A Density Functional Study of the Gold Cages Mau16 (M=Si, Ge, And

ISSN: 0256-307X 中国物理快报 Chinese Physics Letters Volume 30 Number 7 July 2013 A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://iopscience.iop.org/0256-307X http://cpl.iphy.ac.cn C HINESE P HYSICAL S OCIET Y Institute of Physics PUBLISHING CHIN. PHYS. LETT. Vol. 30, No. 7 (2013) 077102 * A Density Functional Study of the Gold Cages MAu16 (M = Si, Ge, and Sn) TANG Chun-Mei(/Sr)**, ZHU Wei-Hua(Á¥u), ZHANG Ai-Mei(张Or), ZHANG Kai-Xiao(张m骁), LIU Ming-Yi(4²熠) College of Science, Hohai University, Nanjing 210098 (Received 20 March 2013) Relativistic density functional calculations are performed to explore the promise of MAu16(M=Si, Ge, and Sn) clusters as magic clusters and building blocks in developing cluster-assembled materials. C1 and Cs, two isomers of SiAu16, GeAu16 and SnAu16 with M (Ge or Sn) at the center of the cage, named, respectively, as SiAu16–C1, SiAu16–Cs, GeAu16-center, and SnAu16-center, are calculated to be the most stable. The Au–M bond should have both ionic and covalent characteristics. Their static linear polarizabilities and first-order hyperpolarizabilities are found to be sensitive to the delocalization of the valence electrons of the M atom, as well as their structures and shapes. PACS: 71.20.Be, 31.15.xw, 36.40.Cg DOI: 10.1088/0256-307X/30/7/077102 − Au16 is a hollow cage with a slightly distorted sets including d polarization functions (DNP) that are ** tetrahedral (Td) symmetry, and has a sufficiently large comparable to Gaussian 6-31G basis sets. Relativis- [1] − internal volume. The diameter of the Au16 cage is tic calculations are performed with scalar relativistic about 5.5 Å, suggesting possible endohedral doping to corrections to valence orbitals relevant to the atomic form a new class of gold cages with tailored proper- bonding properties via a local pseudopotential.[13] ties similar to endohedral fullerenes.[2] There is much The electronic structures are obtained by solving the − [14] research on Au16 clusters doped by many kinds of Kohn–Sham (KS) equations self-consistently. Nat- atoms.[3−5] Common to these previous studies is the ural bonding orbital (NBO) analyses are made to compliance to the electron counting rule,[6] a key fac- obtain the effective charges on each atom, and the tor in the high stability of gold-based clusters. self-consistent field procedures are carried out witha Recently, Wang et al.[7] reported on the photoelec- convergence criterion of 106 a.u. on the energy and tron spectra (PES) and theoretical studies of doping a electron densities. Geometry optimizations are per- − group IV atom into the Au16 cage, and found that the formed by the Broyden–Fletcher–Goldfarb–Shanno dopant atom was exohedral (Ge, Sn) or became part algorithm[15] with a convergence criterion of 103 a.u. 5 of the gold cage (Si), i.e., Cs and C1, two symmetric on the displacement and 10 a.u. on the energy. We − − isomers for SiAu16 and SnAu16, and one Cs isomer confirm the stability of the lowest energy structure as − [8] for GeAu16. Later, Sun et al. discovered that the the minima of the potential energy surface by con- outer surface of the neutral Au16 cage was more reac- sidering vibrational frequency. There is no imaginary tive for Si doping than its interior, similar to the case frequency for the structures reported here. for the gold bulk. In this Letter, we will investigate In this study, first we simply choose the structures [7] the MAu16 (M = Si, Ge, and Sn) clusters, and aim to given by Wang et al. as the initial configurations for answer the following questions. (1) Can the electron the neutral MAu16 (M=Si, Ge, and Sn) and the cor- counting rule be adopted to study the stabilities of responding cationic and anionic structures to explore MAu16 (M = Si, Ge, and Sn)? (2) What are the low- their stabilities. These structures are, respectively, est energy structures of the MAu16 (M = Si, Ge, and signed SiAu16-C1, SiAu16-Cs, GeAu16-Cs, SnAu16-C1, Sn) clusters? (3) What are the electronic properties and SiAu16-Cs. It is found that Si is near two neigh- and polarizabilities of the most stable MAu16 (M = Si, boring triangular facets, while Ge and Sn are outside Ge, and Sn) structures? the center of a four-membered ring in a hexagonal. We 3 [9] We use the DMol program to perform density compare the Eg of the five neutral SiAu16-C1, SiAu16- [10] functional theory (DFT) calculations for all the Cs, GeAu16-Cs, SnAu16-C1, and SiAu16-Cs structures, clusters. The Perdue Burke Ernzerh (PBE) of the as well as those of their corresponding cationic and [11] functional, based on the generalized gradient ap- anionic structures. The Eg, defined as the energy proximation (GGA)[12] method, is chosen. The ba- gap between the highest occupied molecular orbital sis sets used in this work are double numerical basis (HOMO) and the lowest unoccupied molecular orbital *Supported by the Qing Lan Project, the National Natural Science Foundation of China under Grant Nos 11104062 and 10947132, the ‘333 High-Level Talent Cultivation Project’ Special Foundation of Jiangsu Province, the China Postdoctoral Science Foundation under Grant No 20100471307, the Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No 1001001C, the Excellent Innovation Personal Support Plan of Hohai University, and the Fundamental Research Funds for the Central Universities under Grant No 2012B12914. **Corresponding author. Email: [email protected] © 2013 Chinese Physical Society and IOP Publishing Ltd 077102-1 CHIN. PHYS. LETT. Vol. 30, No. 7 (2013) 077102 (LUMO), is a useful quantity for examining the ki- gle faces (one is the triangle in a hexagon and the netic stabilities of clusters. A large Eg corresponds other is the additional triangle between two neighbor- to the high energy required for electron excitation.[16] ing hexagons). Here, we put the M atom, respec- The calculated Eg of the neutral MAu16 (M = Si, Ge, tively, at the center of the cage, inside or outside and Sn) are in agreement with that shown in their of the cage symmetric to two atoms, at the bridge [7] PES. Moreover, the neutral MAu16 (M = Si, Ge, and centers of two kinds of bonds, and at the face cen- + Sn) have larger Eg than those of MAu16 (M = Si, Ge, ters of two kinds of faces. Additionally, the C1 or and Sn) and MAu16 (M = Si, Ge, and Sn), indicating Cs isomers for MAu16 (M=Si, Ge, and Sn) proposed [7] that the neutral MAu16 (M = Si, Ge, and Sn) are the by Wang et al. are also taken into consideration. most kinetically stable. This can be understood by Therefore, a total of 14 or 15 different isomers for [4] the jellium model. The clusters with 2, 8, 18, 20, MAu16 (M=Si, Ge, and Sn) are optimized to explore 40, 58,::: valence electrons show pronounced intensi- the most stable location for the M. It is found that ties in the mass spectra, and thus they are called magic M at six different sites inside the cage all shift to clusters. According to the electronic configuration of the center cage after optimization, and the C1 and the Au atom, the Au16 cluster should have 16 valence Cs isomers are still the most stable for SiAu16. As electrons considering only the 6s electron, and corre- for GeAu16 and SnAu16, the structures with M at the + spondingly, MAu16, MAu16, and MAu16 should have center of the cage have the lowest energy. In order total electrons of 20, 19, and 21, respectively. There- to ensure that the calculated DFT result is reliable, fore, we suggest that the neutral MAu16 (M = Si, Ge, we also perform a global-minimum search for the low- and Sn) are magic clusters and promising as building est energy MAu16 (M=Si, Ge, and Sn) clusters. We blocks in developing novel cluster-assembled materi- employ basin-hopping global-optimization, which has als. Furthermore, removing an electron from MAu16 been previously used to search for low-lying anionic will lead to a significant drop in the stability, result- gold clusters[17] and bimetallic mixed clusters.[18] The ing in a high vertical ionization potential (VIP). To global-minimum search results also confirm the most the contrary, adding an electron to MAu16 will lead stable isomers for MAu16 (M=Si, Ge, and Sn). There- to a small energy release and result in a low vertical fore, Si, Ge, and Sn all prefer to be enclosed inside the electron affinity (VEA). Au16 cage. As we know, the atomic radius of M is in In order to find out the most stable structures for the order Sn>Ge>Si, and thus the Si with the small- MAu16 (M = Si, Ge, and Sn), we next put the M atom est radius can shift more easily to the off-center site, at different sites and take these doped structures into causing the remarkable distortions in the Au16 cage. the calculation. It has been reported that Td-Au16 is However, the Ge and Sn with larger radii can only lo- the smallest gold cage, and has an empty interior with cate at the center of the Au16 cage. Therefore, SiAu16 [9] a diameter of 5.5 Å, four equilateral triangles, and has a different ground-state structure from16 GeAu four regular hexagons. Thus, there are two kinds of and SnAu16. We rename GeAu16-1 and SnAu16-1 as atoms (one is in the hexagon and the other in the GeAu16-center and SnAu16-center.

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