Universiteit Leiden

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Research project

Quantum dynamics of H2 on metal surfaces: researching the role of surface atoms

This research focuses on the (Quantum) Dynamics (QD) of the reactive scattering of H2 from metal surfaces.

Mark Somers

Although we have performed QD on many different H2+metal surface system, the favorite system is the H2 on Cu(111) system. This is because for this typically activated system, the QD is actually very challenging. This is related to the QD basis set size one requires. At the same time a wealth of theoretical and experimental research has been done already. This allows us to really focus on disentangling what steps to take to achieve what we would call ‘quantum supremacy’: accurately describing the reactive scattering and diffraction of H2 from a metal surface fully quantum dynamically.

Currently in most state-of-the-art quantum dynamics on systems like this, the Born-Oppenheimer Static Surface (BOSS) approximation is wildly used. Here one essentially fixes the surface atoms in their ideal lattice positions and then describes the dynamics of H2 without any further approximations using a QD method based on wave packets. Given the 6 remaining degrees of freedom of H2, these are called 6D QD simulations. For this a ground-state Potential Energy Surface (PES) is used. Nowadays these PESs can be of ‘chemical accuracy’ using a Density Functional Theory (DFT) functional especially designed for the system. This is the work Prof. dr. Kroes is doing.

We have a focus on expanding the dynamical method to go beyond the 6D and develop a method that allows to include the dynamical effects of the surface atoms. Clearly, when surfaces are at elevated temperatures, the surface atoms do not remain fixed and most certainly not at the 0K ideal lattice positions. Simply extending the QD to include all surface degrees of freedom is also not an option. Nowadays the state-of-the-art 6D calculations, depending on the desired accuracy, system and results one wishes to obtain, can still be very expensive to perform. i.e. to obtain converged diffraction probabilities for D2 from Cu(111) at 40 meV of incidence energy, still requires 5 weeks of computer time using 16 cores continuously. One can understand, going to 7D would be at ~10 times more expensive and corresponds to only moving a single surface atom in only one direction. Only in very special cases this can be done and the implicit approximation holds. Going to even higher number of degrees of freedom without introducing some kind of an approximation is computationally unfeasible for practical purposes.

New approximations that can be made safely are needed to include the surface temperature effects and progress is steadily being made. See the poster by Bauke Smits from CHAINS 2021. He has shown that the so called Static Corrugation Method (SCM)[1,2] can be used to obtain accurate QD results on the reaction of H2 on Cu(111) for a 925K surface. He has done that by introducing a very accurate Embedded Atom Method (EAM) PES describing the Cu-Cu interactions and before embarking on the task of doing the actual QD, he has extensively tested this EAM and SCM combination using the much cheaper classical dynamics methods[3]. Click on the poster (or here) to get more details.

Performing SCM calculations like this for lower surface temperatures still requires more research. Classical dynamics methods to obtain surface configurations to be used in an SCM approach fail for two reasons. First the surface atom vibrations are best described as phonons and these are considered bosons adhering to the Bose-Einstein statistics instead of the classical Maxwell-Bolzmann statistics. Second, in equilibrating such surfaces using molecular dynamics on encounters problems with thermostats that artificially extract zero point energy from the system.  

So the main research interest lies in developing new QD methods and approximations that one can safely make. Students wishing to perform an internship with me will need to learn not only a lot about QD, but also about high performance computing and programming.


  1. Wijzenbroek, M. & Somers, M. F. Static surface temperature effects on the dissociation of H2 and D2 on Cu(111). J. Chem. Phys. 137, 054703 (2012). DOI
  2. Spiering, P., Wijzenbroek, M. & Somers, M. F. An improved Static Corrugation Model. J. Chem. Phys. 149, 234702 (2018). DOI
  3. Smits, B. & Somers, M. F. Beyond the static corrugation model:Dynamic surfaces with the embedded atom method J. Chem. Phys. 154, 074710 (2021). DOI
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