Stabilization of golden cages by encapsulation of a single transition metal atom

Golden cage-doped nanoclusters have attracted great attention in the past decade due to their remarkable electronic, optical and catalytic properties. However, the structures of large golden cage doped with Mo and Tc are still not well known because of the challenges in global structural searches. Here, we report anionic and neutral golden cage doped with a transition metal atom MAu16 (M = Mo and Tc) using Saunders ‘Kick' stochastic automation search method associated with density-functional theory (DFT) calculation (SK-DFT). The geometric structures and electronic properties of the doped clusters, MAu16q (M = Mo and Tc; q = 0 and −1), are investigated by means of DFT theoretical calculations. Our calculations confirm that the 4d transition metals Mo and Tc can be stably encapsulated in the Au16− cage, forming three different configurations, i.e. endohedral cages, planar structures and exohedral derivatives. The ground-state structures of endohedral cages C2v Mo@Au16−-(a) and C1 Tc@Au16−-(b) exhibit a marked stability, as judged by their high binding energy per atom (greater than 2.46 eV), doping energy (0.29 eV) as well as a large HOMO–LUMO gap (greater than 0.40 eV). The predicted photoelectron spectra should aid in future experimental characterization of MAu16− (M = Mo and Tc).


Introduction
Nanoclusters display many new properties, which are usually not found in their bulk counterparts [1][2][3]. These novel properties can be attributed almost to strong relativistic effects and finitesize quantum effects [4,5]. Gold clusters, in particular, have received special attention due to their potential technological applications as in the fabrication of materials in catalysis [6][7][8][9][10][11], chemical/biological sensors [12], medical sciences [13] and so forth. As the geometry of the cluster is closely related to its properties, an understanding of the cluster geometry is of primary interest. It is very important to identify their geometric structures for the controlled use of clusters in future nanotechnology. In the past couple of decades, both gold clusters and gold cluster doping with impurity atoms of alkali metal or transition metal have attracted the attention of theoreticians and experimentalists working in the field of cluster science [14][15][16][17][18][19][20][21][22][23][24][25][26]. The results of the previous investigations indicate that the introduction of a transition metal dopant atom in the gold cluster can change its structure and electromagnetic properties significantly [22][23][24]. In particular, photoelectron spectroscopy (PES) in combination with density-functional theory (DFT) calculations [27] revealed that the ground-state structure of the Au 16 cluster anion has a highly stable hollow cage with a large internal volume similar to that of fullerenes [28]. This feature leads to the possibility of forming a new class of golden cages with particular properties by endohedral doping similar to those of the endohedral fullerenes. Subsequently, the investigation of doping one guest atom into the Au 16 − cage has prompted immediate extensive interest by both theorists and experimentalists with purpose to design novel endohedral gold-caged clusters, as the chemical and physical versatility can be exploited by tuning the structural and electronic properties of gold clusters [29][30][31][32][33][34]. The most recent ab initio calculations showed the gold-covered bimetallic clusters M@Au n (n = 8-17) with closed-shell structures obeying the 18-electron rule and starting from n = 9 the doped-metal atom prefers to be entirely covered by pure gold atoms to form the lowest energy structure [29]. Subsequently, a series of doped gold anion clusters MAu 16 − (Ag, Zn, In and Cu) have been systematically studied using PES experiment and theoretical calculations by Wang et al. [18,19]. It is found that Ag, Zn and In can all be doped inside the Au 16 − cage with little structural distortion. Similar to Cu, they transfer their valence electrons to the golden cage and form endohedral charge transfer complexes. However, in contrast to a previous theoretical prediction on MAu 16 − (Ag, Zn, In and Cu), the doping Au 16 − cluster with a Si, Ge or Sn atom led to completely different structures, forming exohedral structure where the tetrahedral golden cage is completely distorted due to the strong M-Au local interactions [30]. Many physical chemists have made many efforts to deal with the global optimization of clusters using automated procedures [35][36][37][38]. For example, Car & Parrinello's [35] well-known 'dynamic simulated annealing' combines molecular dynamics (MD) and DFT. Shayeghi et al. [36] present an approach for the global optimization of monoatomic or binary clusters. Very recently, a global optimization technique, using neural network potentials combined with the basin-hopping method, to study medium-sized metal clusters was proposed by Jiang et al. [39,40]. Up to now, Au 16 cluster and golden cage Au 16 doping with impurity atoms of 3d transition metal and alkali metal have attracted the attention of researchers in both theoretical and experimental studies devoting themselves to working in cluster science [16,[18][19][20][21][22][23]. In a recent study, we have provided the first theoretical evidence of endohedral doping of the golden cages by the early 4d transition metals Y, Zr and Nb in Au 16 − cage [24].  [41] combined with DFT calculation (SK-DFT). Recently, we have successfully employed the SK-DFT method for global minimum searches of relatively small clusters, and provided a comprehensive analysis of the ability of current methods to determine the geometry of the ground state of clusters [42][43][44][45][46]. The specific objectives of this work are fourfold: (1) to identify structures of the lowest-energy/low-lying clusters using a global optimization method coupled with DFT calculation; (2) to provide useful information for MAu 16  performed using SK-DFT with previously experimental findings on the host golden cage and some other 3d and early 4d transition metal atoms-doped gold clusters; (4) to characterize the stability of the lowestenergy clusters by computing their binding energy per atom, doping energy and the highest occupied and lowest unoccupied molecular orbit (HOMO-LUMO) gap. At this stage, although other energetically more favourable structures could not be ruled out strictly, we believe that the lowest-energy structures of MAu 16 q found here are at least powerful candidates for their ground states, which are hoped to be verified in the future photoelectron spectroscopy experiments and calculations at more accurate levels of theory. This work should be interesting for future material physicists and chemists, especially those designing new materials.

Computational methods
The structure prediction of MAu 16 q (M = Mo and Tc; q = 0, -1) clusters is based on the Saunders 'Kick' stochastic automation search method [41] combined with density-functional theory calculation (SK-DFT) which has been successfully applied in the structural prediction of a number of cluster systems [22][23][24][42][43][44][45][46]. All the mixed atoms, including 16 gold atoms and a single transition metal atom (Mo and Tc), are placed at the same point initially and then are 'kicked' randomly within a size-controlled hollow sphere with a radius R for avoiding biasing search. The kick size (radius R) in the hollow sphere is 15 Å in this work. The kick method runs at the PBEPBE/LANL2DZ ('PBEPBE' functional [47] with a scalar relativistic effective core potential (RECP) and LANL2DZ basis set [48]) level up to 800 times until no new minima appeared. Afterwards, the top several isomers approximately 0.3 eV from each minimum at the PBEPBE/LANL2DZ level were all regarded as potential candidate lowest-energy structures to be further reoptimized and evaluated with the larger basis set. As no symmetry constraints are imposed, the geometries obtained should correspond to minima. The reoptimization and evaluation used PBEPBE exchange-correlation functional with the large basis set Au/SDD+2f /M/ECP28MWB, followed by vibrational frequency calculations. Here, 'SDD+2f' denotes the Stuttgart/Dresden RECP valence basis [49,50] augmented by two sets of f polarization functions (exponents = 1.425, 0.468) for Au, and 'ECP28MWB' denotes the Stuttgart contracted pseudo-potential basis set for 4d transition metal atom M (M = Mo and Tc) [51,52]. All calculations were performed using the Gaussian 09 package [53]. The accuracy of PBEPBE/Au/SDD+2f /M/ECP28MWB level of theory was validated using five exchange-correlation functionals (PBEPBE [47], B3LYP [54], BP86 [55,56], PW91 [57] and TPSS [58]) with the same RECP valence basis SDD+2f on pure gold clusters Au 16 q (q = 0, -1). The first ADE and vertical detachment energy (VDE) are calculated and photoelectron spectra are also simulated. Furthermore, to quantitatively compare simulated spectrum with the experimental spectrum [18,27], we calculate the root-mean-square deviation (RMSD) for the labelled peaks X ∼ C [18]. Comparing the calculated first ADE/VDE, RMSD and simulated photoelectron spectra with measured results by PES experiment for the Au 16 − , PBEPBE/SDD + 2f level of theory gives very good agreement with the experimental observations (table 1 and figure 1), and, therefore, the same level has been selected as the method of choice for MAu 16 q (Mo and Tc; q = 0, -1) species also. Here, the first ADE is determined by calculating the energy difference between the optimized anion geometry and the optimized neutral geometry. The first VDE is defined as the energy difference between the neutral clusters at optimized anion geometry clusters and optimized anion clusters. Then, the first VDE is added to the orbital energies of the deeper occupied orbitals to obtain VDEs of the higher detachment channels. The VDEs so obtained are fitted with a full width at half-maximum (FWHM) of 0.09 eV to yield the simulated spectra, which are used to compare with the experimental spectra. This method has been used successfully in a number of previous studies and has been shown to yield VDEs in good agreement with experimental photoelectron spectra [59][60][61][62][63][64].

Results and discussion
Two important types of structures A/B, simulated photoelectron spectra of Au 16 − for structures A/B using five different functionals (B3LYP, BP86, PBE, PW91 and TPSS) in comparison with experimental photoelectron spectra [27] for host gold cluster Au 16 − are shown in figure 1. Table 1     a Shown are the spin multiplicity (SM), symmetry type (Sym), total energy (E T , a.u.), the relative energy ( E, eV), calculated first adiabatic/vertical detachment energy (ADE/VDE, eV), and the RMSD (eV). b References [18] and [27].

Geometric structure and stability
For the neutral and anionic host cluster Au 16 , we present two important types of structures: a perfect cage D 2d structure A and a high symmetric planar C 2v structure B. It is somewhat surprising that anionic structure A is 0.042 eV above the planar structure B at PBEPBE/SDD+2f level of theory; however, calculated first ADE and VDE of structure A are in accord with experimental PES data [18,27]   In order to compare the degree of structural change of structure A under different point group symmetry, we calculate the average bond length. The results show that the average bond length of anionic Au 16   the study of gold clusters, which has been confirmed by the study in the pure golden clusters Au n − (n = 16-18) [27].
One of the most important questions that we want to address here is to discover the lowest-energy structures of the MAu 16 − clusters. We have obtained many isomers and determined the lowest-energy       figure 3). Especially, isomers a and b are found to be degenerated in energy at PBEPBE/LANL2DZ level, while isomers a and d are found to be nearly degenerated in energy at PBEPBE/Au/SDD+2f /M/ECP28 MWB. Keeping in mind the inherent accuracy of the DFT, we could not exclude the probability of four isomers by DFT calculations. It is necessary to compare their simulated photoelectron spectra with the experimental photoelectron spectra. Unfortunately, without the experimental photoelectron spectra for TcAu 16 − cluster, we only provide theoretical photoelectron spectra in the present work. In order to compare the various local minimum structures with other 3d or 4d transition metal atom doping, we also present the first three planar shape isomers and two exohedral structures. The first three two-dimensional (2D) planar local minimum structures possess high symmetry by SK-DFT at PBEPBE/Au/SDD+2f /M/ECP28MWB level. As seen from figure 2, the two 2D structures g and i have a relatively high symmetry C 2v , which are less stable than the ground-state structure a by 1

Photoelectron spectroscopy and detachment energy
The first ADE is determined by calculating the energy difference between the optimized geometry of the anionic cluster and the optimized neutral cluster as the initial point at the anion geometry. Single-point energies of the neutral clusters are also computed based on the same optimized anion geometry. The difference in the energy of the anion and neutral cluster gives the first VDE. We examined 11 low-lying isomers by energies from the PBEPBE/Au/SDD+2f /M/ECP28MWB level, including six endohedral cages (isomers a-f), three plane structures (isomers g-i) and two exohedral doping (isomers j-k), but only one candidate (isomer a) for MoAu 16