MgB_n(n=1～17)团簇的密度泛函理论研究

Density-functional theory study of MgB_n (n=1～ 17) clusters

本文从第一性原理出发,采用密度泛函理论(DFT)的杂化密度泛函B3LYP方法,在6-31G(d)全电子基组水平上对MgB_n(n=1～17)团簇各种可能的构型进行结构优化和频率分析,预测了各团簇的最低能量结构.结果表明MgB_n团簇主要有两种生长模式.同时对各团簇最低能量结构的能隙、结合能等电子性质进行了分析,由二阶能量差分及能隙随团簇尺寸的变化规律可以得到MgB_6、MgB_9、MgB_(13)是比较稳定的团簇.通过NBO对自然电荷布居及成键特性进行分析,得到Mg原子带正电,以s轨道参与成键,B原子主要带负电,一部分B原子之间以sp杂化形成离域π键,有利于增强稳定性,其他B原子主要以s、p轨道参与成键.

The possible geometries, relative stabilities, electronic properties and nature of bonding of MgB_n(n=1～17) clusters are investigated by using the hybrid density functional approach (B3LYP) at 6-31G(d) level of the theory. Emphasis is placed on the equilibrium geometries and growth-pattern behaviors. The results show that the growth-pattern behaviors of the structures of MgB_n (n= 1～17) clusters can be classified into two categories. Particularly, the calculated second-order difference of energies and the HOMO-LUMO (highest occupied molecular orbit-lowest unoccupied molecular orbit) gaps indicate that MgB_n (n= 6,9 and 13) clusters are more stable than their neighbors,especially the MgB_9 cluster. We investigate the charge population and nature of bonding of these clusters through NBO (Natural Bond Orbital). The results show that charges on the Mg atoms are positive,while those on the B atoms are mostly negative. The interaction between atoms shows that some B atoms form π bonds through sp hybrid orbits, other B atoms form bonds through s, p orbits, while Mg atoms form bonds through s orbits. Additionally, some size-dependent electronic properties of the clusters are also discussed.