Global optimization studies of atomic clusters

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• Edwin Flikkema (Aberystwyth University)
• Thursday 24 August 2023, 15:00-15:30
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PMVW01 - 5th International Conference on Packing Problems: Packing and patterns in granular mechanics

Within the field of structure prediction of atomic clusters, optimising the interaction energy (and hence finding low-energy geometries of such clusters) is an important problem. This gives geometries that are thermodynamically likely to be formed. Finding minima is also the first step in an “energy landscape” approach, where, alongside minima, “transition states” (i.e., certain saddle points) are also considered. This presentation focuses on atomic clusters made of silicon and oxygen atoms, i.e., SiO2, also called silica.Silica (SiO2) is a versatile material with many applications in such diverse fields as micro-electronics, chemistry (catalysis) and photonics. Many bulk polymorphs exist such as the dense quartz phase or the more open zeolites. This presentation is about trying to find the optimal geometries of various types of silica (nano-)clusters. The methodology consists of a two-step approach, where classical potentials are used first and promising candidates for the energetic global minimum are subsequently refined using Density Functional Theory (DFT) with the B3LYP functional and a 6-31G** basis set.In an initial study (SiO2)N clusters consisting purely of silica were considered. The Basin Hopping global optimization algorithm was used together with a specifically parameterized potential to produce candidate geometries for the energetic global minimum, followed by DFT refinement. The potential used is of the same form as the BKS and TTAM potentials known in the literature. The potential has been re-parameterized to give more accurate results for clusters (rather than the bulk material). Clusters of sizes up to 27 SiO2 units have been considered and global minima were proposed.A second study focuses specifically on `fully-coordinated’ silica clusters, i.e. defect-less clusters where every silicon atom is bonded to 4 oxygen atoms and every oxygen atom is bonded to 2 silicon atoms. This fully-coordinated arrangement of atoms is common in bulk silica, whereas for clusters defects tend to occur. Fully-coordinated clusters are expected to have special properties, such as an improved chemical stability, making them possible building blocks for cluster-assembled materials. An algorithm for specifically searching for (low energy) fully-coordinated clusters was developed. This algorithm is based on performing Monte Carlo moves in the space of graphs (rather than in coordinate space), the graph being the network of chemical bonds between atoms. This approach ensures that the clusters remain fully-coordinated during the search. Fully-coordinated clusters of sizes up to 24 SiO2 units are considered. The main purpose of this investigation is to find out how the energetic difference between the lowest-energy fully-coordinated cluster and the lowest energy defective cluster diminishes with cluster size.Another study focuses on hydroxylated silica clusters (SiO2)M(H2O)N. Such clusters are more likely to occur in nature and are relevant to understanding the processes involved in the synthesis of zeolites. Here, a simplified version of the potential introduced by Hassanali and Singer is used in combination with the Basin Hopping global optimisation algorithm and DFT refinement. Structural and energetic trends with increasing level of hydroxylation are being studied. This has led to a re-interpretation of an experiment on atomic mixing in hydroxylated silica clusters in solution.If time permits, work on two-dimensional foams (in collaboration with Simon Cox) can be discussed as well.

This talk is part of the Isaac Newton Institute Seminar Series series.

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