中文摘要：

采用密度泛函方法对四、六元环组成的所有可能的的23个笼状B28N28结构进行了理论计算和拓扑学特性研究，用三个指标N4x4（x=0，1，2）来描述相邻四元环间的键联类型，结果发现B28N28笼的相对能量随N4x4，值的增大而增大，且N404对稳定性的影响起主导作用．这一简单的拓扑学标准可以给出所有四六结构B28N28异构体的大致能量顺序，并从ISR结构中挑选出能量较低的结构，因此有望用于挑选大尺寸氮化硼团簇的热力学稳定结构．

英文摘要：

The structures and stabilities of twenty-three B28N28 alternant structures have been investigated at the B3LYP/ 6-31G^＊ level of density functional theory. It is found that stability index of all the isomers obey a simple N4x4 （x=0, 1, 2） topological rule characterizing the number of bonds between squares. The relative energies show an increasing tendency with the rising of x in N4x4（x=0, 1, 2）, in which N4x4 is dominant. The present study provides a simple topological criterion that can be used to sort an approximate stability order of all the isomers and select the more stable candidate from the ISR（isolated square rule） structures. The simple filtering scheme is ideally suited for prescreening the thermodynamically viable structures of large boron nitride clusters.