SciDAC Review - NANOSCALE MATERIALS: Recent Trends in Computational CATALYSIS

NANOSCALE MATERIALS

Recent Trends in Computational CATALYSIS

The past twenty years have brought incredible expansion of capabilities and possibilities to all aspects of computing, and the computational catalysis field is no exception. Electronic structure calculations are now readily used to provide computational insight into the chemical and physical processes that determine the properties of different types of catalysts.

Important advances in both physical simulation algorithms and the development of massively parallel computers have greatly expanded the classes of catalytic problems that can be treated with electronic structure-based approaches. Researchers at Argonne National Laboratory (ANL) are developing efficient catalytic processes and are tackling questions of energy production, usage, and security. ANL's emphasis is on both the physical/chemical nature of the problems, as well as the computational software and hardware deployed.

As a field, catalysis spans a significant range of length scales—catalysts can be composed of anything from single metal atoms surrounded by organic ligands (homogeneous catalysts), to clusters of a few dozen metal, oxide, carbide, or nitride atoms (subnanometer heterogeneous catalysts), to metal particles of up to 10 nm or more in diameter (nanoparticle heterogeneous catalysts). Subnanometer and heterogeneous catalysts are generally supported on other complex materials (figure 1), and this adds complexity. Although the support generally plays a secondary role in the catalytic chemistry, the choice of this material, in some cases, can affect the course of the reactions.

Researchers at Argonne National Laboratory are developing efficient catalytic processes and are tackling questions of energy production, usage, and security.

Source: F. Mehmood, ANL

Figure 1. Methanol reacting on a subnanometer platinum cluster (light gray spheres) supported on an alumina substrate. Aluminum atoms are dark gray, oxygen is red, carbon is yellow, and hydrogen is light blue.

Each class of catalysts has unique properties that are useful in different situations. Homogeneous catalysts (which are not treated extensively herein) can demonstrate a remarkable ability to tune product distributions to favor desired reaction products (they are very selective; sidebar "General Principles of Catalysis," p50). They may also show a variety of other unique catalytic properties stemming from the molecular-like nature of the catalysts' electronic orbitals. The drawback of this class of catalysts is they cannot be easily immobilized, and therefore they require sophisticated processing technologies to function efficiently.

Computer codes are providing new opportunities for exploring and understanding the catalytic properties of clusters and particles. New computer hardware is also advancing computational catalysis.

Heterogeneous catalysts, on the other hand, have traditionally shown less selectivity, but they are easy to synthesize and process, and are extremely robust under a variety of reaction conditions. Subnanometer heterogeneous catalysts have only recently been reliably and reproducibly synthesized. These catalysts, therefore, have not yet received extensive attention but hold forth the tantalizing prospect of combining the advantages of homogeneous and heterogeneous catalysts.

Computational catalysis efforts have historically focused on the study of both homogeneous catalysts and single crystal catalysts (the latter structures serve as simplified models for the surface geometries of large nanoparticles). Both classes of systems are readily treated with existing computational approaches and are highly relevant to experimentally studied catalysts. Less attention has been paid, however, to the computational study of subnanometer clusters on support materials (primarily because of the lack of suitable experimental data to which to compare the computational results) or to the explicit, electronic structure-based simulation of large, heterogeneous catalytic nanoparticles (due to the lack of suitable hardware and software to perform the calculations).

Current Computational Resources
Computer codes are providing new opportunities for exploring and understanding the catalytic properties of clusters and particles ranging from a single atom to nanoparticles of 3-6 nm in size. Most existing codes employ, in some form, the Kohn-Sham formulation of density functional theory (DFT; sidebars "Quantum Chemical Methods for Energy Predictions," p51, and "Density Functional Theory," p52). This approach provides a reasonably reliable and computationally feasible methodology of calculating energies and barriers for reactions occurring on a variety of catalytic sites. In addition, DFT provides information on the electronic structures, wave functions, charge distributions, and spectroscopic characteristics of catalysts.

A variety of DFT-based codes is employed, including VASP, Dacapo, CASTEP, Car-Parrinello, CRYSTAL, Gaussian, Jaguar, and others. Each code employs different basis sets, boundary conditions, and density functionals, and each finds a niche in particular types of catalytic problems. In some cases, molecular dynamics functionalities are also incorporated into the codes, either through ab initio MD methods (for example, Car-Parrinello) or through approximate, reactive forcefields.

New computer hardware is also advancing computational catalysis. Numerous researchers employ home-built Beowulf clusters, and high-performance computing clusters at DOE facilities—such as Environmental Molecular Sciences Laboratory (Pacific Northwest National Laboratory), National Energy Research Scientific Computing Center (NERSC, at Lawrence Berkeley National Laboratory), and Blue Gene (ANL; Oak Ridge National Laboratory)—provide the necessary hardware to expand computational studies. Indeed, the dramatic rise in computing power, which will reach petaflop-scale in the next few years and exascale beyond that, will provide researchers in the near future with the unprecedented capabilities to study the catalytic properties of clusters and nanoparticles.

Subnanometer Heterogeneous Catalysis
Metal clusters of less than one nanometer in diameter have, until recently, been difficult to synthesize in a reliable and reproducible manner. Recent advances in synthetic techniques, however, have begun to overcome these problems, and subnanometer clusters are emerging as objects of intense interest in both the experimental and computational catalysis communities.

The clusters are known to possess reactivity properties not observed in their bulk analogs, which makes them attractive candidates for use as novel catalytic materials. The distinct catalytic properties of the clusters are often hypothesized to result from their unique geometric and electronic characteristics, such as the presence of a high density of highly under-coordinated surface atoms. These under-coordinated atoms, in turn, are expected to possess unique capabilities for bond breaking and bond formation.

Given their relatively small size, subnanometer clusters are readily treated with DFT-based computational approaches. Such approaches can provide detailed information about the cluster morphologies and the reactivity properties of individual atomic features on the clusters. This information would be extremely difficult to obtain by purely experimental methods, and as such, the calculations provide a powerful complement to the experimental studies. For example, bonds between carbon and hydrogen are extremely stable and difficult to break in chemical reactions. However, recent computational investigations of the reaction energies and barriers of alkanes adsorbed on metal atom clusters have found that certain very small clusters (containing only four to eight metal atoms) have very small barriers to breaking carbon-hydrogen bonds compared to much larger barriers for the bulk metals. The computations indicate this is because the under-coordinated atoms in the clusters strongly attract electrons from the bond, which thereby weakens the bonds. These results, in turn, suggest subnanometer metal clusters may be highly active for reactions involving small alkanes and alcohols (figure 1, p49). Indeed, these predictions are completely consistent with recent experimental results that show a very high activity of Pt_8-10 clusters for carbon-hydrogen bond cleavage.

The dramatic rise in computing power, which will reach petaflop-scale in the next few years and exascale beyond that, will provide researchers in the near future with the unprecedented capabilities to study the catalytic properties of clusters and nanoparticles.

Electrocatalysis on Subnanometer Clusters
Nanometer- and subnanometer-sized clusters can also show unique reactivity properties in electrocatalytic environments (sidebar "Electrocatalysis"). For a critical reaction of interest in the anodes of fuel cells, carbon monoxide (CO) electro-oxidation, these clusters can show substantially higher intrinsic activity than either smooth or stepped metal electrode surfaces. However, as with the propane/platinum subnanometer clusters described above, the experimental results alone do not provide a molecular-level explanation for the remarkable properties the electrocatalytic clusters display. To develop such an explanation, computational catalytic studies can be of great use.

DFT calculations were used to estimate the energetics of the reactants and products associated with the key elementary steps in this reaction network. Estimates of the relative rates of CO electro-oxidation on various geometrical features were obtained by performing these calculations on subnanometer clusters supported by metal substrates, single crystal models of electrode steps, and perfect single crystal terraces. More significantly, molecular-level explanations for the differences in activity were derived.

CO functions as both a reactant and a poison for this reaction. If the CO is bound too strongly to the surface, it will impede the adsorption of OH (the other key reactant) and will inhibit further reaction. The calculations indicate multiple CO molecules can adsorb on highly under-coordinated atoms on the subnanometer clusters. This high coverage of CO effectively repels neighboring CO molecules and makes them easier to remove from the surface, thus reducing the poisoning effect. On the other hand, the calculations also show hydroxyl (OH) groups, a key intermediate in the reaction, are significantly stabilized on the highly under-coordinated adsorption sites present on the subnanometer clusters, and the geometry of the adsorbed OH is such that it can interact naturally with surrounding water molecules and be stabilized by the associated hydrogen bonding (figure 5). The net result of these two effects is higher CO electro-oxidation activity on the clusters than on steps, terraces, or other surface features.

Source: J. Greeley, ANL

Figure 5. Reaction of carbon monoxide and hydroxyl groups on Pt(111)-supported platinum adatoms. The adatom is shaded dark gray, and the other platinum atoms are light gray. Oxygen is red, carbon is black, and hydrogen is white.

Heterogeneous Catalysis: Single Crystals and Large Nanoparticles
Although the scientific possibilities associated with subnanometer heterogeneous catalysis are very promising, heterogeneous catalysts employing larger nanoparticles remain a crucial and indispensable component of this field. Recent computational efforts in this area have been very fruitful and have added an important new dimension to the understanding of heterogeneous catalysis on nanoparticles.

In particular, periodic DFT codes have permitted the accurate calculation of binding energies, activation barriers, and other key catalytic parameters on a large number of single crystal metal and oxide surfaces. These approaches have been instrumental in elucidating the atomic-scale chemistry and physics that govern the macroscopic properties of single crystal heterogeneous catalysts. Further, by supplementing these calculations with thermodynamic techniques and the Wulff construction (sidebar "Wulff Construction"), it has been possible to extrapolate the behavior of large nanoparticles from the calculated behavior of single crystal facets.

Once catalytic properties have been calculated on various single crystal facets of a given metal or alloy, the Wulff construction can be used to effectively combine these results to build a picture of the catalytic properties of more complex nanoparticles, including the effect of catalyst supports on the reaction chemistry (sidebar "Catalyst Supports," p54). In addition, for smaller particles, energy contributions of edges and even corners become non-negligible and introduce a dependence of particle shape on the particle size. Therefore, such approaches can ultimately yield, for example, ab initio predictions of the catalytic properties of metal nanoparticles as a function of the nanoparticles' size. A recent example of such a prediction, in this case for the oxygen reduction reaction, is shown in figure 7 (p54).

Illustration: A. Tovey; Source: J. Rossmeisl

Figure 7. Calculated reaction rate (TOF) of the Oxygen Reduction Reaction (ORR) on platinum and gold nanoparticles as a function of particle size. The rates are normalized to the calculated rate on a Pt(111) single crystal surface.

Heterogeneous Catalysis—Electrocatalysis
In addition to their longstanding applications to traditional heterogeneous catalysis, highly parallelized electronic structure calculations are being increasingly applied to the study of complex electrocatalytic phenomena. While traditional electronic structure/DFT calculations are not naturally applicable to problems of constant electrode potential, as is found in electrochemistry, various techniques have been recently developed to straightforwardly extrapolate electrochemical environments from standard electronic structure calculations. One particularly simple approach is based on the concept of the "theoretical standard hydrogen electrode." This scheme is used to determine the potential dependence of the free energies of elementary reaction steps involving transfer of protons and electrons. The potential energy change of proton/electron transfer reactions of the type

A→B+H⁺+e^-

is evaluated by replacing the proton/electron pair with half of an H₂ molecule; the energies are then straightforwardly calculated with standard DFT or other electronic structure techniques (to estimate the effect of the aqueous environment on these values, water molecules may be explicitly added to the simulation cell). Simple entropy corrections are then added to get the free energy change of the reaction. The resulting free energy change corresponds to the situation of zero potential on the standard hydrogen electrode scale. To determine how the free energy changes with potential, the potential multiplied by the number of transferred proton/electron pairs is simply subtracted.

The strategy described above is quite powerful in its scope, as it rapidly deploys to electrochemical problems the theoretical and computational approaches that have been developed for traditional heterogeneous catalysis over the past 15 years. Computational approaches can, thus, be used to provide molecular-level insight into catalytic chemistry on metals and other materials in electrochemical environments in much the same way such insight has been obtained in traditional catalytic systems.

For example, the oxygen reduction reaction, an electrochemical reaction essential for the operation of low-temperature fuel cells, has recently been studied using DFT calculations on single crystal surfaces. By calculating the free energies changes for all elementary steps associated with this reaction on metal surfaces for a large number of different elements, a classic volcano plot (sidebar "Volcano Plots") was developed for the reaction. The predictions of the relative catalytic activities of different platinum alloys determined from this volcano plot were subsequently shown to match extremely well with careful experimental measurements. This close match between predicted rates from computational electrocatalytic theory and experimental results suggests, in turn, that computational techniques might be well-suited to screening and design of new alloys for applications in catalysis.

Screening Techniques
Electronic structure-based computational techniques are being increasingly applied to the prediction of novel catalyst properties. The ultimate goal of these predictive efforts is to screen for and design new catalysts for desired reactions of interest. These types of computationally based evaluations can generally be done at a fraction of the cost of analogous experimental screening.

Computational catalyst screening is completely dependent upon modern, high-performance computers. For a screening effort to be successful, it is typically necessary to evaluate the catalytic properties of hundreds of transition metal alloys, oxides, or other catalytic materials. Such evaluations can only be performed if reliable access to high-performance computing systems, such as the new 100 TF Blue Gene/P at the Argonne Leadership Computer Facility, are available.

The basic computational screening procedure is straightforward. First, simple descriptors (catalytic parameters that can be straightforwardly determined with DFT or other electronic-structure methods) are identified for the reactions or processes of interest. These descriptors should, with the aid of simple thermodynamic or kinetic analyses, including the famous volcano plot (sidebar "Volcano Plots"), be able to predict trends in the activity and selectivity of catalysts with a reasonable degree of accuracy.

The ultimate goal of these predictive efforts is to screen for and design new catalysts for desired reactions of interest. These types of computationally based evaluations can generally be done at a fraction of the cost of analogous experimental screening.

The value of these descriptors is then determined on a large search space of possible materials. DFT simulations and correlations between variables in pre-existing computational databases are used to calculate these descriptor values. The most interesting materials for the reaction or process of interest (that is, the materials with descriptor values that lead to optimal properties) are then identified. The stability and durability of these materials in practical reactive environments toward surface segregation, islanding, and dissolution are then assessed. Finally, the most promising catalysts are tested experimentally. This approach can be thought of as a "catalyst filtering" process (sidebar "Materials Filtering," p56), and the end result is the identification of a limited pool of candidate catalysts that are predicted to have excellent properties.

This approach has been used successfully to identify improved catalysts for a limited number of reactions in heterogeneous catalysis and electrocatalysis. Recently, more than 700 bimetallic alloys were evaluated with a computational catalytic screening procedure as candidates for hydrogen evolution catalysts (a reaction of interest in the production of hydrogen from acids and in reversible, low-temperature fuel cells). From this large pool of candidate alloys, a few were identified as suitable for experimental testing, and one such alloy was subsequently shown to have superior experimental performance to pure platinum, the canonical catalyst used in this reaction (figure 10, p57).

Illustration: A. Tovey; Source: J. Greeley, ANL

Figure 10. Computational combinatorial screening results for the Hydrogen Evolution Reaction (HER). Each circle represents a binary surface alloy. The color of the circle denotes the free energy of hydrogen adsorption on the alloy, |ΔG_H|, as calculated by DFT. Lighter colors indicate higher predicted catalytic activity for the HER.

Although computational catalytic design efforts have already been proven to be successful, these efforts could be enhanced by generating and organizing large databases of physical and chemical property data. A "materials design workbench" could be created based on a repository of data generated from accurate electronic structure calculations. Using a mix of artificial intelligence and computer science methods, the workbench would guide users to identify candidate materials—and perhaps, by extrapolation, aid in the proposal of novel candidates that may not have been computationally analyzed.

Using a mix of artificial intelligence and computer science methods, the workbench would guide users to identify candidate materials--and perhaps, by extrapolation, aid in the proposal of novel candidates that may not have been computationally analyzed.

The application of the concept of computational design to new subnanometer catalytic materials will also be very fruitful. The clusters and nanoparticles have a wide range of compositions but are of small enough size so that current and near-future computer capabilities should be adequate for making significant progress in materials by design.

Scaling to Larger Systems
Today's electronic structure methodologies are well-suited to treating systems with a limited number of atoms and electrons. However, the computational cost of electronic structure calculations increases rapidly with system size, which then requires prohibitively long run times. One solution to this problem is, in principle, quite straightforward: simply run the calculations on more processors. However, most electronic structure codes generally do not parallelize well beyond O(100) processors, and fundamentally new codes and algorithms are needed to take full advantage of the processing power of petaflop-scale machines.

Efforts are currently under way to develop DFT-based electronic structure codes capable of parallelizing efficiently out to thousands of processors. Such codes could perform realistic catalytic simulations on nanoparticles with at least 1,000 metal atoms. Entirely new possibilities may then be revealed for both the computational understanding of heterogeneous catalysis and the design of novel catalytic nanoparticles.

Gpaw is a new real-space, projector augmented wave-based DFT code being developed to overcome the limitations described above. Initially developed in Professor Jens Nørskov's group at the Technical University of Denmark, the code represents a very efficient implementation of DFT. The code's projector augmented wave formalism represents one of the most efficient extant approaches for treating systems with large numbers of core electrons. In addition, the real-space algorithm at the heart of the code is inherently more parallelizable than DFT codes that employ basis functions, and encouraging preliminary results about Gpaw's scalability to large numbers of processors have already been obtained. A collaboration between the Technical University and several Argonne divisions has further optimized the code to make it suitable for use on systems of Blue Gene scale. Successful completion of this work should yield a code that can efficiently and accurately treat catalytic particles up to 3-4 nm in diameter and will represent a breakthrough in computational catalytic science.

The tremendous progress in recent years on computational catalysis results from the advanced computational hardware at numerous supercomputing centers around the world.

Summary
The tremendous progress in recent years on computational catalysis results from the advanced computational hardware at numerous supercomputing centers around the world. This research provides important insights into the physical and chemical phenomena that underlie homogeneous and heterogeneous catalysis. This progress continues, and new efforts to extend traditional single crystal catalytic modeling to subnanometer metal clusters, electrochemical systems, and very large—O(1,000) atoms—metal nanoparticles, together with new initiatives in computational catalytic screening and design, are under way. The combination of such diverse areas of inquiry within a single field should ensure its growth and relevance for many years to come.

Contributors: Jeff Greeley, Peter Zapol, and Larry Curtiss, Argonne National Laboratory.