Paper out in Science

Paper out in Science

"Chemically Accurate Simulation of a Prototypical Surface Reaction: H2 Dissociation on Cu(111)"

C. Díaz, E. Pijper, R.A. Olsen, H.F. Busnengo, D.J. Auerbach, and G.J. Kroes, Science 326, 832-834, 2009.

Chemistry by computers: Now an accurate tool for understanding surface reactions underpinning catalysis.

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An international team of scientists from The Netherlands, Spain, Norway, Argentina, and the United States has shown in a paper to be published in Science shortly how the chemistry of surface reactions underpinning catalysis can be modelled accurately with computers.

It is sometimes surprising how little we know about processes that occur right under our very noses. Almost all we see are the surfaces of the objects surrounding us – surfaces pervade our lives, from the walls in our houses, to the piston chambers in the engines of our automobiles.  At each of these surfaces there occur chemical processes, many of which are poorly understood. Determining the mechanisms behind such surface reactions is more than a frivolous academic exercise; reactions of gas phase molecules with metal surfaces are of tremendous practical importance, as the production of most synthetic compounds involves such reactions. One of the achievements recognized by the 2007 Nobel Prize in Chemistry, awarded to Gerhard Ertl, was the detailed description of the sequence of elementary molecule-surface reactions by which vast quantities of ammonia are produced for fertilizer.So far scientists were only able to predict the rate of molecule-surface reactions with semi-quantitative accuracy. But in a recent development, an important step has been taken towards a quantitative understanding of how molecules interact with surfaces.  The team mentioned above has shown that an important class of molecule-surface reactions (dissociation of molecular hydrogen on metal surfaces) can now be modelled by computers “with chemical accuracy”, the standard by which computational chemists measure accuracy. By chemical accuracy we mean that the interaction energy between the molecule and the surface has an error in it that is no greater than 1 kcal/mol. One kcal is “the calorie in our diet”, and the mol is the typical unit by which a quantity of molecules is measured by chemists (1 mol is approximately 6 x 1023 molecules, 1 mol of water weighs about 18 grams).

The new method and main results

A quantitatively correct theoretical prediction of rates of chemical reactions requires an extremely accurate description of the interaction among the atoms involved. This is because reaction rates depend exponentially on the activation energy barriers determined by the inter-atomic forces. In particular, reaching chemical accuracy for reactions on surfaces represents a tremendous challenge because it demands a simultaneous highly accurate description of two subsystems that differ greatly: molecules and metal surfaces. The current state-of-the-art theory allows us to compute the reaction rate of diatomic molecules with metal surfaces using quantum mechanics for the motion of the molecule in all its six degrees of freedom, while making the so-called Born-Oppenheimer and static surface approximations. The precision achieved depends critically on the accuracy of the interatomic forces, as described by the so-called potential energy surface (PES). The lack of accuracy inherent in present-day density functional theory (DFT), the method of choice for computing PESs for molecule-surface interactions, stands in the way of a quantitative description of reactions catalyzed by surfaces. We have developed an implementation of the so-called specific reaction parameter (SRP) approach to DFT that allows a quantitative description of the molecule-surface interactions. In the new implementation of the SRP approach the exchange-correlation functional is a weighted average of two standard DFT functionals calculated within the so-called generalised gradient approximation, in which the energy depends only on the electron density and its gradients. The philosophy behind the method is that by fitting a single parameter of this functional (the “mixing coefficient”) to one suitable experiment, one can obtain a functional that yields a PES that enables an accurate description of other, more detailed, experiments. We have shown that our SRP-PES allows a chemically accurate description of the prototypical molecule-surface reaction of H2 and D2 on the Cu(111) surface in molecular beam experiments, of the influence of the initial rotational and vibrational state of H2 on reaction on that surface, and of rotational excitation of H2 scattering from Cu(111).

A historical perspective

One of the Laureates receiving the 1998 Nobel Prize in Chemistry was Walter Kohn for his contributions to the development of DFT. Together with his co-workers he showed in the mid-sixties that, in order to compute the electronic energy of a system, in principle it suffices to find the average number of electrons located at any point in space, i.e., its electronic density. This alternative way of thinking has led to a computationally cheaper method: DFT that, thanks also to many other important contributions during the last three decades, makes feasible the atomistic study of systems composed of a large number of atoms including metal surfaces and molecules. There is only one hitch: whereas the so-called Hohenberg-Kohn theorems tell us that in principle the interaction energy of a system composed of atoms can be determined from the system’s electron density, a full prescription of how that should be done to full accuracy (in the form of the penultimately accurate density functional) is lacking, and chemists have to make do with approximate density functionals providing varying levels of accuracy.  In addition, the interaction energy among the atoms of a system, essentially due to the interaction of their electronic clouds, is only part of the story. Chemical reactions involve a dynamic rearrangement of the atoms involved during the time and therefore the solution of the quantum and/or classical equations of motion of the atoms in mutual interaction is also a must. It was in the mid nineties when the first dynamical studies accounting for the evolution in time of all the six degrees of freedom of a diatomic molecule on metal surfaces based on DFT interaction energies did appear. The calculations are still computationally quite expensive, and the present calculations were carried out in the framework of a “Dutch computing challenge project” on the Dutch national supercomputer “Huygens”.

Geert-Jan Kroes started his work on modelling molecule surface-reactions in the early nineties. In 1997, together with Evert-Jan Baerends (VU University Amsterdam) and Richard Mowrey (Naval Research Lab), he published the first quantum dynamical calculation of the rate of an activated diatomic molecule-surface reaction, modelling motion in all the six degrees of freedom of the molecule. Improving the modelling of such reactions has been a main theme of his research since then. Daniel J. Auerbach has been involved in experimental work on chemical dynamics at surfaces since the late seventies, with the crucial experiments relevant for the present work dating back to the early nineties. At that time there was a raging controversy on whether vibrationally excited H2 contributed to the reaction of H2 on Cu surfaces.  Using a combination of laser and molecular beam techniques Auerbach and his co-workers at IBM were able to resolve this controversy. They went further and made a wide ranging set of measurements on the effect of translational motion, vibrational motion, rotational motion, and alignment on H2 and D2 reactions at Cu.  Central to the present state-of-the-art of computational modelling has been the development of accurate methods for representing PESs, a step taken in the late nineties by H. Fabio Busnengo, Antoine Salin and Wei Dong, and later refined together with Roar A. Olsen. Cristina Díaz and Ernst Pijper have devoted their research efforts towards understanding molecule-surface reaction during both their PhD studies and subsequent post-doc work.

Towards new frontiers

The natural next step in our quest to understand how molecules interact with surfaces is to extend the SRP-DFT method to reactions where heavier molecules than hydrogen are involved. It then becomes important to include also the motion of the surface atoms in the modelling. In such applications, the dynamics calculations should incorporate the motion of the surface atoms at the stage when the SRP functional is fit to experimental data. Approximate ways of including the effect of atomic surface motion can now be incorporated in quantum dynamical and ab initio molecular dynamics simulations. It may even be possible to extend SRP-DFT to improve the description of molecules interacting with surfaces involving electronically excited states, thus taking us beyond the almost always used Born-Oppenheimer approximation. This could be done for instance by adjusting the SRP functional for each (spin or charge) state of the molecule involved. Finally, whereas the SRP-DFT procedure used here is semi-empirical (i.e., fit to experimental data), applications may be envisaged in which the SRP functional is parameterised to reproduce a limited set of molecule-surface interaction energy data obtained with a computationally intensive electronic structure method with a claim to high accuracy.

The team

Cristina Díaz obtained her master’s degree in physics in 1999 at the University Autónoma de Madrid (Spain) and her PhD degree in chemistry in 2004 simultaneously at the University Autónoma de Madrid (Spain) and University of Bordeaux I (France), under the supervision of Prof.dr. Fernando Martín and Prof.dr. Antoine Salin. After her PhD she moved to the Leiden Institute of Chemistry, Leiden University (The Netherlands) working for 3 years as a post-doc under the supervision of Prof.dr. Geert Jan Kroes. In 2008 she obtained a “Juan de la Cierva” research fellowship and now works at the University Autónoma de Madrid.

Ernst Pijper obtained his master's degree in physics at the University of Amsterdam in 1996. He started his PhD in 1997 in the theoretical chemistry group of Prof. Geert-Jan Kroes at Leiden University and received his PhD degree in 2002. After a 2 year post-doc at the Radboud University in Nijmegen where he studied quantum effects on the diffusion of light diatomic molecules on surfaces, he returned to Leiden to continue his work on scattering of H2 from metal surfaces. Currently he is employed as a system programmer by SARA, the Dutch National Computing and Networking Services in Amsterdam, where he is part of a team that is responsible for maintaining the grid infrastructure.

Roar A. Olsen studied physics at the University of Oslo (Norway) where he obtained a master’s degree in theoretical physics in 1992. After having started his PhD in 1994 at the University of Oslo, he moved to The Netherlands in 1995 and obtained his PhD degree in theoretical chemistry in 1998 at the Free University of Amsterdam working with Prof.dr. Evert Jan Baerends. The next 4 years he worked at the Free University as a post-doc before taking up an assistant professorship in the theoretical chemistry group at the Leiden Institute of Chemistry, Leiden University. He moved back to Norway in 2008 and now works as an associate professor at Akershus University College in Lillestrøm, just outside Oslo.

H. Fabio Busnengo studied Physics at the University of Rosario (Argentina) where he started working on theory of high energy ion-atom and ion-molecule collisions under the supervision of Prof.dr. Roberto D. Rivarola and obtained the PhD degree in Physics in 1997. In 1998 he moved to France for a three-year post-doc during which he started working on molecule-surface dynamics with Prof.dr. Antoine Salin in the Laboratoire de Physicochimie Moléculaire (today part of the Institut des Sciences Moléculaires), University of Bordeaux I. In 2001, he moved back to Argentina, and now works in the Rosario Physics Institute (Instituto de Física Rosario, IFIR) as Researcher (Investigador Independiente) of CONICET (the National Research Council of Argentina) and as Teaching Assistant in the Facultad de Ciencias Exactas, Ingeniería y Agrimensura of the University of Rosario.

Daniel J. Auerbach is currently Chief Technology Officer of GRT Inc., a small Santa Barbara based company working on technology for the conversion of natural gas into liquid fuels and high value chemicals. GRT is particularly interested in developing technology to deal with “stranded gas”, i.e., gas that is too remote from natural gas markets or is present in fields that are too small for conventional technologies to be economically viable. Before joining GRT, Auerbach worked for many years in the microelectronics and computer industry, initially for IBM and later for Hitachi Global Storage Technologies.  At IBM Auerbach served for 10 years as Department Group Manager of the Science and Technology Department at the IBM Almaden Research Centre. Auerbach holds a PhD degree in Physics from the University of Chicago. Before joining IBM in 1978, he served on the faculty of Johns Hopkins University.  He is known world wide for his scientific research in the area of surface science and chemical dynamics.  Auerbach is perhaps best known as a pioneer in the application of molecular-beam and laser-spectroscopic techniques to understanding of the microscopic details of chemical dynamics at surfaces.  His research interests also include information storage systems, the design of parallel computers, and chemical dynamics.

Geert-Jan Kroes
studied chemistry at the University of Utrecht where he obtained a Doctorandus degree in chemistry in 1987. He performed his PhD research at the university of Amsterdam under supervision of Prof. Rudolph P. H. Rettschick, obtaining his PhD degree in 1990. He next performed post-doctoral research at Leiden University and at Cambridge University. In 1993 he started research on a KNAW-fellowship at the Free University of Amsterdam, working with Prof.dr. Evert-Jan Baerends. He returned to Leiden in 1996, where he became an assistant professor in the theoretical chemistry group at the Leiden Institute of Chemistry in 1998. He obtained a “PIONIER” grant in 2002, and became a full professor at Leiden in 2003.