Resumen de Theoretical investigations into single-atom catalysts on ceriumdioxide: deposition and activation
This doctoral thesis centers around electronic structure calculations and is divided into two parts. The first and main part focuses on single-atom depositions of platinum. Ceria heavily influences the adatoms' properties via the Strong Metal-Support Interaction and so is integral to the full picture. Experimental observations indicate that starting from ŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁsingle-atoms and applying a fine-tuned reduction pulse enhances its performance in oxidation reactions. The operating conditions of catalytic activity now make it a suitable candidate for the DOE 150°C challenge. This is a challenge from the US Department of Energy towards Research and Industry to develop novel car-exhaust catalysts that operate at lower temperatures. These catalysts will then be compatible with the latest generation of greener, fuel-efficient engines. Current catalysts already include platinum nanoparticles on a ceria support and could thus act as precursors to the single-atom catalyst. A three-way catalyst converts three types of toxic gases: carbon monoxide, nitric oxide, and hydrocarbons. In the thesis, I evaluate the stability of the single-atoms on the pristine (100) surface both in their resting and activated state.ŁŁ Considering the prominence of carbon monoxide as a probing molecule in experiments, I verified their reactivity for CO oxidation. It should be noted that the oxidation state of activated platinum was originally undetermined. This prompted an in-depth study into its characterization. Finally, the scope was extended to other metal elements of group X, such as nickel and palladium.
The second part discusses the recent developments in methodology and tests them on ceriaŁŁŁŁŁŁŁŁŁŁŁŁ. Two kind of issues are tackled separately. On the one hand, there is the sensitivity of the Hubbard correction to the orbital filling of the ions. This introduces a charge dependent bias in all ceria redox reactions. A novel, low-scaling implementation of second-order Møller-Plesset perturbation theory (MP2) is tested on bulk ceria to evaluate its accuracy. Since MP2 is a post-Hartree-Fock (HF) correction, it does not suffer from this self-interaction error and on average its accuracy should ŁŁŁŁŁŁŁŁŁeven exceed post-DFT RPA. To model the processes of interest in bulk, the case of CeO2 reduction to Ce2O3 is examined. This would be the first step towards a feasible benchmark of reducible transition metal oxides and their reactions within periodic boundary conditions.
The other issue is that of constructing multi-scale models. The current state-of-the-art was applied in the single-atom project and departs from ab initio mechanisms that are coupled in micro-kinetic models. In case spatial resolution is required, a Monte-Carlo simulation would be more appropriate. Here, I investigate force fields as an alternative to the latter. Force fields are already common-place in simulations of biomolecules. They are parametrized in function of their nuclear geometry, ignoring the electronic structure. This renders them unsuitable in Solid State calculations. One of the main applications of Machine Learning for Chemistry is exactly the fitting of the potential energy surface. With the maturation of this field, I decided to try and apply its techniques to ceria. More specifically, I will fit a high-dimensional potential using a multi-layer Neural Network (HDNNP) and evaluate its performance. The scope in this thesis however will be restricted to a general strategy and some first attempts.
The single-atom platinum on ceria was predominantly studied using density functional theory equipped with a Hubbard correction. The correction is there to mitigate the self-interaction error of density functional theory, to which heavy metals in particular are prone. This is the state-of-the-art approach to computing ceria. A benchmark of physically more accurate methods was performed on a selection of structures. This benchmark served foremost to evaluate the oxidation states of various coordinations. It includes variation of the Hubbard parameter, hybrid functionals (HSE06, HSE03-13) and Perdew-Burke-ErnzerhofŁŁŁŁŁŁ (PBE) post-processed by the random phase approximation. Using PBE+U, I performed a scan of the local minimaŁ and ab initio Molecular Dynamics simulations. The simulations proceeded as follows: a heating period from 0 to 300 K; an equilibration period at 300 K to ensure no energy leakage; another heating to 600 K; and finally the actual simulation at 600 K. The preparation was conducted using time steps of 1 fs, the data generation in 3 fs time steps. For all steady-state simulations I employed the Nosé-Hoover thermostat. The mechanism for the activation and CO oxidation was computed similarly. The reactivity of the latter was confirmed using micro-kinetics simulations performed by Minttu Kauppinen from the Honkala group.
The bulk phase transformation was performed ŁŁŁŁalong two routes: DFT and wavefunction. The DFT route uses HSE03, Hartree-Fock (HF) starting from HSE03, and a correction with RPA. The wavefunction route consisted of HF and MP2. The latter includes correlation beyond RPA added to the exact hartree exchange. Normally, it would not have been feasible to perform such a heavy calculation. The new VASP 6 however will contain two low-scaling implementations. In collaboration with the developer Dr. Tobias Schäfer, I tested it out the deterministic version. Some methods only provide energy corrections but no forces. Therefore, a volume energy curve was fitted for each method. The comparison happens between their minima.
For machine learning a two-layered Neural Network was used to fit a ŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁHDNNP. This machine learning approach starts from a general function free of any physical or chemical preconceptions. Its only constraints are mathematical in nature and guarantee symmetry as well as upscaling to larger models. The state-of-the-art approach to symmetrization is the mapping of atomic environments onto a vector of projection functions. These functions are tuned to return high values in a specific region of the coordinate space.Ł The set of all environments is then fitted to the energy, while the derivatives of their individual vectors areŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁ fitted to the forces. I used the RuNNer code from the Behler group for the training cycle and LAMMPS with the n2p2 interface for the molecular dynamics simulations. The dataset was computed using PBE+U and filtered using an in-house method. Filtering is necessary to remove correlation in Molecular Dynamics trajectories. This saves time during training without much loss of information and ensures a more homogeneous weight among the data points. Our in-house filter compares the root mean squared deviation of the geometry and forces to a reference structure. It samples the space density via a 3D grid and enforces equal density per voxel by removing superfluous points. Conversely, the symmetry functions are used to gauge the coverage of the input.
