[BxAl13-x]-(x=0～13)二元团簇的密度泛函理论研究

doi:10.6023/A16050230

摘要/Abstract

采用遗传算法（Genetic algorithm，GA）对B-Al二元团簇[B_xAl₁₃_-_x]^-（x=0～13）进行了全局结构搜索，并在密度泛函理论（Density Functional Theory，DFT）下对其进行了优化计算. 结果表明在二元团簇中，随着硼原子的数量逐渐增加，团簇的结构由二十面体（3D）逐渐转化为准平面（2D）且团簇结构由B与Al原子的比例所决定的. 当x=0～7时，Al原子占多数，团簇保持3D结构；反之团簇呈现2D构型；在x=7～8时，团簇的结构发生由3D向2D的转变. 能量决定着团簇的稳定性（例如相对能量）. 能量越小，其结构越稳定. 在计算相对能量E_rel，当x=1时，其相对能量最低，团簇结构最稳定. 为了进一步了解团簇的稳定性，计算了[B_xAl₁₃_-x]^- 团簇的HOMO-LUMO能级差（E_H-L）和垂直电离能（Vertical Detachment Energies，VDE），并且发现它们的值在整体上是随着B原子数量的增加而减小，表明其团簇的稳定性逐渐减弱. 在所有的团簇中，BAl₁₂^-的能级差最大，结构最稳定. 因此文章中对其进行了分子轨道分析，发现当一个B原子替代了Al₁₃^-团簇中的中心Al原子时，所得到的BAl₁₂^-的电子壳层结构的1s²和1p⁶几乎和Al₁₃^-团簇保持一致. 此外，对于x=13时的准平面全硼团簇B₁₃^-，文章中用适应性自然密度划分（Adaptive Natural Density Partitioning，AdNDP）对其化学成键进行了分析，结果显示B₁₃^-有8个π电子，具有π反芳香性.

关键词: 密度泛函理论, [B_xAl₁₃_-x]^- (x=0～13)团簇, 优化, 分子轨道, 适应性自然密度划分

In this paper, the global minimum search and structural optimization for the B-Al binary clusters [B_xAl₁₃_-_x]^- (x=0～13) are performed using the genetic algorithm (GA) method coupled with density functional theory (DFT). The effects of composition on the atomic structures, electronic properties including the energy gaps and vertical detachment energies of B-Al binary clusters are discussed. The results distinctly reveal a three dimensional (3D) to (quasi-)planar (2D) structural transition as a function of x upon increasing the number of boron atoms. When x is in the range of 0 to 7, the clusters are Al-rich and the B-Al binary systems maintain the 3D structure. Whereas, the binary system trends to be quasi-planar structure, and the critical B:Al ratios for the 2D-3D transition are between x=7 and 8. To study the stability of the [B_xAl_13-x]^- clusters, we defined the relative energy (E_rel=E([B_xAl₁₃_-x]^-)-xE(B₁₃^-)/13–yE(Al₁₃^-)/13), where the cluster with a more negative E_rel is more stable. At x=1, E_rel is the most negative, indicating the highest stability. In order to further understand the stability of clusters, the vertical detachment energies (VDE) and the HOMO-LUMO energy gaps (E_H-L) of [B_xAl₁₃_-_x]^- (x=0～13) clusters are also calculated. The results show that the energy decreases with the increasing number of B atoms, indicating a lower stability. The largest E_H-L of BAl₁₂^- cluster indicates that it is the most stable among all the series of this clusters. Molecular orbitals (MO) of BAl₁₂^- cluster are analyzed and the result shows that the electronic shells of 1s² and 1p⁶ are virtually unchanged when the central Al atom is replaced by the B atom. It also indicates that the electron shell closing model could be regarded as a simple but valid tool for explaining the structures and stabilities of metal clusters. Chemical bonding analysis by Adaptive Natural Density Partitioning (AdNDP) method for the B₁₃^- cluster reveals that it is a π-antiaromatic system with 8 delocalized π-electrons.

Key words: density functional theory, [B_xAl₁₃_-x]^- (x=0～13) clusters, optimization, molecular orbitals, adaptive natural density partitioning

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黄敏, 徐畅, 程龙玖. [B_xAl₁₃_-x]^-(x=0～13)二元团簇的密度泛函理论研究[J]. 化学学报, 2016, 74(9): 758-763.

Huang Min, Xu Chang, Cheng Longjiu. Density Functional Theory Studies of the Binary Systems[B_xAl₁₃_-x]^- (x=0～13)[J]. Acta Chim. Sinica, 2016, 74(9): 758-763.

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[B_xAl₁₃_-x]^-(x=0～13)二元团簇的密度泛函理论研究

Density Functional Theory Studies of the Binary Systems[B_xAl₁₃_-x]^- (x=0～13)

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