Metal sub-nano clusters are important materials for catalysis of chemical reactions such as dehydrogenation of hydrocarbons. However, their potential energy surface (PES), which is responsible for explaining relative stability of different cluster geometries, can be complicated. The complexity can be greatly reduced by describing the PES by low-energy isomers, which can be found by the standard mathematical method called global optimization. We have proposed global optimization acceleration schemes using Force Field (FF) fitting, or deep neural network (DNN) fitting, for gas phase metal clusters. Both these models can be trained to give an approximation to the PES at the density functional theory level. For surface supported clusters, we found that Basin Hopping (BH) global optimization can usually give satisfactory results. To address the difficulty in performing structural search for surface supported clusters at high hydrogen coverage, we proposed a revised BH approach with core-shell separation scheme. The application of this new approach shows that the cluster shape can be very different from that of their adsorbate-free counterparts.
After the structure of isomers is found, it is also necessary to define the geometry similarity between two isomers with the same chemical formula. Structure similarity measurement is an important part of any PES exploration techniques. We have investigated existing algorithms and introduced two new algorithms, namely, atomic matching based on depth-first search and bipartite model atomic matching, for gas phase and surface supported clusters, respectively.
Additionally, isomers may interconvert across barriers, i.e., exhibit fluxionality, during catalysis. To study the big picture of the fluxional behavior for surface supported clusters, we model such process as isomerization graph using bipartite matching algorithm, harmonic transition state theory (HTST), and paralleled nudged elastic band (NEB) method. Detailed inspection shows that, at temperatures typical for catalysis, the cluster geometry changes frequently within several regions in the graph, while transition across regions is less likely. This local fluxionality picture provides a new perspective on understanding finite-temperature catalytic processes.