Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil.
Phys Chem Chem Phys. 2011 Oct 14;13(38):17242-8. doi: 10.1039/c1cp21233h. Epub 2011 Aug 30.
The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation--LDA) and semilocal (generalized gradient approximation--GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA+U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA+U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.
过渡金属（TM）的晶体结构已经被人们了解了几十年，然而，我们对于 TM 团簇的原子结构的认识仍然远远不够，这妨碍了我们对 TM 团簇反应性的原子水平理解。例如，几乎所有 TM 团簇的密度泛函理论（DFT）计算都是基于局域（局域密度近似-LDA）和半局域（广义梯度近似-GGA）交换关联泛函，然而，众所周知，单纯的 DFT 无法纠正自相互作用误差，这会影响到几个系统的性质。为了提高我们对 TM 团簇原子和电子性质的基本认识，我们报告了两种非局域泛函（即 Heyde、Scuseria 和 Ernzerhof 的杂化 HSE 和 GGA+U 泛函）对 Co(13)、Rh(13)和 Hf(13)团簇的结构和电子性质的 DFT 研究。对于 Co(13)和 Rh(13)，我们发现改进的交换关联泛函降低了开放式结构（如六边形双层（HBL）和双简单立方（DSC））相对于紧凑的二十面体（ICO）结构的稳定性，然而，DFT-GGA、DFT-GGA+U 和 DFT-HSE 对于 Hf(13)得到了非常相似的结果。因此，我们的结果表明，通过几种单纯 DFT 计算得到的 Rh(13)的 DSC 结构可以通过使用改进的泛函来改进。通过 sd 杂化分析，我们发现强杂化有利于紧凑结构，因此，sd 杂化的正确描述对于相对能量稳定性至关重要。例如，对于 Co(13)和 Rh(13)，HBL 和 DSC 的 sd 杂化减少，而 ICO 的 sd 杂化增加，而对于 Hf(13)，所有构型的 sd 杂化都减少，因此，它不会影响开放式和紧凑式构型之间的相对稳定性。
