Molecular simulations in heterogeneous catalysis

Molecular simulation is contributing to many facets of the catalyst industry. Here we discuss the role of model-based optimization in heterogeneous catalyst research and development.

Clive M. Freeman
George Fitzgerald
Dominic King-Smith
John M. Newsam

Catalysis is a molecular-level phenomenon. Although the commercial value of molecules produced catalytically is immense, our perspective of the molecular-level details of catalysis is often fragmented. Ambiguities exist even for homogeneous catalyst centers, such as the single-site polyolefin catalysts, which have been well-defined at the molecular level but are complicated by solvation effects and cocatalysts that are less understood. Despite such difficulties, molecular simulation has a valuable role in increasing our knowledge and ability to optimize such systems (1-5).

The need for simulation is particularly acute for heterogeneous catalysts. Experimental characterization of active sites is challenging, and it is rarely possible to perform discrete, systematic adjustments of the active site to probe the influence of discrete variations on performance. Simulation allows specific questions to be asked and can focus costly experimental work on solving particular problems.

Empirical screening in the discovery and development of new catalysts and their formulations is a rich source of experimental information with which to validate molecular models. Molecular simulation provides a framework whereby chemical data can be structured, used to build chemical knowledge, and predict behavior. The recent confluent evolution of modeling and database technologies in the pharmaceutical industry suggests that similar synergistic interactions can be anticipated in heterogeneous catalysis (6).

Methods of molecular simulation
Four main families of methods make up the standard toolkit of molecular simulation (see Figure 1). Each of these methods relies on the infrastructure of the modeling environment, which includes structural libraries and capabilities for building, editing, analyzing, and visualizing. The methods serve as engines accessed via a graphical user interface.

Quantum methods are used to compute interactions at the electron and nuclear levels. Traditional Hartree-Fock procedures construct a molecular wave function from individual atomic orbitals and compute the potential energy that arises from the nuclear attraction and the average electronic repulsion from other electrons in their approximate orbitals. Post-Hartree-Fock procedures add varying treatments of electron correlation beyond this mean-field approximation.

Density functional theory provides a computationally attractive method for studying catalysis. This approach introduces approximate functionals to describe exchange and correlation. For example, density functionals can be derived from the properties of uniform electron gas. The resulting local density approximation method is particularly effective in treating heterogeneous catalyst systems. Several forms of higher order correction, nonlocal functionals, or generalized gradient approximation methods have been developed which extend the applications of the method. Quantum methods yield information on chemical structure, energetics, and reactivity (7, 8).

Molecular mechanics methods are used to parameterize analytical expressions that describe the interaction between atoms. These analytical expressions, called force fields or interatomic potentials, have differing forms, depending on the nature of the bonding in the system being studied. Molecular species are described by an expression that includes bond stretches, bond angle bends, and torsional terms. The terms are augmented by Coulomb (charge-charge) interactions and the nonbonded dispersive attractive and overlap repulsive terms described by a Lennard-Jones or similar potential. Various simulation drivers use the energy and derivatives of the atomic coordinates to locate energy minima, evaluate configuration integrals, or perform dynamical simulations. Molecular mechanics methods include tools such as docking, molecular similarity searching, and de novo structure design. Molecular mechanics methods provide energetic and structural information.

Statistical methods are used to accumulate averages for thermodynamic parameters, develop averaged descriptions of disordered systems, and develop structure-activity relationships. Macroscopic properties, although governed by molecular-level behavior, are often not amenable to direct calculation by quantum or molecular mechanics methods. In such cases, quantum or molecular mechanics methods can be used to compute atomic-level attributes or "descriptors" for a family of materials for which experimental data have been measured. Statistical tools, such as partial least squares, neural network, or genetic algorithms, can then be used to develop a correlative framework that relates determining atomic-level descriptors to macroscopic properties. Once validated, this framework can be applied to predict properties for comparable systems. Statistical methods are also being applied in the design and analysis of combinatorial libraries of materials as a component of high-throughput experimentation (HTE) (9).

Analytical methods are used to compute a variety of scattering and spectroscopic data based on atomic- or molecular-level models. Analytical data fingerprints can be computed on the basis of atomic models, in the form of simulated single crystal, powder, or fiber diffraction patterns for X-ray, neutron, or electron radiation; wide angle X-ray and neutron scattering; small angle scattering; infrared spectroscopy; high-resolution transmission electron micrographs; particle morphologies (as measured by scanning electron microscopy); NMR; extended X-ray absorption fine structure (EXAFS); and temperature-programmed desorption (TPD) data. These methods are also being applied in the process of structure solution and structure refinement based on experimental diffraction data. Such methods are useful in the direct determination of atomic- and molecular-level models from their analytical fingerprints.

The modeling environment that links these simulation methods supplies a toolkit of common capabilities that permit, for example, the construction of models, comparison of calculated and observed properties, and iterative adjustment to maximize agreement. Crystallographic capabilities provide a route to structural knowledge for materials such as the large-pore zeolite material UTD-1 (10, 11). Advancing structural knowledge for a given catalyst system makes it possible to apply increasingly sophisticated modeling methods (Figure 2); and at each stage in advancing structural knowledge, simulation provides valuable information and insights.

Application framework
Because each catalyst research problem is unique, a broad suite of methods is needed. The appropriateness of a selected method is dependent on the nature of the system, its parameters and conditions. A sensible objective is to solve the problem by the simplest and most expeditious simulation route possible. There is value in having access to a simple discrete calculation; however, such value is typically small compared with the benefits of an integrated approach to the problem.

Many of the methods in the four simulation families have a long history of validation. The literature details the corresponding theory and numerical formalisms and typically includes a large number of exemplary applications of a given method to a variety of problem types (12). This validation is cumulative and expands steadily as new reports of successful or innovative applications are published.

In addition to the scientific methods, various software engineering aspects are important. The methods of simulation must be integrated smoothly with transparent data interchange. The methods must be robust and efficient in terms of CPU throughput, memory, and storage requirements. Ideally, they should be configured and executed from a streamlined interface and coupled closely with dynamic graphical displays of structures, simulation processes, analytical data, and results. Another requirement is that the simulation infrastructure be integrated with a laboratory's information and knowledge management system.

Advances in computational hardware technology have fostered continuous improvements in application methods and allow for more "brute force" calculations. These improvements make it possible to study larger and more complex systems and require less time to achieve simulation results. However, this increased opportunity for brute force calculations by no means obviates the requirements of a carefully selected simulation strategy and validation plan.

A systematic approach
A key advantage of simulation is that it permits well-defined, discrete questions to be addressed. Molecular simulation is applied to two classes of research. In the first, a general material or process research domain is defined, but without a clearly articulated goal. For example, a researcher might be interested in a better understanding of a selective oxidation catalyst as a means of enriching our knowledge base or defining possible development opportunities.

In the second (and more frequently encountered) class, a target is articulated, and a structured approach to applying simulation begins with a simple, lucid statement of the goal. The subsequent step, and probably the most crucial to the success of the effort, is the problem analysis, which is conveniently approached by developing a full set of "Is it ...?" type questions that span all of the pertinent issues. This analysis has input from all of the perspectives on the problem, bringing synthesis, characterization, screening, simulation, and possibly also other expertise to bear.

In a given case, several of the initial "Is it ...?" questions will need to be resolved by experiment; several, though, usually can be answered via molecular simulation. For each of these latter questions, the next step in a simulation strategy is to establish a validation plan, execute the simulations themselves, and analyze and collate the results. The subsequent step is either the practical implementation or testing of these conclusions, the full process usually being iterative. As the experiment goes through successive cycles, the "Is it ...?" questions can be better phrased and the simulation protocols consequently better focused. The key steps in the systematic application of simulation to problems in catalysis and the responsibility for each step are summarized in Figure 3. The indicated roles may be provided by one or more individuals.

This general framework was originally developed by the Catalysis and Sorption Consortium, which comprises commercial, academic, and nonprofit organizations dedicated to the development and validation of scientific tools for the solution of problems in catalysis and sorption. The consortium has been a useful vehicle for implementing innovative, problem-focused methods and accumulating experience on how best to use simulation as an integral element of a total catalyst R&D project. Often, a particular combination of methods or a new approach is necessary to tackle a specific problem case. Being able first to implement such a capability in prototype form and test it against the specific target example enables its full implementation as a general-purpose capability. There are many examples of this interactive process, some of which are set out in the Examples of molecular simulation. Other examples can be found at http://www.msi.com/science/online/references.

Areas of recent progress
Scientific, algorithmic, and computational developments have made first principles quantum methods increasingly practical for comparatively large (~100 atoms) systems (33-35). Although such methods are computationally demanding, their use of quantum mechanics rather than parameterization is a particular strength.

The molecular mechanics simulation of large systems extended over time is enhanced by the use of quantum methods to tune the parameterizations. Long time-scale, high-accuracy simulation for the products of catalyzed polymerization, for example, combines extensive thermodynamic simulation with parameters that reproduce the quantum mechanically derived energy surface of component molecules (36, 37). The Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field and parameter set developed by Molecular Simulations Inc.'s polymer consortium was derived in this manner (37).

Although computational methods are generally applicable to catalytic systems, tuning may be required for specific problems or for high-throughput applications such as the methods used to locate extra-framework cations in microporous materials (23). First-generation protocols required protracted computation times for typical system sizes; however, algorithmic enhancements, using grid-based energy evaluations in place of brute force summations, have increased significantly the range and scope of simulation applicability (39, 40).

Looking forward
Several simulation techniques now being pioneered will enrich the catalyst simulation field. Interesting developments include improved interatomic potentials for organic-inorganic interactions, techniques for computing the diffusivities of slowly moving molecules, and new routes to structure solutions from analytical diffraction data. It is also clear that accelerated quantum methods at the semiempirical and first-principles levels (including order N methods), first-principles molecular dynamics, and improved quantum mechanical embedding methods will also benefit catalyst studies. Over the next five years, significant progress will likely emerge from the intelligent application of molecular simulation technology, much of which is in hand now.

A set of new requirements is presented by combinatorial or high-throughput experimentation methods for catalyst R&D (9). The enumeration of possible molecular configurations, prior to library synthesis, is commonplace in pharmaceutical research. Although the extent of compound libraries can be large, the potential design landscape is essentially boundless, and practical efficiency dictates that libraries be efficiently subdivided. Chemical principles and synthesis constraints are therefore applied in library design. Currently, molecular simulation methods are used for virtual screening before more costly experimental activities are pursued (Figure 6). High-throughput experimentation will increasingly draw upon such computational schemes.

In catalysis, bridging the time and length scales is primarily an issue associated with total behavior within a catalyst pellet or the mechanical performance of such a composite (41). Catalyst problems are often approached from a systems perspective. The overall performance of a catalyst reflects the combination of discrete properties that results from synthesis and processing conditions at the atomic and molecular levels. Rather than considering each of these domains independently, a systems view considers their relationships and attempts to map the desired performance characteristics through defined properties and necessary structural elements to the required synthesis and processing conditions.

At some point, with an appropriate knowledge base and simulations framework in place, we will be able to directly design full-scale plants without the need for intermediate scale-up stages. This scenario will be possible only when chemistry and engineering elements are combined, requiring the appropriate integration between molecular-level and macroscopic-level simulation. The impact of molecular simulation as a technology thus far is modest relative to its ultimate potential.

The four main families of molecular simulation methods (quantum, molecular, statistical, and analytical) all have value in the discovery and development of homogeneous and heterogeneous catalysts. The benefits of a broad suite of methods arising from the diversity of issues in a given stage can be seen in the breadth of applications that have appeared in the open or patent literature. There are significant opportunities for developing and integrating novel and innovative simulation methods into a catalyst system. Much of the progress expected in the next few years will arise from the methodical and structured application of simulation technology that is available today.

Acknowledgments
The MSI Catalysis and Sorption Consortium is sponsored by several industrial, governmental, and academic groups. The approach to problem tackling, many of the ideas for new methods, and the application successes reflect contributions by the consortium participants whom we thank for their ongoing support, ideas, input, and guidance.

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