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Catalysts Design


The development of nanotechnology is crucial for the progress of sustainable society. Although nanoscience is not a new term, there still are many question links to the nano-regime and its applications in a wide range of fields, including catalysis. Nano- and especially sub-nano metal clusters, in which there are only tens of atoms per cluster, have unique and extraordinary properties. In this size regime, every single atom is essential and should not be ignored [Heiz U, Sanchez A, Abbet S, Schneider WD. Catalytic oxidation of carbon monoxide on monodispersed platinum clusters: Each atom counts. J Am Chem Soc. 1999;121:3214–3217.] Moreover, extrapolating properties from more massive metal clusters do not work in this regime, a clear case being a noble metal like gold [Haruta & Hutchings publications]. This non-scalability feature also means that the cluster of each size has unique properties, e.g. geometric and electronic. The difference in activity between the clusters of different sizes has been again attributed to their morphology, which depends on the number of atoms present in the cluster. The size and morphology also determine the number of low-coordinated atoms, which have been attributed to different behaviour compared to extended terraces. Hence, atomically precise size control is required for particular activity or selectivity of the catalyst although this presents a challenge for experimentalists in the catalyst preparation. Additionally, keeping the small clusters at the desired size rather than sinter on the support under operando conditions (i.e. catalyst resilience) is also challenging. Computational modelling helps to validate the hypothesis as it provides atomic control. Nevertheless, simulation reactivity under realistic conditions and environment is genuinely complicated for surface-supported cluster catalysts, and the models are largely simplified. Often, a strong metal-support interactions (SMSI) changes the shape of nanostructures while the presence of the solvent modifies the clusters’ electronic structure and the catalytic properties [Ren Z, Liu N, Chen B, Li J, Mei D. Theoretical investigation of the structural stabilities of ceria surfaces and supported metal nanocluster in vapour and aqueous phases. J Phys Chem C. 2018;122:4828–4840]. Thus, whether or not the support can significantly affect the cluster geometry and electronic structure depends on the nature of cluster and the support, and it is hard to predict whether or not and to what degree the cluster will change shape upon adsorption, but it is definitely unsafe to assume that it would not.

Cluster-Support Simulations

Computational simulation on the supported cluster as catalysts became a search of the most stable structure (the global minimum) of the nanocluster on different surfaces and in few occasions considering also adsorbates. The central assumption in these works was (and still is) that the global minimum would contain the active site although there are pieces of evidence that the metal catalysts under reaction conditions are dynamic and change their structure as a function of adsorbates’ nature, temperature, flow and static reactors among others. Generally, the global minimum structure cannot be guessed, because chemical bonding in clusters is generally not well understood. Hence, the structures need to be found using stochastic global optimisation and smart sampling techniques, many of which have been developed for this purpose, including particle swarm optimisation [Avendaño-Franco G, Romero AH. Firefly algorithm for structural search. J Chem Theory Comput. 2016;12:3416–3428. Call ST, Zubarev DY, Boldyrev AI. Global minimum structure searches via particle swarm optimization. J Comput Chem. 2007;28: 1177–1186], random search [Pickard CJ, Needs RJ. Structures at high pressure from random searching. Phys Status Solidi Basic Res. 2009;246:536–540. Pickard CJ, Needs RJ. Ab initio random structure searching. J Phys Condens Matter. 2011;23:053201–053223], genetic algorithm [Deaven DM, Ho KM. Molecular geometry optimization with a genetic algorithm. Phys Rev Lett. 1995;75:288–291. Davis JBA, Shayeghi A, Horswell SL, Johnston RL. The Birmingham parallel genetic algorithm and its application to the direct DFT global optimisation of IrN (N= 10–20) clusters. Nanoscale. 2015;7:14032–14038. Kanters RPF, Donald KJ. CLUSTER: Searching for unique low energy minima of structures using a novel implementation of a genetic algorithm. J Chem Theory Comput. 2014;10:5729–5737. Alexandrova AN, Boldyrev AI. Search for the LiN0/+1/−1 (N= 5–7) lowest-energy structures using the ab initio gradient embedded genetic algorithm (Gega). Elucidation of the chemical bonding in the lithium clusters. J Chem Theory Comput. 2005;1:566–580. Alexandrova AN. H_(H2O)n clusters: Microsolvation of the hydrogen atom via molecular ab initio gradient embedded genetic algorithm (GEGA). J Phys Chem A. 2010;114:12591–12599], basin hopping [Zhai HJ, Zhao YF, Li WL, et al. Observation of an all-boron fullerene. Nat Chem. 2014;6:727–731. Oganov AR. Modern methods of crystal structure prediction. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2010. Wales DJ, Doye JPK. Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem A. 1997;101:5111–5116], and simulated annealing [Wang J, Ma L, Zhao J, Jackson KA. Structural growth behaviour and polarizability of CdNTeN (N=1–14) clusters. J Chem Phys. 2009;130: 214307–214315.], in combination with electronic structure calculations commonly based on the density functional theory (DFT). These simulations are intensely expensive, particularly for surface-deposited clusters, and so empirical potentials [Ferrando R, Fortunelli A, Rossi G. Quantum effects on the structure of pure and binary metallic nanoclusters. Phys Rev B Condens Matter Mater Phys. 2005;72:085449–085457. Heiles S, Johnston RL. Global optimisation of clusters using electronic structure methods. Int J Quantum Chem. 2013;113:2091–2109] and potential energy surface fitting techniques [Ouyang R, Xie Y, Jiang DE. Global minimization of gold clusters by combining neural network potentials and the basin-hopping method. Nanoscale. 2015;7:14817–14821. Zhai H, Ha MA, Alexandrova AN. AFFCK: Adaptive force-field-assisted ab initio coalescence kick method for global minimum search. J Chem Theory Comput. 2015;11:2385–2393. Zhai H, Alexandrova AN. Ensemble-average representation of Pt clusters in conditions of catalysis accessed through GPU accelerated deep neural network fitting global optimization. J Chem Theory Comput. 2016;12:6213–6226], have been utilized to accelerate the optimization process and to enable modelling bigger clusters in an attempt to get closer to the experiments [Pittaway F, Paz-Borbón LO, Johnston RL, et al. Theoretical studies of palladium–gold nanoclusters: Pd–Au clusters with up to 50 atoms. J Phys Chem C. 2009;113:9141–9152].


We aim at shed light on the drivers controlling cluster morphology as a function of the cluster size as well as metal and support nature. From a DFT derived dataset of accurate descriptors, we will develop Deep Learning-based surrogates, which combined with genetic algorithms, will predict global and local minima. The validation of these minima using electronic structure calculations will inform us of the contribution of these descriptors on the optimised structures. The relation between these driving forces will explain the morphology of supported catalysts.

Future Work

Unlike extended surfaces, catalytic clusters do not stay put in their starting global minimum during the reaction, so which particular cluster composition or compositions represent the active site(s)?. Indeed, a single structure is not alone in conditions of catalysis, and instead, many structural forms of the cluster are thermally accessible, jointly constituting the nature of the catalyst [Baxter ET, Ha MA, Cass AC, Alexandrova AN, Anderson SL. Ethylene dehydrogenation on Pt4,7,8 clusters on Al2O3: Strong cluster size dependence linked to preferred catalyst morphologies. ACS Catal. 2017;7:3322–3335. Zhai H, Alexandrova AN. Fluxionality of catalytic clusters: When it matters and how to address it. ACS Catal. 2017;7:1905–1911. Ha MA, Baxter ET, Cass AC, Anderson SL, Alexandrova AN. Boron switch for selectivity of catalytic dehydrogenation on size-selected Pt clusters on Al2O3. J Am Chem Soc. 2017;139:11568–11575. Zhai H, Alexandrova AN. Local fluxionality of surface-deposited cluster catalysts: The case of Pt7 on Al2O3. J Phys Chem Lett. 2018;9:1696–1702]. As metals, these clusters that nanoclusters have nearly flat (low-barrier) potential energy surfaces, allowing them to easily isomerize, visiting dozens of isomers on the timescales on the order of nanoseconds at catalytic temperatures [Zhai H, Alexandrova AN. Local fluxionality of surface-deposited cluster catalysts: The case of Pt7 on Al2O3. J Phys Chem Lett. 2018;9:1696–1702.] Hence, the nature of the catalyst is dynamic, and the active site (and potentially catalytic mechanism) might not be just one, but a swarm of many. This has major implications for how we think about cluster catalysis, and how we model it. Indeed, a paradigm shift is needed toward a new accurate methodology considering multi-step-size dynamism.

Study case Au/MgO

The initial study is based on gold (Au) supported on magnesium oxide (MgO) surfaces. Gold is a conventional catalyst since Haruta and Hutchings discovered its activity and selectivity at the nanoscale. Although magnesia is not the most popular support in heterogeneous catalysis, its surface is very well understood as it can be crystallised practically free of defects in perfect cubes exposing flat {001} terraces.


Au/MgO Dataset

The dataset contains the information of 21 structures with AuN (N= 1, 6) monolayers and bilayers of the (111) and the (001) surfaces covering, hence, a wide range of systems. These structures were placed at different positions and heights relative to the surface leading to different positions Figure 1. Overall, there are ~1800 structures in the dataset accounting for ~14,000 entries of geometric and electronic data.