The ground state configurations of phosphorus clusters, P_n (n = 20–36), were investigated by using the comprehensive genetic algorithm combined with the first-principles calculation method. The medium sized phosphorus structures are assembled with small subunits P₁, P₄, P₆, P₇, P₈, and P₁₀, which are jointed by a P₂ dimer. These phosphorus clusters can be divided into three groups by the subunit number, i.e. P₂₀ with two, P_21–30 with three, and P_31–36 with four subunits, respectively. All the P_n clusters in the third group can be regarded as adding a P₈ subunit and a P₂ dimer to the corresponding clusters P_n−10. The binding energy per atom and the HOMO–LUMO gap show distinct odd–even oscillations. It was found that the even-sized clusters are more stable than the odd-sized ones. All the atoms of the even-sized clusters are threefold, while the odd-sized clusters always have only one twofold atom in P₁ or P₇ unit. For larger sized P_n clusters with 38 ≤ n ≤ 78, we compared the configurations consisting of pure P₈ units and mixed P₈ and P₁₀ units. Clusters with mixed P₈ and P₁₀ units are always energetically favorable.

中文翻译：

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从头算全局搜索到中等大小的磷团簇（P 20 –P 36）的结构演变

利用综合遗传算法结合第一性原理计算方法，研究了磷团簇的基态结构P _n（n = 20–36）。中型磷结构由小的亚基P ₁，P ₄，P ₆，P ₇，P ₈和P ₁₀组装而成，这些亚基通过P ₂二聚体连接。这些磷簇可以按亚基数分为三组，分别是P ₂₀具有两个亚基，P _21–30具有三个亚基和P _31–36具有四个亚基。所有P _n第三组中的簇可以被认为是将P ₈亚基和P ₂二聚体添加到相应的簇P _n-10。每个原子的结合能和HOMO-LUMO间隙显示出明显的奇偶振荡。发现偶数大小的簇比奇数大小的簇更稳定。偶数簇的所有原子都是三倍原子，而奇数簇的P ₁或P ₇单元中始终只有一个两倍原子。对于38≤n≤78的较大尺寸的P _n簇，我们比较了由纯P ₈单元以及混合P ₈和P ₁₀单元组成的配置。混合P _8的簇P ₁₀单位始终在能源方面有利。