中文摘要：

金纳米团簇（Aum）由于其特殊的几何结构和独特的物理化学性质近年来引起了人们的广泛关注。本文运用密度泛函理论系统研究了Aun（n=2—60）团簇的结构和电子性质。研究结果表明，A‰在原子数n≤13时为平面结构，n=14，15时开始由二维结构向三维结构过渡，Au20转变为金字塔结构。之后，随着团簇尺寸的增大，Aun分别经历了类金字塔结构、双层扁平结构、中空笼状结构、密堆积结构和富勒烯结构等，并逐渐向核壳层结构、面心立方结构及堆垛错层结构等演变，当n〉32时，具有奇数原子的Aun结构主要以堆垛层错结构的稳定构型存在。通过对金团簇的平均结合能、二阶能量差分和前线轨道能级差等随Aun尺寸的变化趋势的计算和分析，发现偶数原子的Aun比邻近的奇数原子的Aun团簇更稳定，且在这些团簇中，Au20，Au32,Au58等团簇表现出特殊的稳定性，具有一定的幻数效应。该研究结果将为Aun构效关系的理解和研究及其应用结构的设计等提供重要的理论依据和数据参考。

英文摘要：

The gold nano-clusters （Au,） have attracted increasing attentions due to the special geometric structures and unique physical and chemical properties in recent years. The structures and electronic properties of Aun （n=2-60） are explored by density functional theory in the present work. The results show that Au, prefer to be in two-dimension planar structures when n≤13, and the transformation from two-dimensional structure to three-dimensional structure occurs at n=14, 15. Furthermore, Au20 adopts a pyramid structure and subsequently the Au, have experienced the pyramid-like structure, the double-layer structure, the hollow cage structure, the compact structure, the fullerene-like structure, and gradually evolute to the core-shell structure, the face-centered cubic and stacking fault structure with the increasing of Au atomic number. Moreover, Aun with odd atoms mainly exist in stacking fault struc- ture when n〉32. It is also found that Au20, Au32, Au58 exhibit special stability and have a certain magic number effect by analyzing the variations of the average binding energy, the second order energy difference and the energy gap of frontier molecular orbitals of Aun with the number of Au atom growth. In addition, Au, with the even atoms are steadier than that with the odd atoms. The results of this work can provide important theoretical reference and data support for understanding and researching of the Aun structure-properties relationship, and designing of the Aun application structure.