Global Optimization Of Cluster Geometries Based On The Topological Algorithm

Searching the ground state cluster structures is one of the most fundamental and important issue in the cluster science. The number of isomers on the potential energy surface is tremendous for large size clusters. Thus it is very difficult to search for the lowest-energy structure when the cluster size becomes large. With the aid of the definition of graph in graph theory, we searched for the ground state structures for nonclassical fullerenes with heptagons, ZnO cage clusters, TiO2clusters as well as MgO clusters based on the topological structures of clusters. In addition, we explored systematically the H2O cage clusters encapsulated with methane molecules in order to shed some light on the nucleation mechanism of methane hydrate.Nonclassical fullerene may be involved in fullerene growth, fragmentation and preparation of endohedral fullerene complex. Compared with classical fullerenes, less attention has been paid to noncalssical ones. In this article, we comprehensively explored the nonclassical Cn (30≤n≤40) and C50fullerenes with heptagons using generalized Spiral algorithm and DFT methods. A new empirical index was proposed. When noncalssical isomers with heptagons exist, this index performs better for estimating the relative stabilities of fullerene isomers compared with the PAPR (Pentagon Adjancy Penalty Rule) which is presented for classical fullerenes.ZnO is one important kind of optical materials. In the past decades, ZnO nanostructures had wide range of technological applications. Previous theortical works suggested that cage/tube structures are ground state structures for (ZnO)n (n=9-25) clusters. However, the reported structures can not be guaranteed to be the true global minima due to the insufficient exploration for the initial structures. In this article, the structures of (ZnO)n(n=15-24) cage clusters were comprehensively studied using generalized Spiral algorithm and the lowest-energy structures were determined for each cluster size.Methane hydrate has significant impacts on the energy and environmental science. Previously, both theoretical and experimental works indicated that nonstandard cages appeared during the nucleation process of methane hydrate. In order to understand the effect of nonstandard cages during the nucleation of methane hydrate, we studied the CH4@(H2O)n (n=16,18,20,22,24) clusters with four-, five-, six-and seven-membered rings impolying generalized Spiral algorithm. We found that aqueous environment is favorable for the formation of water cage configurations. Many nonstandard cages have small energy difference and large structural similarities with the standard ones. These low-energy structures can transform each other in two ways:the insertion of water dimmers and the orientation of hydrogen bonds, which may truly exist in the nucleation process of methane hydrate. In addition, for the methane molecules in some low-energy isomer cages, we calculated their OH stretching modes and the13C NMR chemical shifts. These theoretical data may be helpful for the identification of these nonstandard cages experimentally in future.For clusters with ionic characters, we presented a new algorithm for global optimization of clusters based on their topological structures. Under given rule for the coordination number of atoms, our method can explore all possible structures on the potential energy surface. We applied this method to (TiO2)n (n=1-6) and (MgO)n(n=17) clusters. Except the structures reported previously, some new low-energy isomers were obtained. We have simulated the photoelectron spectra of anionic (TiO2)n (n=1-6) clusters, which agree well with experiments.