Major Successes of Theory-and-Experiment-Combined Studies in Surface Chemistry and Heterogeneous Catalysis

The phenomenon of electron diffraction was first predicted by de Broglie [29] due to the quantum particle-wave duality in 1924, and was observed 3 years later by Davisson and Germer [30, 31] when a well-collimated beam of electrons was directed onto a crystallized nickel sample. It was soon realized that, in principle, the LEED pattern contains the structure information of the first few layers of atoms at the surface of materials.

However, it took almost 60 years after the Davisson and Germer experiment to develop LEED fully into a prime tool for quantitatively determining complex surface structures [3, 32, 33]. The major obstacles in this development resided in both experimental technique and theoretical interpretation of the experimental data. From the experimental aspect, it is crucial firstly to create clean surfaces and maintain the sample in this state within the duration of the LEED measurement; secondly, the inelastically scattered electrons, which plague the diffraction pattern formed by the elastically scattered electrons, must be filtered out in the experiment. In the early 1960s, the first problem was solved by the development of Ultra-High-Vacuum technology together with methods such as Auger electron spectroscopy (AES) for preparing clean surfaces and monitoring their cleanliness [34].

A clever design of the experimental setup shown in Fig. 1a further improved the detection of LEED pattern. The introduction of a fluorescent screen enabled the simultaneous monitoring of the diffracted electron beams in different directions and shortened the time duration of experiments. By applying appropriate voltage bias on the hemispherical concentric grids (Fig. 1b), the inelastically scattered electrons were filtered out and the elastically scattered electrons were accelerated onto the fluorescent screen to make the diffraction pattern more readily detectable. With these technical advances, the qualitative information such as the symmetry of the surface structure, the size and the rotational alignment of the adsorbate unit cell with respect to the substrate unit cell were readily obtained by analysis of the diffraction patterns from clean surfaces and surfaces with a given atomic adsorbate [2]. A spectacular example is the (7 × 7) reconstructed Si(111) surface shown in Fig. 1c. A total number of 49 surface atoms per unit cell are involved in the reconstruction of silicon surface atoms to generate this highly symmetric surface.

The quantitative information about exact atomic locations in surface layers can be extracted by theoretical analysis of the so-called I–V curves, where the intensities of diffracted electron beams are recorded as a function of incident electron beam energy. In the 1960s, the theoretical method available for analyzing the I–V curves was the kinematic theory derived from the X-ray diffraction theory. Figure 2a shows a successful analysis of I–V curves for the (111) surface of solid xenon using the kinematic theory [35]. In this theory, it is assumed that every incident electron is scattered once by an atom in the surface layer before reaching the detector (Fig. 2b). This is true for the xenon case because of the uniquely short inelastic mean free path of low-energy electrons in solid xenon. For most materials, the multiple scattering processes as shown in Fig. 3a usually cannot be ignored. Figure 3b demonstrates the necessity of the multiple scattering theory for fitting the I‐V from the Cu(001) surface [36].

Two computationally efficient methods developed by John B. Pendry [33] in the early 1970s revolutionized the calculation of the I–V curves for comparison with experimental data. The first method was the so-called layer-doubling method which treats the multiple scattering in the surface layers explicitly. In this method, the surface is represented as a stack of identical 2D atomic planes. The basic idea is that once one has computed the transmission (t ₁) and the reflection (r ₁) coefficients for the single atomic layer (Fig. 4a), the reflection (r ₂) and the transmission (t ₂) coefficients of two atomic layer as shown in Fig. 4b can be obtained asand

Now the reflection (\( r_{{2^{i} }} \)) and transmission (\( t_{{2^{i} }} \)) coefficients of 2 ⁱ layers as shown in Fig. 4c can be obtained recursively asand

This layer doubling method is highly computationally efficient because the computational time needed for the calculation of a M-atomic-layer system, log₂ M, scales sublinearly with the number of atomic layers.

Another bottleneck of the computational efficiency remained in the layer doubling method was the matrix inversion of \( \left( {1 - r_{{2^{i} }} r_{{2^{i} }} } \right) \), which has to be performed at every recursive step, and whose computation time is scaling cubically with the matrix dimension of the reflection coefficient. Pendry proposed a method to get around this bottleneck based on a perturbation expansion, recognizing that the strong forward scattering of low energy electrons implies that the reflection coefficient, |r| ≪ 1. Therefore, the expansion should be in order of powers of the small parameter r. However, it was found that a simple perturbation approach failed in giving the converged result at the expense of affordable computational time. A more sophisticated perturbation scheme, the so-called renormalized forward-scattering perturbation theory, was finally developed to solve the problem.

With these theoretical advances, the calculations of I–V curves were capable to solve surface structures with up to five atoms in a unit cell. In the period from the early 1970s to the mid 1980s, several hundred structures of clean surface and simple adsorption systems were determined by the LEED crystallography. These studies unveiled that the reconstruction is a common phenomenon at the clean surfaces. For example, the top atomic layer of the Ir(100) surface undergoes a (5 × 1) reconstruction [37] (Fig. 5a). This structure similar to the close-packed fcc(111) surface lowers the surface energy of the system. The studies of ethylene chemisorption on transition metals such as Pt and Rh suggested that ethylene is not necessarily laying flat on the surface, and that, at the room temperature, C–H bonds may break and reform to produce ethylidyne on the surface [38, 39] (Fig. 5b).

As the complexity of the surfaces increased so did the computational resources required to perform both the LEED calculations and the fitting of the calculated I–V curves to the experimental data. By the mid of 1980s, it became crucial for the field to develop more computationally efficient methods for data analysis of disordered adsorption systems and reconstructions involving multiple surface layers.

For disordered adsorption systems, a surface unit cell has effectively infinite area (or says, infinite number of atoms). To tackle this problem, diffuse LEED (DLEED) theory was developed by Pendry [40] and Van Hove [41], separately. In the Van Hove’s method (known as Beam Set Neglect method), the disordered adsorption surface is approximated by an ordered structure with a unit cell area less than λ ², here λ is the mean free path of electron in the solid (typically around 10–100 Å). The physics behind this approach is that the low energy electrons have a relatively short mean free path, and that an electron can only contribute to the diffraction pattern if it has traveled a distance of less than the mean free path. Pendry’s approach is based on the observation that a disordered adsorption system can be viewed as a disordered overlayer of atoms adsorbed on an ordered substrate. The electrons scattered from the ordered substrate generate the Bragg spots. Any electron contributing to the diffuse component of the pattern must have interacted with at least one adsorbed atom. Depending on the traveling path taken by the diffracted electrons, the diffraction pattern can be broken into three components, which could be computed using either conventional LEED theory or methods borrowed from the theory of surface extended X-ray absorption fine structure spectroscopy (SEXAFS). With the help of DLEED theory, the structures of weakly adsorbed molecules such as benzene on Pt(111) could be determined [42] (Fig. 6). The benzene structure unveiled that the preferred adsorption site is the bridge site on Pt(111), and that the adsorption also induces subtle restructuring of the benzene molecules.

The development of tensor LEED theory by Rous and Pendry [43] finally brought the LEED technique into its mature state. Tensor LEED is a perturbative approach to the calculation of LEED intensities. One starts by defining a reference structure: a particular surface structure that we guess to be as close as possible to the actual surface structure. We then distort this surface by moving some of the atoms to new positions. In this way we generate a trial structure that is a structural distortion of the reference structure related by a set of atomic displacements.

If the atomic displacements are small enough (typically within 0.4 Å), the difference between the amplitude of a given LEED beam scattered from the reference and the trial surface, δA, can be approximated to the first order. Assuming δr _ni (n = 1, 2, …, N; i = 1, 2, 3) are the 3D displacements of N atoms, the amplitude difference can be written by

The quantity T is the tensor which depends only on the scattering properties of the reference surface and can be calculated once by the conventional multiple LEED theory. Once T is known, then the diffraction intensities for many trial surfaces can be evaluated extremely efficiently by summing Eq. 5. This linear version of tensor LEED is limited to atomic displacements of less than 0.1 Å. A more sophisticated version of the theory allowed the displacements of up to 0.4 Å. Figure 7 shows the tensor LEED approach which combines the experimental measurement and the theoretical data analysis.

Tensor LEED represented a revolution in structural surface chemistry. The knowledge accumulation of tensor LEED studies leads to the concept of ‘flexible surface’ which changed our static view of surface structure to a dynamic one. The relaxation at Pt(210) stepped surface involves the displacements of atoms in up to four surface layers [44] (Fig. 8a), and the marked restructuring of metal surfaces may be induced by strong chemisorption as shown in the cases of the ethylene adsorption on the Pt(111) [45] and Rh(111) [46] surfaces (Fig. 8b). The creative applications of tensor LEED to the covalent-bonded and ionic-bonded materials such as NaCl [47] and ice [48, 49] further proved the generality of the concept of ‘flexible surface’ (Fig. 9a, b).

Recently, the structure studies of nanostructures pose another challenge to the LEED technique. It can be envisioned that, with the advances both in new experimental design and theoretical data analysis, this technique will become one of the prime tools for determining complex structures of nanostructures in near future [50].

In recent years, the formation of thin well-ordered but complex surface oxides on later transition metals has been discovered [51]. These surface oxides may serve as a protective layer against corrosion, as insulation layers in microelectronic devices, and as oxygen reservoir during catalytic reactions. Due to the structural complexity of these surface oxides, a multi-method approach of experimental and theoretical techniques has to be employed in the atomic scale studies. These studies provide perfect examples for demonstrating the complementary roles of experimental and theoretical techniques in surface chemistry studies.

The multi-method approach starts with applying the qualitative structural methods such as LEED and STM. These two techniques give a good approximation of the symmetry of surface structure and in-plane lattice distances. Figure 10a and b shows the LEED pattern and the STM image of a surface oxide on Rh(111) formed under conditions: 1 × 10⁻³ mbar of O₂ and 700 K [52]. These experimental results suggest the formation moiré pattern consisting of a hexagonal layer with a larger in-plane lattice distance being on top of hexagonal Rh(111) substrate. The periodicity of the oxygen-induced hexagonal pattern is close to a (9 × 9) Rh(111) cell. The lattice distance of the overlayer is around 3 Å, which can also be confirmed by using surface X-ray diffraction (SXRD) measurement.

Applying high resolution core level spectroscopy (HRCLS), a type of XPS technique, the chemical composition of surface oxides can be studied quantitatively. For the Rh (9 × 9) surface oxide (Fig. 10c), the HRCLS spectrum in O1s region indicates there are two Rh-coordinated O species existing in the surface oxide layer; In the Rh 3d_5/2 region, there are two major peaks. The peak at higher binding energy (~307.9 eV) is originated from a highly-O-coordinated Rh species. The abundances of these surface species can be deducted qualitatively from their peak intensities in the HRCLS spectra. The obtained coverages for the highly O-coordinated Rh species and the Rh-coordinated O species are 0.9 and 1.8 monolayer, respectively, which indicates a layered O-Rh-O surface oxide.

Using the experimentally obtained structural information such as symmetry and the abundances of surface species, the atomic structural models can be proposed and examined by the DFT studies. In the DFT studies, a O-Rh-O trilayer with a (7 × 7) cell on a (8 × 8) Rh(111) cell (Fig. 11a, b) is found to be stable at the given oxygen partial pressure and temperature [52]. The simulated STM image (Fig. 11c) for this structure is in good agreement with the experimental result shown in Fig. 10b; further, the calculated core electron binding energies agree well with the measured values as shown in Fig. 10c. The DFT-predicted structure disagrees slightly with the SXRD result which suggests a structure with a (8 × 8) cell on a (9 × 9) Rh(111) cell. However, DFT calculations also indicate that the free energy difference between these two structures is very small.

Once the structures are obtained, the thermal and chemical stability of surface oxides can be investigated in detail. The calculated phase diagram of various surface oxides indicates that the (8 × 8) and the (9 × 9) Rh surface oxides are actually metastable under the conditions where bulk oxide is already stable [52]. Therefore, these oxides serve as kinetic barriers for the further growth of thick oxides on the surface.

The investigation of the reduction of the (9 × 9) Rh surface oxide by CO at CO partial pressure of 2 × 10⁻⁸ mbar and 375 K found that the surface oxide can be reduced even though CO does not adsorb easily on the surface under the given experimental conditions [53]. Both HRCLS and STM results showed that atomic oxygen is expelled from the oxide layer onto the reduced metallic areas. The observations can be again explained by the DFT calculations. The DFT result showed that the (9 × 9) structure is not stable, if its surrounding metal is free of oxygen. Therefore, the surface oxide may serve as an oxygen reservoir during the CO oxidation reaction.

Once the geometric structures of chemisorption systems are determined by various surface science techniques, the further questions are how strong these surface chemical bonds are, and how the strength of the surface chemical bond depends on the properties of the adsorbed molecules and the substrates. In experiments, the strength of surface chemical bonding can be determined by deriving the heat of adsorption from the adsorption isotherms at different temperatures, or by monitoring desorption temperature of adsorbate in the temperature-programmed desorption (TPD) experiment. By the late of 1970s, large amount of experimental data had been accumulated, and the surface chemical bonding strength across the periodic table was tabulated [54]. It was found that, over transition metal surfaces, the chemical bonding strength of an adsorbed atom generally increases from the right to the left in the periodic table. On the other hand, the development of the electron spectroscopy techniques, such as ultraviolet photoelectron spectroscopy (UPS) [55‐57] and X-ray photoelectron spectroscopy (XPS) [58, 59], enabled the detailed investigation of electronic structures of chemisorptions systems [60]. All these experimental advances set a stage for the development of theoretical approaches to rationalize the experimental observations, and to understand how the electrons in the adsorbates and the metal surface interact with each other to form surface chemical bonds.

A major contribution by Norskov in the early stage of this theoretical development was extending and applying the effective medium theory to understand the trends of chemical bonding over the transition metal surfaces [13, 61, 62]. The effective medium theory is based on density functional theory (DFT), a general theory for studying molecular electronic structures. The full-blown DFT study of surface chemical bonding is very time consuming due of the large number of electrons involved. The basic idea behind the effective medium theory is to calculate the energy of an atom in an arbitrary environment by first calculating it in some properly chosen reference system, the effective medium, and then estimate the energy difference between the real system and the reference system [62]. The total energy of the system is given bywhere E _c,i is the energy of atom i in the reference system. The essence of the method is then to choose the reference system so close to the real system that the correction, ΔE = E − ∑ _i E _c,i, is small enough that it can be estimated using perturbation theory or some other approximation form. The choice of the reference system also ensures that the binding energies of the reference system, E _c,i, can be easily obtained.

In the simplest form, the adsorbed atom is considered to be embedded in a homogenous electron gas (the reference system) with an average electron density corresponding to the given metal. The binding energy of each atom is calculated to the first order of approximation as a function of the average electron density from its neighbors in the vicinity of the atom. The correction ΔE is calculated by the News-Anderson model which considers subsequent interaction of the valence electron of adsorbed atom with the sp bands and the d band in the metal. It turned out that, as shown in Fig. 12, this simple treatment was good enough to predict the bonding trends observed experimentally for the chemisorption of hydrogen and oxygen over the transition metal surfaces [13].

The further refinement of the effective medium theory by Norskov and coworkers leads to a simple yet powerful theory, the d-band model [14‐16], for understanding the variations of chemisorptions energy from one to another metal, from one surface structure to another on the same metal. In the d-band model, the adsorption energy is given by [63]where ΔE ₀ is the bond energy contribution from the free-electron-like sp electrons and ΔE _d is the contribution from the extra interaction with the transition metal d electrons. It is assumed that ΔE ₀ is independent of the metal. ΔE _d can be calculated by the News-Anderson model aswhere the first term is the Pauli repulsion between the adsorbate states and the metal d states, which is proportional to |V _ad |², the square of the coupling matrix element between the adsorbate states and the metal d states. The second term is the attraction contribution from the hybridization of the adsorbate states and the metal d states. The hybridization leads to a bonding orbital below the Fermi level and an antibonding orbital close to the Fermi level as shown in Fig. 13. Just like the situation in the chemical bonding between two atoms, the strength of the surface chemical bond is determined by the occupancy of the antibonding orbital. The number of electrons in the antibonding orbital is approximately equal to the initial filling of the d band of the free metal surface. ɛ _d and ɛ _a are the energy at the center of the metal d band and the adsorbate states, respectively.

When comparing the chemisorptions energies of a given molecule on different metals, the d-band model suggests that the adsorption energy variations are mainly due to the changes of V _ad and ɛ _d . Figure 14 shows variations of the O adsorption energy over the 4d transition metals [16]. The results of the simple d band model are in good agreement with that from the full DFT calculations and the experiments. It also shows that the adsorption energy increases as the d band center shifts up to the Fermi level and the d band becomes less filled.

It was observed experimentally that the adsorbed atoms and molecules have higher heats of adsorption at defect sites such as the steps and kinks on the surface [64] (Fig. 15a). The calculations by DFT show that the d band centers at the defect sites shift up relative to the sites on the flat surface, which leads to the increase of the adsorption energy [65] (Fig. 15b). Using the same argument, the d band model has been applied to explain and predict the alloying effect on the chemisorptions observed in the experiment. The examples shown in Figs. 14 and 15 clearly demonstrate that the simple d-band model captures the main factors that determine the chemisorption energies of atoms and small molecules on the transition metal surfaces.

For more complex chemisorption systems in which adsorbates can form multiple bonds with several surface atoms, a scaling relation has been proposed recently based on extensive DFT calculations of adsorption energies of CH _x species on the metal surfaces [66]. Figure 16 shows that, for a given x, the adsorption energies of CH _x on different metal surfaces is scaled almost linearly with the atomic adsorption energies of carbon, which implies a scaling relationhere γ(x) and ξ are fitting constants. From the fitting constants shown in Fig. 16, we can further see that the values of γ(x) is very close to that predicted byhere x _max for carbon atom is 4, that is the maximum number of bonds carbon can form with the surface atoms. This scaling relation, which has been also observed in several other chemisorptions systems [19], provides a semi-quantitative method to predict the adsorption energies of complex adsorbates from the simple calculation of atomic adsorption energy.

Heterogeneous catalytic reactions involve elementary processes: adsorption and dissociation of reactants from the gas phase, diffusion of surface species, surface reactions to form surface intermediates and products, and desorption of products into the gas phase. The ultimate goal of surface science research is to obtain the molecular level details of these elementary processes, and to control reactivity and selectivity of catalytic reactions by using the obtained molecular level knowledge. Apparently, neither experimental study nor theoretical study can fulfill this endeavor alone. The capability of experimental study is always limited by the spatial, time, and energy resolutions achievable by experimental techniques. For example, monitoring the surface intermediates during catalytic hydrocarbon conversion under the realistic reaction conditions has been proved to be extremely difficult; on the theoretical side, theoretical model usually tends to oversimplify the local chemical environment in which the elementary reaction processes take place. The complexity of the local chemical environment includes the coadsorption of surface species and their coverages on the catalyst surface, the distribution of active surface sites, etc. Therefore, combining experimental and theoretical approaches is a must in the molecular level study of catalytic reactions.

A recent study of ammonia synthesis over a ruthenium nanoparticle catalyst by Norskov and coworkers demonstrated how the theoretical modeling and experimental techniques can complement each other to achieve the molecular level understanding of this simplest catalytic reaction under industrially relevant reaction conditions [67, 68]. In this study, the potential energy diagram for the full reaction was constructed based DFT calculations. The activation barriers for the reactions taking place on the terrace site and the step site were compared (Fig. 17). It was shown that the dissociation of nitrogen (the rate limiting step) on the step site has a much lower activation barrier than that on the terrace site. The step site is the active site for this reaction. The potential energy diagram also provided all necessary information to calculate the rates of the individual elementary steps in the catalytic reaction by the micro-kinetic model. In the calculations of the dissociative adsorption rate of N₂, the coadsorption effect was also considered by investigating the activation energy changes induced by coadsorption of atomic nitrogen or hydrogen. In parallel to the theoretical study, the ruthenium nanoparticle catalyst was synthesized and the particle size distribution and the surface morphology of nanoparticles were investigated by transmission electron microscopy (TEM) experiment (Fig. 18a, b). Based on the TEM results, the number of active sites per gram of catalyst can be estimated. Using the experimentally obtained active site concentration, the NH₃ productivity from a plug flow reactor loaded a catalyst containing 0.2 g of the 11.1% Ru/MagAl₂O₄ catalyst was calculated under realistic reaction conditions. The agreement between experimental and theoretical results shown in Fig. 18c is surprisingly well considering the complexity of the catalytic reaction over the nanoparticle catalyst.

The success of this study also gives hope to develop theoretical computer-based method into a indispensable tool in rational design of catalyst. One of major bottlenecks for the computational study of reactivity and selectivity in heterogeneous catalysis is identifying the transition states of surface reactions and computing the activation energies. Fortunately, there are some empirical relations correlating the activation energy and reactivity with the chemisorption energy of reactants. One of them, the Brønsted–Evans–Polanyi (BEP) relation [69‐72], states that the activation energy for an elementary reaction step on surface depends linearly on the reaction energy, that is, the difference between the chemisorption energy of the products and the reactants. An example [72] for the activation energies for N₂ dissociation over various metal surfaces are shown in Fig. 19a. Another relation is the famous principle of Sabatier [73]: the best catalyst is one that binds the intermediates not too strongly and not too weakly. Figure 19b shows how the rates of ammonia synthesis depends on the nitrogen chemisorption energies on various metal surfaces [74]. These relations offer an efficient way to estimate the activation energy and the reactivity using the chemisorption energies of the reactants and products, since the chemisorptions energies can be computed efficiently by the d-band model as we discussed in the previous section. With the help of these relations and the chemisorption model, catalytic properties of alloy combinations can be investigated computationally in the search for the low-cost yet highly activity and selective catalysts [27, 74‐79].

We have shown, by examples, the importance of experiment-and-theory-combined approaches in the development of experimental techniques in surface science, resolving the surface structures, and studying chemisorption and catalytic reactions. The contributions by Prof. Norskov and coworkers to the chemisorption theory and the computer-based catalyst design have been highlighted with emphasizing their deep appreciation of experimental developments and their extensive collaboration with experimentalists in the effort to achieve the molecular level understanding of complex catalytic processes.

The major challenges of surface science in the twenty-first century are to explore the unique physical and chemical properties of nanomaterials, and to design new generation of catalytic processes with high reactivity and selectivity. To face these challenges, experimentalists and theorists have to come together, and be aware of the advantages and the disadvantages of each others’ techniques. Here we finish our paper with three interesting problems raised in the study of the nanostructured surfaces and catalytic reactivity and selectivity. These problems need attentions from both experimentalists and theorists.

The first problem is regarding SFG vibrational spectroscopy, a prime in situ technique to monitor the orientation and ordering of adsorbates. Recently, a number of studies have applied this technique to the nanostructured surfaces [80‐82]. A general observation in these studies is the reduction of the sum frequency signal due to the nanometer scale corrugation on sample surfaces. Moreover, the surface corrugation also makes it difficult to derive the adsorbate orientation from the SFG measurements with different polarization combinations, since the common SFG theory was initially developed for the flat surfaces [83]. Apparently, further experimental and theoretical development of the SFG technique is needed to improve its sensitivity in the nanomaterial studies.

The second problem is concerning the synthesis of alloy catalysts. At present, the computer-based method is capable to perform large scale screening of alloy catalysts for important catalytic reactions [78, 79]. However, the proposed alloy catalysts are not necessarily stable under harsh reaction conditions, especially, when these catalysts are in the form of nanoparticles. On the one hand, in order to optimize the reactivity and selectivity of alloy nanoparticle, certain surface composition is usually required [22, 27, 75]. On the other hand, the surface composition of alloy nanoparticles may change dramatically with the reaction conditions as shown by an ambient pressure XPS study on bimetallic nanoparticles carried out recently at Berkeley [84]. Therefore, the development of new synthesis schemes for producing alloy catalysts with relatively stable surface composition is extremely important to the rational design of catalyst.

Finally, as a third example of the challenges in catalysis science, obtaining information about the nature and conversion of surface reaction intermediates is the key to understanding the selectivity of complex catalytic reactions [85‐87]. Performing in situ spectroscopy techniques such as polarization-modulated reflection–absorption infrared spectroscopy (PM RAIRS) and SFG under reaction conditions usually results in complex spectra [81, 88‐91]. The development of reliable theoretical methods for predicting the vibrational frequencies of surface intermediates will provide tremendous help in the spectrum interpretation and in determining the coverages of the reaction intermediates that may adsorbed simultaneously on the catalyst surface [92, 93].