of catalysis first. Catalysis is a kinetic phenomenon, where a material (the catalyst) changes the rate of a chemical reaction without being part of the products [1, 2]. This is Ostwald’s definition put forward during the nineteenth century . Most frequently in catalytic literature we encounter “micro-kinetic models” which describe the complex system of elementary reaction and transport steps by a limited, ideally minimum set of rate equations . This important aspect is not subject of the present article.
We look at experiment and theory separately, knowing, however, that progress in the spirit of understanding phenomena at the atomic level will only be achieved by going hand-in-hand. We are trying to approach the situation encountered on the real working catalyst and—although it is not always possible—characterization—down to the detail necessary—by following an axis of increasing complexity. We clearly move, as outlined above from the simple to the complex, and not vice versa, which is important. The chart is only made up to look complete, while in reality it is not, since, as indicated above, characterization of the working catalyst is not really possible at present, and it is this missing knowledge that justifies the entire approach. We believe to know the ingredients of the working catalyst and may verify it to a certain extent by our arsenal of characterization tools, but to unravel how they interact and perform can only be taken apart by systematically increasing the complexity, hoping to mimic the observation on the working catalyst.
The bottom of the chart refers to clusters in the gas phase in different charge states. Through a comparison or better a combination between experiment and theory it is possible to unravel details of the reactions taking place in such systems. It has, indeed, been possible to see catalytic reactions, characterized by turnover, on those materials, and this is a first step—The “Ultimate Single Site Catalysis” . The small window indicates, that systems at this level of complexity have been investigated in uhv/ambient molecule level in gas phase and/or in interaction with a gas phase/crossed beams. However, the distance in complexity of the isolated cluster level with respect to supported clusters is far, and the size of clusters, possible to study, has, until now, been limited, although steadily increasing. Having said this, still very useful and unique information on details of reaction mechanisms may be unraveled. At the next level in the chart (Fig. 1), single crystal and well-ordered thin film surfaces have been used successfully in the past to start to understand fundamental phenomena at surfaces. This culminated in the Nobel Prize for Gerhard Ertl in 2007 [9, 10]. Given the enormous success of those studies, the valid question that has been asked is: What comes next? In fact, not too long ago, people have argued: Surface science is dead!! We believe, it is clear from what we argued so far that this statement is definitely wrong, if one is interested in unraveling the details of catalytic reactions. But not only in this respect! Single crystal metal studies lack important ingredients of real catalysts: One is the finite size of the metal particles, typically used in the catalyst, and, secondly, the oxide-metal interface realized by the fact that dispersed metals are typically supported on oxides, which, according to all reports so far, is of enormous importance for the reactions, their activity and selectivity, observed. Not to speak of the addition of modifiers such as poisons or promoters. So we certainly have to move to higher levels of model studies as shown in Fig. 1 before we will have a chance to reach a level, which may be directly compared and connected to situations encountered on real catalytic material. This is the point where the two arrows bottom up and top down meet. Through the interplay between experiment and theory, those additional ingredients, indeed, have been identified as essential, and it is the task of researchers in the field, both from theory and experiment, to work together to bring the field forward along the complexity axis shown in Fig. 1. Next to the various levels of complexity, the partially green and red bars indicate how far theory and experiment have come in an effort to describe systems at those levels of complexity properly. Also, it is important to indicate whether studies have been possible under uhv conditions and in addition comparison has been made to in situ studies under ambient conditions. This is indicated by the little window.
While for experiment, as we change the level of complexity, the number of components change, the kind of experiments employed are the same. For theory and computations, on the other hand, different types of approaches are relevant. Only the simplest experimental model catalysts, such as gas phase clusters and single crystal surfaces may be directly studied by quantum methods yet including ambient conditions, whereas the treatment of more complex structures requires adopting computational models such as embedded cluster models or periodic models . Last but not least, quantum chemical calculations always require approximations. In his Nobel lecture John Pople describes “Quantum Chemical Models”  as a hierarchic approach to better approximations. At each model level there is a well-defined set of approximations whose performance for different types of chemical compounds has been empirically tested.
We will try to exemplify the approach of experimental and computational model systems by choosing a number of examples, which the authors have partly worked on jointly, using a variety of experimental and theoretical techniques. The examples are basically taken from heterogeneous catalysis, but, at the end of this article we will comment on the other two areas of interest, i.e. homogeneous catalysis and enzymatic catalysis, and we will see that many aspects of the complexity encountered for heterogeneous catalysis also need to be addressed for homogeneous catalysis and enzymatic catalysis, even though there are claims that molecular catalysts are more easy to understand than solid catalysts. This may be true to some extent, but when we look at the full complexity of the situation, all three subfields are at the same stage of knowledge pretty much. The more important it is to try to unify approaches, a goal that a cluster of excellence in Berlin between the three Berlin Universities and two Max-Planck Institutes in the Berlin area try to tackle.
1.1 Example #1: Gas Phase Reactivity of Metal Oxide Clusters
To examine the active site at terraces, steps or corners we applying periodic boundary conditions to large super cells or embed geometrically constraint clusters in their crystal environment . Computationally, we can also study neutral Li-doped clusters and compare the results with those for cationic pure MgO clusters. The structure type of cationic gas phase clusters can be very different from that of the bulk solid , and the calculations may be performed for the most stable (global minimum) structure or the local minimum structure that resembles the rock salt structure of MgO. Figure 2 shows that this has consequences, for example, on the spin density distribution.
The first conclusion is that the cationic pure magnesium oxide clusters indeed show the same reactivity as the Li-doped neutral clusters. The barriers of the (MgO) n + clusters, 20, 23, and 6 kJ/mol for n = 2, 4, 7, respectively , are in a very similar range as the values of 11, 23, and 19 kJ/mol for the neutral LiO(MgO)n−1 clusters with n = 4, 6, and 9, respectively. The calculated barrier for the surface model is also very close, 27 kJ/mol , showing that the gas phase clusters are indeed useful models for studying the reactivity of oxygen radical sites as they may occur on Li-doped MgO. Figure 3 reveals an important detail of the computational modeling. The correct solid state result is only obtained from cluster models, if they are properly electrostatically embedded and a sufficient number of atoms is relaxed. Just putting geometric constraints on the models yields to high barriers (61 kJ/mol). If a cluster of the same size is allowed to assume its lowest energy structure, the active Li+O·− site accommodates at corner sites.
When comparison with mass spectrometric experiments was made, it was found that the dimer cation, (MgO) 2 + does not react with methane , and neither do larger cations. It needs an alkane with a more reactive C–H bond, e.g. propane, to observe hydrogen transfer. With methane, this reaction is only observed for the diatomic MgO+ radical cation, for which a negative apparent barrier is predicted. For all larger (MgO) n + cations and all neutral LiO(MgO)n−1 clusters the energy of the transition structure is above the energy of the reactants and no reaction is observed.
Gas phase models have an additional advantage. Their limited size of the makes it possible, to apply much better, more reliable, wave-function-based methods allowing an assessment of the density functionals used for large, periodic systems. For example, coupled cluster calculations for CH4/MgO+ and CH4/(MgO) 2 + show that the B3LYP/TZVP results are affected by errors of +1.3 and −6.5 kJ/mol, respectively, almost within the chemical accuracy range of ±4.2 kJ/mol (≈1 kcal/mol) .
In summary, from experiments on gas phase models when combined with quantum chemical calculations we learn that oxygen radical species in metal oxides are actives sites for hydrogen abstraction from C–H bonds and that density functional theory yields accurate barriers (with errors smaller than 6.5 kJ/mol) when the B3LYP hybrid functional is applied.
For surface sites of Li-doped MgO the apparent energy barrier will be affected by dispersion interactions between methane and the oxide surface. If this is taken into account, and if it is also taken into account that oxygen radical sites may not only be located at terrace sites, but also at corner sites, the conclusion is reached that the apparent barrier should be between 7 ± 6 and 27 ± 6 kJ/mol which is in obvious conflict with the much higher observed values, between 85 and 160 kJ/mol. From CH4/CD4 isotope exchange experiments a barrier of 85 kJ/mol has been deduced for C–H bond activation , while 90 kJ/mol have been reported for C2 hydrocarbon formation in OCM reactions . From microkinetic schemes fitted to kinetic OCM data, a barrier as high as 147 kJ/mol has been deduced for the generation of methyl radicals by hydrogen abstraction . The activity of Li-doped MgO catalysts was found to vary strongly over the catalytic runs and depend also on the preparation conditions [21, 28]. The reported barriers for the stationary state of the catalysts were 90–160 kJ/mol  and 133 kJ/mol .
This has been also demonstrated for vanadium oxide supported on oxides, a catalyst for selective oxidations. Vanadyl groups, O = V(O–)3 have been identified as active sites , and two different types of cationic clusters have been used for gas phase studies. The V4O 10 ·+ radical cation proved highly reactive, abstracting hydrogen easily from methane , while the closed shell V3O7 + species showed similar reactivity as the surface species . Although it was not reactive enough to activate a C–H bond of propane in the gas phase, but hydrogen abstraction from butene could be observed  The reactivity differences between the two gas phase species have been explained and can be predicted using a simple reactivity descriptor, the vanadium–oxygen bond dissociation energy or, in physical terms, the oxygen defect formation energy , which is 277–287 kJ/mol for vanadyl sites on silica supports. For the neutral V4O10 with a tetrahedral arrangement of four vanadyl groups, O = V(O–)3 it is very similar, 257 kJ/mol. On ionization, in the V4O 10 ·+ radical cation, a much weaker ·O–V+(O–)3 bond is created with a bond dissociation energy as low as 14 kJ/mol, while for the O = V+(O–)3 site in V3O7 + a value of 165 kJ/mol is obtained, of the same order of magnitude as for the surface species.
1.2 Example #2: Nanoparticles and the Metal Oxide Interface
In the left panel the electron sources or drains for electron-transfer are the oxide-metal and metal-oxide interfaces, and in the right panel a properly chosen dopant in a bulk material takes the role of the electron source. In order to systematically go through the evidences, we will start with the discussion of adsorbate properties on thin, metal-supported oxide films starting from a single atom, moving towards nano-particles, and then take those findings as reference to compare them with the situation on doped oxides. Then, we will discuss, and exemplify the consequences of general considerations in catalysis and oxidative methane coupling in particular. As a marker for charge transfer, we are using Au because of its large electronegativity .
The presence of single gold atoms on the surface of a thick MgO film was proven by STM (Fig. 6b) and investigated further by electron paramagnetic resonance (EPR) spectroscopy . The latter technique for in situ surface studies has been developed at the Fritz Haber Institute [43, 44, 45]. The EPR spectrum is characterized by a quartet of lines caused by the hyperfine interaction of the electron spin (S = 1/2) with the nuclear spin of the neutral gold atoms (Fig. 6a). By a full analysis of the spectral angular dependence and the additional super-hyperfine interaction with O of an 17O enriched MgO film, the Au atoms were shown to adsorb on top of oxygen ions in agreement with theoretical predictions [46, 47, 48]. DFT calculations showed, that these observations are indicative of polarization of the singly occupied 6s orbital of neutral Au atoms away from the MgO surface . Adsorbing probe molecules such as CO onto the Au atoms provide the opportunity to apply IR spectroscopy to this system (Fig. 6c). Two signals at 2,120 and 1852 cm−1 are observed.
The former signal can be assigned to CO adsorbed on small neutral Au clusters, whereas the latter one, red-shifted by 291 and 180 cm−1 compared with gas-phase CO and the Au–CO complex , respectively, is associated with single Au atoms. A detailed theoretical analysis of this system reveals that the large red shift is caused by the largely polarized valence electrons of the adsorbed Au atoms, which create an (Au+)–CO−-complex on the surface. It is important to note at this point again, how important the collaboration between experimentalists and theorists is. In the present case, a straightforward application of simple, heuristic concepts may have led to false conclusions, namely, that the Au atoms are negatively charged.
A first hint for the formation of charged adsorbates on thin oxide films came from low-temperature scanning tunneling microscopy (STM) experiments performed on a much thinner, 3 mL MgO/Ag(001) exposed to small amounts of Au . Whereas on bulk oxides, gold shows a strong tendency for aggregation, mainly isolated atoms are detected on the thin film even at high gold exposure.
Charged species tend to maximize their interatomic distance in order to reduce the mutual Coulomb repulsion. A similar phenomenon was found for alkali atoms on metal and semiconductor surfaces before and was assigned to a positive charging upon adsorption [50, 51, 52]. Conversely, the Au atoms on the MgO films charge up negatively, as their 6s orbital gets filled with electrons from the Ag(001) support below the oxide spacer layer. The charge exchange is enabled by the high electronegativity of gold, as mentioned above, in combination with a small work function of the Ag–MgO system [53, 54]. The experimentally deduced charging scenario was corroborated by DFT calculations yielding a computed Bader charge of −1|e| at the Au atoms in addition to the expected increase in binding energy .
What are the consequences of negatively charged Au atoms for larger Au particles? This question was first addressed in a theoretical paper by Pacchionis and Landman´s groups : While a Au20 cluster keeps its pyramidal, three-dimensional shape when supported on bulk MgO, the same Au20 cluster supported on a 2 mL MgO film on Ag takes shape of a flat single layer Au raft. The reason is simply the tendency of Au to pick up electrons, which in this case stem from the MgO/Ag interface. In order to optimize the electron transfer the Au atoms assume positions as close as possible to this interface, i.e. single layer Au rafts, where charge is located at the rim of the Au raft. We realize that electron transfer may influence the morphology of supported nano-particles and lead to charge localization at particular sites.
For flat Au islands on MgO/Ag(001), STM conductance spectroscopy can be exploited to determine their charge state . A particularly instructive example shows an ultra-small Au cluster with 10 Å diameter and 0.8–0.9 Å apparent height grown on a 2 mL MgO/Ag(001) film (Fig. 4) .
Another example is electron transfer from the NiAl metal substrate through a thin alumina film into Au chains formed on its surface . Formation of an Au–Al bond involves breaking of an oxide Al–O bond below the ad-atom and at the same time forming a new bond between the hence under-coordinated O ion to an Al atom in the NiAl. Combining low temperature STM with DFT, it was possible to count the number of electrons transferred by analysing the nodal structure of the highest occupied orbitals.
The concept of charge-mediated control of the metal-oxide adhesion is not restricted to ultrathin films but other electron sources may be explored. One possibility to extend the concept of charge-mediated particle growth to bulk oxides is the insertion of suitable charge sources directly into the oxide material, preferentially into a near-surface region to allow for charge exchange with adsorbates. The fundamental approach to insert charge centers into a material is doping, and the underlying concepts have been introduced and brought to perfection already in the mature field of semiconductor technology. Oxides are subject to self-doping either by native defects or by unwanted impurities, the concentration of which is difficult to control experimentally . Both lattice defects and impurity ions may adopt different charge states in the oxide lattice [64, 65], a variability that leads to pronounced compensation effects. Finally, the dopants may be electrically inactive in a wide-gap insulator, as thermal excitation is insufficient to promote electrons from defect states into bulk bands. As a result, the excess charges remain trapped at the host ions. Whereas high-valence dopants may serve as charge donors and provide extra electrons, undervalent dopants have acceptor character and may accommodate electrons from suitable adsorbates. Based on the above considerations it is now expected that charge donors in an oxide lattice have a similar influence on the particle shape as the metal support below a thin oxide film.
Especially, the latter one is in an energetically unfavorable position and therefore susceptible to be transferred into an acceptor state with lower energy. Such acceptor states are provided by Au atoms, which expose half-filled Au 6s levels at lower energy. DFT calculations revealed a spontaneous transfer of the topmost Mo 4d-electron into the Au 6s affinity level, resulting in the formation of an Au−-anion (Fig. 9). We emphasize that the charge transfer does not require the presence of a Mo ion in the surface but remains active over relatively large Mo–Au distances of up to ten atomic planes.
The increase of the metal-oxide adhesion due to dopant-induced charge transfer fully explains the 2D growth regime of gold observed in the experiment. Gold tends to wet the CaO surface in an attempt to maximize the number of exchanged electrons, hence the interfacial interaction. Further DFT calculations suggested that also a Mo3+ species that has already lost one electron remains a potential donor, as two of the residual d-electrons are still higher in energy than the Au 6s affinity level . Consequently, even a second and third electron may be transferred into the ad-metal, leaving behind thermodynamically stable Mo4+ and Mo5+ ions in the CaO lattice. It is this behavior of the Mo ions that is responsible for the robust donor behavior of Mo-doped CaO . The presence of suitable dopants is, however, not the only requirement for a stable donor characteristic, but also the interplay between dopants and host oxide determines the redox activity. One conclusion from detailed studies on Mo dopants is that the donor behavior of a transition-metal-doped oxide cannot be predicted by simple valence arguments but needs to be checked in every single case.
The influence of overvalent dopants on the equilibrium morphology of metal particles can, to a certain extent, be annihilated by undervalent dopants in the oxide lattice [68, 69]. Dopants with lower charge state generate holes in the oxide electronic structure that are able to trap the extra electrons provided by the charge donors. This mutual compensation between donors and acceptors has been explored for CaO films co-doped with Li and Mo ions . As a result, charge transfer to the surface ceases at a critical Li doping level and the Au deposits adopt the typical 3D geometry of pristine CaO films.
Gold forms monolayer islands if deposited onto a Mo-doped CaO under vacuum conditions, but 3D particles if oxygen is present during growth. The reason is that O2 molecules bound to the surface act as electron acceptors and trap charges in their O 2p* antibonding orbitals. These electrons are lost for the Au islands, resulting in a gradual transition from a 2D to a 3D growth regime with increasing O2 partial pressure. Whereas in 5 × 10−7 mbar of oxygen, 50 % of the Au islands still adapt monolayer shapes, all Au deposits turn 3D when grown in a 5 × 10−5 mbar O2 background. The interplay between the observed growth mode and the composition of the gas environment emphasizes the pivotal importance of excess electrons from donor species for the reactivity of oxides towards adsorption of metallic and gaseous species.
This observation also opens up other options to control surface reactivity. One is to use dopants to activate oxygen to participate in oxidative methane coupling a reaction of potential for applications .
In empty-state images, the adsorbates appear as circular depressions 0.6 Å in depth and 10 Å in diameter (Fig. 10f). Exposing them to electrons from the STM tip reveals their molecular nature, as they split into pairs of identical minima that are assigned to the respective O atoms (Fig. 10d, e) .
The bond cleavage occurs as a second electron enters the anti-bonding states of the already weakened superoxo species. Whereas a mean O–O distance of 10–15 Å is observed directly after dissociation, this number increases with time due to a repulsive character of the O–O interaction on the surface. The two types of oxygen species can be distinguished also in bias-dependent topographic images. While the molecules show pronounced negative contrast, the atomic species appear fainter and are surrounded by a bright halo (Fig. 10e).
The adsorption efficiency of oxygen strongly depends on the preparation of the CaO films, in particular on the concentration of the Mo dopants. Whereas Mo-poor films are unable to bind oxygen, a rather high adsorbate concentration is found for Mo-rich preparations, indicating the crucial role of the dopants in binding O2. Dopants and O2 molecules are expected to interact directly with each other. Experimental evidence comes from O desorption experiments, in which isolated molecules are removed from the surface by a bias pulse with the tip. In 50 % of these experiments, a Mo donor is detected below the molecule. Interestingly, the dopant never occupies a position directly in the top layer but sits in sub-surface oxide planes, as deduced from the diameter of characteristic charging rings emerging in the STM images . It is concluded that the Mo ions are able to exchange charges with the surface O2 molecules even over distances as large as 1 nm, most likely via electron tunneling. The electron transfer between Mo donors and O2 acceptors has been investigated with DFT calculations performed at the B3LYP + D level. On non-doped CaO(001), a neutral O2 molecule binds with 13 kJ/mol (mostly from dispersion forces) to a Ca–Ca bridge position, while Ca2+ top sites are less preferred. In contrast, an O2 − species binds to the same bridge site with a binding energy of 87 kJ/mol when a Mo3+ ion is present in the third subsurface plane. The charge transfer to oxygen becomes even more favorable for Mo2+ donors in the oxide film, given their low ionization energy . Further evidence for the formation of superoxo species comes from the calculated bond elongation (121–133 pm) and the reduced stretching frequency (1,537–1,200 cm−1) computed for O2 molecules on the doped oxide. Moreover, the total spin of the system decreases from 5/2 (3/2 for Mo3+ (d3) plus 1 for O2) to 3/2 (1 for Mo4+ (d2) plus 1/2 for O2 −) in response to the charge transfer. And finally, the lower apparent dissociation barrier for super-oxo species on doped CaO (66 kJ/mol) compared to that of neutral O2 on pristine CaO (110 kJ/mol) has been calculated, following the trend observed experimentally. It is concluded that dopants may play a pivotal role in the activation of hydrocarbons on wide-band-gap oxides. Given the activated oxygen one might easily envision its participation in hydrocarbon activation, in fact, the latter has been confirmed in a study by Schlögl’s group, who investigated the reaction yield for the oxidative coupling of methane over Fe-doped MgO powder .
1.3 Example #3: Olefin Hydrogenation: Nanoparticles Versus Single Crystals
Industrially used catalysts often require small amounts of additives, such as halogens or alkali metals, to ensure high catalytic activity and selectivity . One of the most important modifiers for surface processes involving transformation of hydrocarbons is carbon, which is formed as a decomposition product at early stages of a reaction. It has been recognized for a long time that accumulation of dehydrogenated carbonaceous deposits affect the activity and selectivity of hydrocarbon conversions with hydrogen on transition metals [75, 76, 77]. While for a long time carbon was considered a site blocker, Geoff Webb  suggested that it is the hydrogen directly connected with the carbon is the relevant species involved in hydrogenation. The traditional opinion that only surface hydrogen species participate in the hydrogenation process was also questioned by Ceyer and co-workers studying ethylene hydrogenation on Ni(111) . More recently, other experimental and theoretical evidences for the important role of subsurface hydrogen were reported and it has been suggested that the carbonaceous species control the hydrogen distribution on and in the particle [80, 81, 82].
The existence of different hydrogen species in and on the nanoparticles may potentially result in some important implications for the overall activity and selectivity of the hydrogenation catalyst: if one of the key reaction steps—the formation of subsurface hydrogen, which is known to be a structure sensitive process—is slow under reaction conditions, the hydrogen permeability of the metal surface may be decisive for hydrogenation activity.
In recent studies the hydrogenation activity of a Pd(111) single crystal surface and Pd nanoparticles supported on Fe3O4/Pt(111) model catalyst was investigated using a combination of isothermal pulsed molecular beam (MB) methods and resonant nuclear reaction analysis for hydrogen depth profiling (r-NRA) to further clarify the microscopic mechanisms active for hydrogenation over Pd catalysts [83, 84, 85, 86, 87].
This permitted to address the question of how does the activity and selectivity of competing reaction pathways in olefin conversions with hydrogen depend on the structure of the metal nanoclusters, and on the presence of surface modifiers such as e.g. carbon.
It was found that: (i) hydrogenation of the olefinic double bond requires the presence of subsurface hydrogen, and a particular reaction step—the second half-hydrogenation (see the scheme below)—was identified as linked to the availability of sub-surface hydrogen species; (ii) sustained hydrogenation can be achieved on Pd nanoparticles only when low-coordinated surface sites (edges, corners) were modified by adsorbed carbon or carbonaceous species. Neither C-free Pd nanoparticles nor C-free or C-modified Pd(111) surfaces were found to be capable of maintaining hydrogenation activity under steady state conditions; (iii) carbonaceous deposits influence the reactivity by a pronounced facilitation of hydrogen diffusion into the subsurface of Pd nanoparticles through C-modified low-coordinated surface sites.
Olefin conversions with H2 are described by the Horiuti–Polanyi mechanism, which proceeds through a series steps . Specifically for cis-2-butene the molecule used in this model study a first half-hydrogenation step forms a surface butyl species, which is an intermediate for both a cis–trans isomerization, which leads to the desorption of trans-butene and if performed using D2 to trans-2-butene-d1 and as full hydrogenation to butane-d2. Dehydrogenation of the adsorbed alkene to other carbonaceous surface species is also possible, giving rise to the accumulation of dehydrogenated hydrocarbon species. Two independent molecular beams were used to dose the reactants—cis-2-butene and D2—with the evolution of gas phase products under iso-thermal conditions, monitored as a function of time by quadrupole mass spectrometry. As a model catalyst, Pd nano-particles supported on a thin, planar Fe3O4(111) film were prepared under UHV conditions. The Pd nanoparticles are on average 6 nm in diameter and exhibit mainly (111) facets (abundance 80 %) and a smaller fraction of (100) facets and other low-coordinated surface sites such as edges and corners (abundance 20 %). IR-spectroscopy of CO probe molecules adsorption has been used to show that sub-monolayer amounts of C are produced on the Pd nanoparticles, which selectively block the low-coordinated surface sites while leaving the majority of the regular (111) facets C-free. Both types of catalysts—C-free and C-modified (with the edges and corners covered by C)—were used to compare their catalytic activities and selectivities with regard to the competing hydrogenation and cis–trans isomerization pathways.
Upon inspection, it is obvious that due to the higher binding energy of surface hydrogen, the surface saturates at a hydrogen pressure below 10−6 mbar via a non-activated molecular hydrogen dissociation process. The sub-surface hydrogen, on the other hand, shows a pronounced pressure dependence between 10−7 and 2 × 10−5 mbar, indicative of the activated step of hydrogen penetration through the surface layer. Via molecular beam experiments at two different pressure conditions, where the surface hydrogen concentration was in saturation but the sub-surface hydrogen concentration varied considerably, it was demonstrated that the full hydrogenation step of cis-butene required the presence of sub-surface hydrogen, while the cis–trans-isomeraization was independent of it.
In further studies on H2 + D2 ⇒ 2HD exchange reactions direct experimental evidence for a faster subsurface H diffusion through C-modified low-coordinated surface sites on Pd nanoparticles .
The microscopic origin of the proposed C-assisted subsurface H diffusion was revealed by computing for model particles (in collaboration with K. Neyman) the activation barriers for hydrogen diffusion into the volume of Pd nanoparticles on C-free and C-containing surfaces . It was shown that deposited carbon dramatically enhances the hydrogen diffusion rate into the subsurface region of Pd nanoparticles, mainly due to local elongation of Pd–Pd bonds, which results in a lowering of the activation barrier for subsurface hydrogen diffusion. In contrast, the lateral rigidity of the extended Pd(111) surface was predicted to hinder this effect and does not allow facilitation of subsurface H diffusion by deposited C atoms. This result demonstrates the conceptual importance of atomic flexibility of sites near nanoparticle edges that, in contrast to the intrinsically rigid regular single crystal surfaces, play a crucial role in subsurface hydrogen diffusion on Pd.
The steady state HD formation rates obtained during D2 and H2 exposure for reaction temperatures of 260 and 320 K on clean and C-modified Pd nanoparticles using a range of pressure conditions with a constant D2 : H2 ratio are shown in Fig. 10. Whereas at 320 K pre-adsorbed C reduces the overall reaction rate by about 30 %, the reaction rate increases by about 100 % at 260 K on the C-modified nanoparticles for all pressures studied. The decreased HD formation rate in the high-temperature regime, where HD formation is dominated by the recombination of the surface H and D species is due to the blocking of surface adsorption sites by C. The increase in HD formation rate in the low-temperature regime, where desorption involves at least one subsurface H(D) species can be explained only by the higher formation rate of the sub-surface H(D) species on the C-modified nanoparticles resulting in a higher steady state concentration of subsurface hydrogen species. At the microscopic level the facilitation of subsurface H diffusion through C-modified low-coordinated sites is most likely even more pronounced, since the nearly 100 % increase of the overall reaction rate arises from modification of only 20 % of the surface sites constituting edges and corners of Pd nanoparticles. In summary, the molecular beam experiments on olefin conversions with hydrogen over well-defined Pd nanoparticles supported on Fe3O4/Pt(111) oxide films and Pd(111) allowed us to obtain a comprehensive microscopic picture of hydrogenation and isomerization processes on the nano-structured catalysts.
Coming back to the statement at the outset of this case study, we note that based on model studies, where we systematically increase the complexity from metal single crystals to clean oxide supported metal particles, which are modified by carbon or carbonaceous species deposition in strategically relevant sites, it is possible to unravel the detailed interplay of components of the system—It is, finally, the combination of the structural flexibility of a nano-particle with the strong binding of the carbon modifier on particles edges and corners that controls hydrogen population at the surface and thus guaranties the sustained catalytic activity of the system as a function of temperature by influencing hydrogen diffusion between the surface and sub-surface. It is hard to envision how one could have reached detailed atomic insight of this nature without relying on model systems with increasing degree of complexity.
2 Summary and Outlook
We have discussed a number of case studies in order to show how a model studies approach may be linked to the investigation of real catalytic material and catalytic reactions. The advantage of the model study approach is the possibility to identify factors that determine the properties of catalytic materials with respect to reactions by systematically increasing the complexity of the system. With this approach we are now in the position to answer well-defined questions by capturing specific aspects that are thought to be of important for particular materials and reactions. We have done this by choosing case studies that address some of those well-defined questions and have tried to relate this to real catalysis. The approach has led us to certain points, indicated in the schematic diagram shown in Fig. 1 by combining both theory and experiment. This was only possible because, both, in theory and experiment the scientific community has made considerable progress in advancing the ability to address, by computational techniques systems of relevant size, as well as by developing novel experimental approaches that may be applied to the study of surfaces under ultrahigh-vacuum and ambient conditions. The development has, by far, not reached a point where we may address the relevant questions of structure-relationships under operating conditions. In fact, further, increasing efforts have to be made to develop the field further in this direction. It has been impossible, in this short review to cover all innovative developments, in particular with respect to in situ experimental studies, where a lot of innovative approaches have been launched recently, including ambient pressure X-ray photoelectron spectroscopy , non-linear optical spectroscopy , ambient pressure scanning tunneling microscopy , in situ transmission electron microscopy with Cs correction  and many more, but we have rather chosen here to address the development of model systems that move towards capturing structural and functional features of real catalysts, which then in the future may be addressed with this increasing toolbox of new techniques, which are under rapid development at present.
We would like to thank our coworkers, who are mentioned in the references for their important contributions to the work described. HJF also thanks Gianfranco Pacchioni and Hannu Häkkinen for decisive contributions to the results discussed in case study #2. We are grateful to the funding agencies that have provided financial support, i.e. German Science Foundation (DFG), Alexander von Humboldt Foundation (AvH), Fonds der Chemischen Industrie (FCI), as well as the institutions we are members of, i.e. Humboldt Universität zu Berlin and Max-Planck Gesellschaft.
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