密度泛函理论研究Zr_n(n=2—16)团簇的基态结构及其稳定性

Ground-state structures and stabilities of Zr_n(n=2—16) clusters studied with density-functional theory

从第一性原理出发,利用密度泛函理论中的广义梯度近似(GGA)对Zrn(n=2—16)团簇进行了结构优化、能量和频率计算.在充分考虑自旋多重度的前提下,对每一具体尺寸的团簇,得到了多个平衡构型,并根据能量高低确定了团簇的基态结构.综合团簇的结合能、离解能、二阶能量差分以及团簇的最高占据轨道(HOMO)和最低未占据轨道(LUMO)间的能隙可知Zr2,Zr5,Zr7,Zr13和Zr15比其他团簇的稳定性高.Zr13团簇的结构是具有Ih对称性的正二十面体,而且Zr13的稳定性在所有团簇中是最高的.

The geometries,total energies,and frequencies of Zrn（n=2—16） clusters have been systematically investigated by using density functional theory with the generalized gradient approximation.The equilibrium geometries for different spin multiplicities as well as the ground-state structures have been determined.The calculated results on the averaged binding energy, fragmentation energy, second-order difference of cluster energies as well as the HOMO-LUMO gap of the Zrn（n=2—16） clusters indicate that the relative stabilities of Zr2,Zr5,Zr7,Zr13 ,Zr15 are stronger than clusters of other sizes. The true ground state for Zr13 cluster has icosahedral structure with Ih symmetry,and the stability of Zr13 is the strongest of all the investigated clusters.