基于拓扑算法的团簇结构全局搜索
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摘要
团簇的基态结构确定,是团簇研究中最为基础和重要的课题之一。当团簇尺寸较大时,势能面上异构体的数目非常多,这使得对团簇基态结构的寻找变得非常困难。本论文借助于图论中图的定义,通过第一性原理计算,从团簇的拓扑结构出发搜寻了非经典碳富勒烯、ZnO笼状团簇、TiO2团簇及MgO团簇的基态结构。另外,对包络甲烷分子的笼形水团簇进行了全面考察,以帮助进一步理解甲烷水合物的成核机制。
非经典富勒烯可能在富勒烯的生长、分解和包络富勒烯复合物的合成过程中发挥一定的作用,但是人们对非经典富勒烯的结构和稳定性了解得比较少。本论文中,我们用扩展的Spiral算法结合密度泛函理论(DFT)计算对含七元环的非经典富勒烯C。(30≤n≤40)及C50的结构和稳定性进行了全面研究,在此基础上,提出了一个新的经验指标。当有含七元环非经典富勒烯存在时,这个指标相比于原来针对经典富勒烯提出的PAPR (Pentagon Adjacency Penalty Rule),能够更好地反映异构体的相对稳定性。
ZnO是一种重要的光学材料,近年来,它的纳米结构在科技上得到了广泛的应用。前人的理论工作表明中等尺寸的(ZnO)n (n=9-25)团簇的基态构型是笼状／管状的结构,但是他们对可能的笼状结构的考察不够全面,因此不能保证得到的结构是真实的基态结构。本论文中,我们用扩展的Spiral算法对含四、六、八元环的(ZnO)n (n=15-24)笼状团簇进行了全面考察,确定了它们的基态构型。
甲烷水合物对人类的能源和环境有显著的影响。前人的实验和理论工作表明在甲烷水合物的成核过程中,有大量的非标准笼子存在。为了研究这些非标准笼子在甲烷水合物成核过程中的作用,本论文利用扩展的Spiral算法对含四、五、六、七元环的包络甲烷分子的笼状水团簇CH4@(H2O)n (n=16,18,20,22,24)的结构和稳定性进行了全面考察。我们发现水环境有利于水的笼状结构的形成,很多非标准笼子与标准笼子的总能差很小,并且它们在构型上有很大的相似性。这些低能的水笼异构体之间能通过两种方式相互转化：水分子二聚体的插入及氢键的转动。这两种结构转化方式均可能在甲烷水合物的成核过程中真实存在。另外,我们计算了甲烷分子在一些异构体笼中的C-H伸缩振动频率及13C的NMR化学位移,这些数据为未来实验上探测这些非规则笼子提供了理论依据。
针对带有离子性的化合物团簇,我们提出了一种基于拓扑结构的新的团簇全局优化算法。这种算法在给定团簇中原子配位数和成键规则的情况下,能对势能面上所有可能的异构体进行全面考察。我们把这种算法应用于(TiO2)n(n=1-6)(?)团簇和(MgO)n (n=1-7)团簇,除了前人报道的结构外,我们得到了一些新的低能异构体。另外,我们模拟了(TiO2)n-(n=1-6)负离子团簇的光电子谱,获得了与实验非常一致的结果。
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.
非经典富勒烯可能在富勒烯的生长、分解和包络富勒烯复合物的合成过程中发挥一定的作用,但是人们对非经典富勒烯的结构和稳定性了解得比较少。本论文中,我们用扩展的Spiral算法结合密度泛函理论(DFT)计算对含七元环的非经典富勒烯C。(30≤n≤40)及C50的结构和稳定性进行了全面研究,在此基础上,提出了一个新的经验指标。当有含七元环非经典富勒烯存在时,这个指标相比于原来针对经典富勒烯提出的PAPR (Pentagon Adjacency Penalty Rule),能够更好地反映异构体的相对稳定性。
ZnO是一种重要的光学材料,近年来,它的纳米结构在科技上得到了广泛的应用。前人的理论工作表明中等尺寸的(ZnO)n (n=9-25)团簇的基态构型是笼状／管状的结构,但是他们对可能的笼状结构的考察不够全面,因此不能保证得到的结构是真实的基态结构。本论文中,我们用扩展的Spiral算法对含四、六、八元环的(ZnO)n (n=15-24)笼状团簇进行了全面考察,确定了它们的基态构型。
甲烷水合物对人类的能源和环境有显著的影响。前人的实验和理论工作表明在甲烷水合物的成核过程中,有大量的非标准笼子存在。为了研究这些非标准笼子在甲烷水合物成核过程中的作用,本论文利用扩展的Spiral算法对含四、五、六、七元环的包络甲烷分子的笼状水团簇CH4@(H2O)n (n=16,18,20,22,24)的结构和稳定性进行了全面考察。我们发现水环境有利于水的笼状结构的形成,很多非标准笼子与标准笼子的总能差很小,并且它们在构型上有很大的相似性。这些低能的水笼异构体之间能通过两种方式相互转化：水分子二聚体的插入及氢键的转动。这两种结构转化方式均可能在甲烷水合物的成核过程中真实存在。另外,我们计算了甲烷分子在一些异构体笼中的C-H伸缩振动频率及13C的NMR化学位移,这些数据为未来实验上探测这些非规则笼子提供了理论依据。
针对带有离子性的化合物团簇,我们提出了一种基于拓扑结构的新的团簇全局优化算法。这种算法在给定团簇中原子配位数和成键规则的情况下,能对势能面上所有可能的异构体进行全面考察。我们把这种算法应用于(TiO2)n(n=1-6)(?)团簇和(MgO)n (n=1-7)团簇,除了前人报道的结构外,我们得到了一些新的低能异构体。另外,我们模拟了(TiO2)n-(n=1-6)负离子团簇的光电子谱,获得了与实验非常一致的结果。
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.
引文
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