Fisicaro Giuseppe, Schaefer Bastian, Finkler Jonas A, Goedecker Stefan
Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi (CNR-IMM), Z.I. VIII Strada 5 I-95121 Catania Italy
Department of Physics, University of Basel, Klingelbergstrasse 82 CH-4056 Basel Switzerland.
Mater Adv. 2023 Feb 28;4(7):1746-1768. doi: 10.1039/d2ma01088g. eCollection 2023 Apr 3.
In this work we study isomers of several representative small clusters to find principles for their stability. Our conclusions about the principles underlying the structure of clusters are based on a huge database of 44 000 isomers generated for 58 different clusters on the density functional theory level by Minima Hopping. We explore the potential energy surface of small neutral, anionic and cationic isomers, moving left to right across the third period of the periodic table and varying the number of atoms and the cluster charge state (X , with X = {Na, Mg, Al, Si, Ge}, = -1, 0, 1, 2). We use structural descriptors such as bond lengths and atomic coordination numbers, the surface to volume ratios and the shape factor as well as electronic descriptors such as shell filling and hardness to detect correlations with the stability of clusters. The isomers of metallic clusters are found to be structure seekers with a strong tendency to adopt compact shapes. However certain numbers of atoms can suppress the formation of nearly spherical metallic clusters. Small non-metallic clusters typically also do not adopt compact spherical shapes for their lowest energy structures. In both cases spherical jellium models are not any more applicable. Nevertheless for many structures, that frequently have a high degree of symmetry, the Kohn-Sham eigenvalues are bunched into shells and if the available electrons can completely fill such shells, a particularly stable structure can result. We call such a cluster whose shape gives rise to shells that can be completely filled by the number of available electrons an optimally matched cluster, since both the structure and the number of electrons must be special and match. In this way we can also explain the stability trends for covalent silicon and germanium cluster isomers, whose stability was previously explained by the presence of certain structural motifs. Thus we propose a unified framework to explain trends in the stability of isomers and to predict their structure for a wide range of small clusters.
在这项工作中，我们研究了几个具有代表性的小团簇的异构体，以找出它们稳定性的规律。我们关于团簇结构基本原理的结论基于一个庞大的数据库，该数据库包含通过最小跳跃法在密度泛函理论水平上为58个不同团簇生成的44000个异构体。我们探索了小型中性、阴离子和阳离子异构体的势能面，从周期表的第三周期从左到右移动，并改变原子数量和团簇电荷状态（X ，其中X = {Na, Mg, Al, Si, Ge}， = -1, 0, 1, 2）。我们使用键长和原子配位数、表面积与体积比以及形状因子等结构描述符，以及壳层填充和硬度等电子描述符来检测与团簇稳定性的相关性。发现金属团簇的异构体是结构探寻者，具有强烈的采用紧凑形状的倾向。然而，一定数量的原子可以抑制近球形金属团簇的形成。小型非金属团簇通常也不会为其最低能量结构采用紧凑的球形形状。在这两种情况下，球形电子气模型都不再适用。尽管如此，对于许多通常具有高度对称性的结构，科恩 - 沈（Kohn-Sham）本征值会聚集成壳层，如果可用电子能够完全填充这些壳层，就会形成特别稳定的结构。我们将这样一种团簇称为最佳匹配团簇，其形状会产生可以被可用电子数量完全填充的壳层，因为结构和电子数量都必须特殊且匹配。通过这种方式，我们还可以解释共价硅和锗团簇异构体的稳定性趋势，其稳定性此前是通过某些结构基序的存在来解释的。因此，我们提出了一个统一的框架来解释异构体稳定性的趋势，并预测广泛的小型团簇的结构。
