Clarifying Surface Catalysis

Theoretical modeling requires decisions about when and where you can simplify the mathematics that describe a particular system. Recent work by three research teams demonstrates new ways to simplify computational approaches to the complex systems of molecules interacting with metal surfaces. These interactions often are catalytic and play a critical role in the industrial production of many synthetic compounds.

One group used experimental data on a surface reaction to calibrate a mixture of mathematical approaches and then applied the resulting combination to probe other aspects of the system. A second group looked at the effect of a molecule-surface collision to narrow down how much surface movement must be incorporated into computations. And the third group found a way to avoid a computational approximation to better account for the effects of the metal conduction band.

A better fundamental understanding of catalytic systems will have an impact on catalyst design, says Stephen Holloway, a chemistry professor and provost for science and engineering at the University of Liverpool, in England. But more important, it’s basic research that involves “people thinking quite deeply about how to describe nature,” Holloway says.

One recent study that has led to a deeper understanding of molecule-surface interactions used density functional theory to quantitatively describe the reactive scattering of H₂ from a copper surface. Chemistry professor Geert-Jan Kroes of Leiden University, in the Netherlands, who led the international team that carried out the study, notes that previous efforts to model such systems resulted in a potential energy surface with reaction barriers that were off by 4–5 kcal/mol. “That’s too high,” he says of the deviations from experimental values. “We wanted to achieve chemical accuracy, meaning errors less than or equal to 1 kcal/mol.”

To that end, Kroes and colleagues combined two density functionals—mathematical ways to describe a system, each one based on a set of assumptions or approximations—in such a way that the computational results reproduced experimental data from molecular beam experiments (Science 2009, 326, 832). The functionals incorporated the so-called generalized gradient approximation, which describes how electron density changes over time. After establishing the calibrated computational system, Kroes’s team then used it to evaluate other properties of the system, such as the effect of the rotational and vibrational states of H₂ on its interaction with a copper surface.

The general approach of combining functionals can be applied to other systems, but the functionals used and how they are mixed would likely differ, and they would again need to be calibrated against experimental data. Kroes is further improving the calculations by incorporating into them the effects of phenomena such as electronic transitions from the metal valence band to the conduction band.

In a separate study, Bret Jackson, a chemistry professor at the University of Massachusetts, Amherst, tackled the problem of how to deal with motion in the metal lattice in the dissociation of methane from a nickel surface. “The barrier to the reaction changes significantly when the lattice atom over which the dissociation takes place moves in and out of the surface plane,” Jackson says. This effect results experimentally in temperature-dependent reactivity.

When Jackson and coworkers looked more closely at what happens when a methane molecule interacts with a surface, they found that the lattice atom at the collision point is not that perturbed by the interaction and that the surface doesn’t pucker, as other work had suggested (Phys. Rev. Lett. 2009, 103, 253201). The results mean that computations can be simplified on the surface end, allowing theorists to devote more resources to the detailed behavior of the methane molecule.

Both Kroes’s and Jackson’s work—indeed, most computational modeling of chemical reactions—rests upon the Born-Oppenheimer approximation, which simplifies theoretical modeling considerably by allowing nuclear motion and electronic transitions to be treated separately in quantum mechanical calculations.

The approximation works fine for things like reactions of organic molecules, in which the potential energy surfaces of the electronic states are far apart, says John Tully, a chemistry professor at Yale University. The conduction band of a metal lattice, however, has a continuum of electronic states spaced infinitesimally; molecule-surface reactions, therefore, also have an infinite number of potential energy surfaces also spaced infinitesimally. The result is that the energy of nuclear motion can be transferred into electronic excitations. This behavior is contrary to that assumed by the Born-Oppenheimer approximation and, Tully says, is believed to be an important component of surface reactivity.

Tully and colleagues have now developed a computational approach that incorporates non-Born-Oppenheimer behavior into modeling of molecule-surface reactions. Specifically, they looked at NO scattering from a gold surface (Science 2009, 326, 829). With so many potential energy surfaces involved, the problem sounds hopeless, Tully says, but the key is recognizing that the transitions are really single-electron events.

He and his group found that the rate of transitions between potential energy surfaces depends on the N–O internuclear separation and the molecular orientation. They also found that a common effect known as dynamical steering—in which a slow-moving molecule turns around as it approaches a surface, allowing one end to bind more strongly than another—moves NO molecules into positions that promote strong coupling of electrons to nuclear motion.

Ultimately, it’s unlikely that researchers can nail down every last detail of these reactions, says Liverpool’s Holloway, who used to work in this area but now classifies himself as an informed observer. “It would be demonic to try to understand everything to the last decimal point,” he says, adding that in his view it would be a success if people could get to about 70% of the way, to the point of understanding reaction trends as functions of experimental parameters. We can all look forward to the research advances that will lead us toward that goal, he notes.