Icosahedral Au clusters with three and four shells of atoms are found to deviate significantly from the commonly assumed Mackay structures. By introducing additional atoms in the surface shell and creating a vacancy in the center of the cluster, the calculated energy per atom can be lowered significantly, according to several different descriptions of the interatomic interaction. Analogous icosahedral structures with five and six shells of atoms are generated using the same structural motifs and are similarly found to be more stable than Mackay icosahedra. The lowest energy per atom obtained here is for clusters containing 310, 564, 928 and 1426 atoms, as compared with the commonly assumed magic numbers of 309, 561, 923 and 1415. Some of the vertices in the optimized clusters have a hexagonal ring of atoms, rather than a pentagon, with the vertex atom missing. An inner shell atom in some cases moves outwards by more than an Ångström into the surface shell at such a vertex site. This feature, as well as the wide distribution of nearest-neighbor distances in the surface layer, can strongly influence the properties of icosahedral clusters, for example catalytic activity. The structural optimization is initially carried out using the GOUST method with atomic forces estimated with the EMT empirical potential function, but the atomic coordinates are then refined by minimization using electron density functional theory (DFT) or Gaussian approximation potential (GAP). A single energy barrier is found to separate the Mackay icosahedron from a lower energy structure where a string of atoms moves outwards in a concerted manner from the center so as to create a central vacancy while placing an additional atom in the surface shell.

中文翻译：

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重新分配二十面体 Au 簇的幻数：310、564、928 和 1426

发现具有三个和四个原子壳的二十面体 Au 簇明显偏离通常假设的 Mackay 结构。根据对原子间相互作用的几种不同描述，通过在表面壳层中引入额外的原子并在簇中心产生空位，可以显着降低计算出的每个原子的能量。具有五个和六个原子壳的类似二十面体结构是使用相同的结构基序生成的，并且同样被发现比 Mackay 二十面体更稳定。与通常假设的幻数 309、561、923 和 1415 相比，此处获得的每个原子的最低能量是包含 310、564、928 和 1426 个原子的簇。优化后的簇中的一些顶点具有六边形环原子，而不是五边形，缺少顶点原子。在某些情况下，内壳原子在这样的顶点位置向外移动超过 Ångström 进入表面壳。这一特征，以及表面层中最近邻距离的广泛分布，可以强烈影响二十面体簇的性质，例如催化活性。最初使用 GOUST 方法进行结构优化，使用 EMT 经验势函数估计原子力，然后使用电子密度泛函理论 (DFT) 或高斯近似势 (GAP) 通过最小化来细化原子坐标。