58th Annual Report on Research 2013 Under Sponsorship of the ACS Petroleum Research Fund

The design of new, high-performance heterogeneous catalysts continues to play an important role in the global economy. However, the structures of the active sites on many supported catalysts are often not well-defined, which presents a formidable challenge for computational modeling. The ACS-PRF proposal suggested new ab initio  modeling strategies are needed to study catalytic sites on amorphous supports.

A typical strategy uses cluster models with constraints on the peripheral atoms to mimic anchors to a solid matrix.  However, the lack of structural information about amorphous materials requires arbitrary placement of the constrained peripheral atoms and different choices lead to model sites with different activities. Another strategy is to allow the peripheral atoms of the cluster model to move during the course of a reaction, but models of this type are unrealistically flexible for sites embedded in a solid matrix.  To correctly model a solid structure one must impose geometric constraints on the peripheral atoms of the cluster model. When modeling crystalline solids, as one can constrain the peripheral atoms to their crystallographic positions. However, in amorphous materials, the peripheral atom positions are not obvious. Actually, amorphous materials have an unknown distribution of site environments and there is no single configuration to constrain the peripheral atoms!

Our new algorithm uses a reduced potential energy surface framework with sequential quadratic programming.  The new algorithm finds the lowest energy catalyst site structure for each value of the activation barrier.  This knowledge allows one to distinguish between highly active sites and 'dead' sites. In the process, we learn the minimum site formation energies to create active sites, dead sites, and everything between.  The formation energies, we hypothesize, are related to the populations of each site.  This information allows us to predict quantities like the distribution of activation energies, the rate-averaged 'apparent' activation energy, and the results of active site counting experiments.   We refer readers to our published paper for algorithmic details: "Isolated catalyst sites on amorphous supports: a systematic algorithm for understanding heterogeneities in structure and reactivity", Goldsmith, Sanderson, Bean, Peters, J. Chem. Phys. 138, 204105 (2013).   Additional algorithmic details can be found in the ACS-PRF supported publication:

1)     "Understanding reactivity with reduced potential energy landscapes: recent advances and new directions", Goldsmith, Fong, Peters, in "Reaction rate computations: theories and applications" Eds. Ke-Li Han and Tian-Shu Chu, RSC Theoretical and Computational Chemistry Series no. 6.  (in press)

The new algorithm partitions the coordinates into two complementary subspaces.  The "interior coordinates" include everything near the reaction center – often these are details which can be at least partially observed in EXAFS.   The "periphery coordinates" are positions of atoms at the edge of the molecular model where, because of the amorphous nature of the support, we have no information about structure.  In this two dimensional model, there is only one interior and one peripheral coordinate.  The new algorithm systematically generates models of the active site with higher (to the left) or lower (to the right) activation energies by changing the peripheral coordinate.  The collection of sites generated represents heterogeneity in the distribution of sites on the amorphous catalyst surface.

The algorithm has been applied to olefin metathesis by an Mo catalyst on Si/Al, and also to the Phillips catalyst (isolated Cr supported on amorphous SiO2). 

Model for active sites in the Phillips catalyst:  The terminal fixed F atoms mimic locations at which the site is anchored to an electron withdrawing SiO2 support.  The locations of the F atoms are uncertain because of the amorphous nature of the support, and others have arbitrarily chosen their locations. Our algorithm generates an activation-energy-ordered family of models with terminal atoms in the optimal position for each activation energy.

The new algorithm reveals that the activation energy of sites in the Phillips catalyst is highly sensitive to the geometry of the model, in particular, to the placement of the periphery atoms.  If one assumes (approximates) that sites are created in numbers consistent with a Boltzmann distribution based on their formation energy, and if one then computes the rate on a catalyst with this distribution of active sites, one finds that the activity is dominated by faster sites, even though they are less common than sites with the lowest energy. 

The new algorithm predicts how subtle differences in the active site structure change the activation energy.  These structural differences emerge from local structure differences in the sites at which different metal atoms (Cr in this case) are grafted to the amorphous support.  In this case the calculation reveals that compressed rings are far more active for olefin polymerization than stretched rings. 

The results reveal the danger in building these models by minimizing the energy.  Energy minimized sites may not be representative of sites which dominate the kinetics.  With ACS support, we have made a seminal contribution with the first algorithm to quantify (approximately) the degree to which isolated sites on amorphous catalyst supports are sensitive to the details of their anchors to the underlying support.  Along the way, we wrote two other papers acknowledging support from ACS-PRF:

2)     "Recent advances in transition path sampling: accurate reaction coordinates, likelihood maximization, and diffusive barrier crossing dynamics", B. Peters, Molecular Simulation, 36, 1265-1281 (2010).

3)     "Transition state theory, dynamics, and narrow time scale separation in the rate-promoting vibrations model of enzyme catalysis", B. Peters, J. Chem. Theory and Comp., 6, 1447-1454 (2010). 

Anthony Fong will publish a comprehensive study of ethylene polymerization on the Phillips catalyst in the near future.  His analysis makes use of the new framework for understanding catalysis on amorphous supports. 

4)     "Computational analysis of ethylene polymerization by the Phillips catalyst: test of four hypothesized propagation mechanisms", A. Fong, Y.Yuan, S. Ivry, S. Scott, B. Peters, (in preparation) 

Anthony, now supported by different funds, is continuing to study olefin metathesis by methylrheniumtrioxide on amorphous Si/Al catalyst supports.