A DFT based prediction of gold fullerene Au₉₂Si₁₂ with the aid of silicon

Abstract

Structural evolution of the gold Bucky ball Au₉₂Si₁₂ has been studied via a systematic investigation of Au_nSi clusters within the framework of DFT with spin-polarized generalized gradient approximation (GGA). Beginning with low energy isomers of Au_n (n = 1–16), we find that Si, being hypervalent, can attach onto the Au cluster in more than one valence configuration, leading to several possible geometrical arrangements of surrounding Au atoms. One such geometry has a Au–Si unit dangling over a quasi-planar arrangement of gold atoms. It is observed that a pentagonal unit of gold atoms attached with a Au–Si dangling unit can only exist in the presence of other neighbouring gold atoms to present a quasi-planar cluster. By repeating such quasi-planar clusters, a stable geometry of golden Bucky ball Au₉₂Si₁₂ with a binding energy per atom (E_b/n) of 3.814 eV and a HOMO–LUMO gap (E_g) of 0.6 eV has been optimized. The current work suggests the exciting possibility of a golden Bucky ball that has the same rotational symmetry as the C60 molecule with a much larger volume.

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Introduction

At the nanoscale, gold clusters have attracted considerable attention owing to their unique electronic and optical properties, as well as for their potential medical applications. Biocompatible gold nanostructures have reportedly found possible applications in photothermal therapy, radiotherapy and imaging of cancerous tissue.^1–11 Free Au_n clusters exhibit a variety of fascinating geometrical structures, e.g. planar structures for n = 3 to 12, anionic cages for n = 16 to 18, bulk-fragment pyramidal structures for n = 19 to 23, possible tubular cages for n = 24 and 26 (ref. 11b) and a gold fullerene at n = 32. The tetrahedral isomers of Au₁₆⁻ and Au₁₇⁻ were the first to be experimentally¹² confirmed as small gold cages and Au₃₂ was first suggested to be a “24-carat golden fullerene.”^13,14 The large empty space inside the cage clusters immediately suggested that they can be doped with a foreign atom to produce a new class of endohedral gold cages analogous to endohedral fullerenes, which are expected to have potential medical applications owing to their biocompatibility and large cage volume that may facilitate encapsulation of biomolecules and drugs.

It is well known from a large number of previous studies that impurity atoms strongly influence the geometric, electronic, and structural properties of doped gold clusters that are sensitive towards the nature of the dopant atom. Wang et al.¹⁵ studied a series of doped gold anion clusters, Au₁₆M⁻ (M = Si, Ge, Sn), and found that the global minima were dominated by the strong M–Au interactions, reminiscent of the Au₁₄M cluster. Au_nSi⁻ has a tetrahedral coordinated Si with an Au–Si dangling unit, resembling that of the larger Si doped gold cluster Au₁₆Si⁻, while Au_xM⁻ (M = Ge, Sn) have quasi-planar structures based on square-pyramid motifs. With the exception of sulfur, p-electron (M = Al, Si, P) doped gold clusters yield nonplanar geometries for Au₅M, while those doped with s-electrons (Na, Mg) yield planar geometries.¹⁶ Zhang et al.¹⁷ have systematically investigated the properties of doped clusters Au₆M (Al, Si, P, S and Cl), with the exception of the argon atom, doping enhances the binding strength of these clusters in comparison to Au₇. Wang et al.¹⁸ have systematically investigated the electronic and structural properties of the doped clusters Au₁₆M⁻ (M = Ag, Zn, In) by photoelectron spectroscopy and theoretical calculations and they found that the dopant atom does not significantly perturb the electronic and atomic structure of Au₁₆⁻, but simply donates its valence electrons to the parent Au₁₆⁻ cage.

Doping of Au_n clusters with Si is of particular interest and the Au–Si interface has been studied extensively owing to its importance in microelectronics. Sun et al.¹⁹ have examined the stability of Au₁₆Si endohedral clusters and found that Si atoms prefer to bind to the exterior surface of the Au₁₆ cage. Au₁₆Si clusters may no longer be viewed as 20-electron closed-shell systems in the sense of the Jellium model and should rather be considered as 16-electron systems because four electrons are needed for the local Au–Si bonding. This is consistent with the fact that Group IV elements tends to make covalent bonds. Particularly for Si and Ge, Kiran et al.²⁰ reported experimental and theoretical evidence that a series of Si–Au clusters [SiAu_n, n = 2–4] are structurally and electronically similar to SiH_n. Walter et al.²¹ have performed DFT studies on the endohedral doping of the Au₁₆ cage by Al or Si and observed that the O₂ molecule adsorbed over the Au₁₆Si cluster is activated to a superoxo-species.

Though several measurements and much theoretical research have examined the properties of Au_nSi clusters, there remain some open questions, such as how can silicon be incorporated into nano gold, what would be the effect of dopant Si atoms on the doped clusters with increase of cluster size, how the enhancement of doping concentration would influence the Au cage structure, and can we expect quasi-planar Au–Si clusters by increasing the doping concentration, which may lead to the design of new hybrid Au–Si nanostructures for potential applications in microelectronics, catalysis, and jewellery making.

With the objective to find answers to the above questions, in the current work we doped Au_n gold clusters with silicon atoms starting from n = 1 to n = 16 and obtained a large number of geometric isomers. One geometrical arrangement that attracted our attention was a Au–Si dangling unit over a gold pentagon surrounded by neighbouring gold atoms, which had quasi-planar structure. These quasi-planar isomers are the genuine minima on the potential energy surface and eventually led us to a stable gold cage. The present study provides evidence of a stable Si doped gold nanocluster, Au₉₂Si₁₂, which may be designated as a gold fullerene with enhanced functionality and a large cage volume in comparison to C₆₀.

Computational method

The geometry optimizations were carried out within the framework of DFT with spin-polarized generalized gradient approximation (GGA)²² implemented with Gaussian-03 code.²³

The accuracy and reliability of the PW91 functional for small gold clusters has been verified in earlier studies.²⁴ Previously reported^25–27 global minima of Au_n (n = 1–14) clusters, which are known to be planar geometries, were used for Si atom doping. The initial geometries were prepared by placing a Si atom as a cap on the possible sites of low energy 2D isomers of the Au_n (n = 1–14) clusters. Beyond this, the initial geometries (for n = 15 and 16) were generated by extending the quasi-planar isomer of Au₁₄Si by adding one and two gold atoms, respectively. We investigated a large number of isomers of Au_nSi clusters in the size range n = 1–13 and to the best of our knowledge the isomers reported here are the lowest energy ones. However, beyond n = 13, other low energy isomers in the size range studied here are reported in the literature. This work does not contradict them and focuses on a quasi-planar arrangement of Au atoms including either tetrahedral or square-planar local arrangements around the dopant Si atom. Although such structures are not the global minima, they are the genuine minima on the potential energy surface as confirmed by frequency analysis. The main objective of this study is to demonstrate the evolution of a golden Bucky ball of 92 Au atoms with the help of Si atoms via the formation of quasi-planar silicon doped gold clusters. The triplet-valence basis set 6-311++g(d) was used for the Si atoms, while a Stuttgart/Dresden SDD²⁸ basis set was adopted for the Au atoms. Frequency analyses have also been performed at the same level of theory, PW91/SDD at default spin, to ensure that all the reported isomers are the genuine minima on the potential energy surface.

The geometry optimization of the predicted Au₉₂Si₁₂ golden cage was performed using DFT formalism as implemented in VASP.²⁹ The total-energy calculation was carried out based on the plane-wave expansion method employing scalar relativistic ultra-soft pseudo potentials and the spin-polarized version of the generalized gradient approximation (GGA) for exchange and correlation. A simple cubic cell of 15 Å dimension with the γ point for the Brillouin-zone integration was considered for these calculations. The geometries are considered to be converged when the force on each ion becomes 0.01 eV Å⁻¹ or less. The cut-off energy for the plane-wave basis set was 300 eV. The total-energy convergence was tested with respect to the plane-wave basis set size and simulation cell size, and the total energy was found to be accurate to within 1 meV. This cage molecule needs verification in future experiments as well as calculation at an enhanced level of accuracy to determine its useful properties.

Results and discussion

Optimized geometries of various isomers of Au_nSi

Based on the optimized lowest energy structures of pure gold clusters, we carried out an extensive lowest energy structure search on silicon doped medium sized gold clusters. The fully optimized geometries of the Au_nSi (n = 1–16) clusters, including some low-lying geometric isomers with higher energies, are depicted in Fig. 1.

Fig. 1 The lowest energy structures of optimized isomers of Au_nSi clusters. The isomers are designated by na–nd, where n represents the number of Au atoms in the Au_nSi cluster and a–d rank the isomer in descending order of binding energy. ΔE represents the relative energy of an isomer with respect to the lowest energy isomer.

The excellent agreement of our calculated parameters for Au₂ (bond length (BL): 2.55 Å and binding energy per atom (E_b/n): 1.09 eV per atom) as well as AuSi (bond length (BL): 2.28 Å and binding energy per atom (E_b/n): 1.64 eV per atom) with previously reported experimental and theoretical values^30,31 established faith in the accuracy of the employed method and the reliability of the atomic pseudo-potentials used in this work.

Table 1 presents the binding energy per atom (E_b/n) and HOMO–LUMO gap (E_g) of pure gold (Au_n) and silicon doped gold clusters Au_nSi. In all the optimized geometries of the Au_nSi clusters, silicon prefers to occupy the most highly coordinated position (see Fig. 1). This observation is concordant with the fact that Si is well known to exhibit hypervalency. Consequently, doping the Au_n clusters with Si results in early 3D onset geometry relative to pure Au_n clusters. It has been reported that small gold clusters doped with impurity elements possessing p-electrons adopt 3D structures due to sp³ hybridization,¹⁶ while doping with transition metals induces planar structures.^32–35

Table 1 Binding energy per atom (E_b/n) and HOMO–LUMO gap (E_g) of pure gold clusters (Au_n) and silicon doped gold clusters (Au_nSi) with PW91/SDD for Au and 6-311++G(d) for Si

Cluster	Symmetry	Energy (in a.u.)	Eb/n (in eV)	Eg (in eV)
Au2	C1	−271.68299	1.09	2.04
(Au2Si) 2a	C2v	−561.16878	1.94	1.81
2b	Cs	−561.13278	1.60	0.40
Au3	C2v	−407.52958	1.13	2.10
(Au3Si) 3a	Cs	−697.06531	2.10	2.00
3b	D3h	−697.05971	2.06	1.25
3c	C1	−697.03805	1.91	0.87
Au4	C2v	−543.41941	1.45	0.96
(Au4Si) 4a	Td	−832.97586	2.27	2.02
4b	C4v	−832.96825	2.23	2.11
Au5	C2v	−679.2997	1.59	0.87
(Au5Si) 5a	Cs	−968.8265	2.11	0.76
5b	C4v	−968.8057	2.02	0.54
Au6	D3h	−815.2104	1.82	2.14
(Au6Si) 6a	CS	−1104.7222	2.18	1.63
6b	C2v	−1104.7192	2.16	1.41
Au7	Cs	−951.0678	1.78	1.26
(Au7Si) 7a	Cs	−1240.5971	2.15	1.30
7b	Cs	−1240.58986	2.13	1.42
7c	Cs	−1240.58389	2.11	0.65
Au8	D4h	−1086.96915	1.90	1.54
(Au8Si) 8a	Cs	−1376.48048	2.17	0.61
8b	Cs	−1376.46608	2.12	1.32
8c	C4v	−1376.45870	2.09	0.75
Au9	C2v	−1222.8364	1.88	0.87
(Au9Si) 9a	Cs	−1512.36956	2.19	0.84
9b	C1	−1512.3503	2.13	0.85
Au10	D2h	−1358.73812	1.97	1.32
(Au10Si) 10a	Cs	−1648.26052	2.21	1.03
10b	Cs	−1648.25394	2.19	1.36
Au11	Cs	−1494.6119	1.55	1.10
(Au11Si) 11a	C1	−1784.1332	2.19	0.42
11b	C1	−1784.1319	2.18	1.01
Au12	D3h	−1630.51568	2.04	0.97
(Au12Si) 12a	C1	−1920.02117	2.20	0.75
12b	C1	−1920.01706	2.19	0.64
12c	C2v	−1919.98455(img freq. = 1)	2.12	0.47
Au13	C1	−1766.38596	2.02	0.30
(Au13Si) 13a	Cs	−2055.91299	2.22	0.92
13b	C1	−2055.90439	2.20	0.63
Au14_a	C2v	−1902.29955	2.08	1.57
(Au14Si) 14a	C1	−2191.81375	2.25	0.84
14b	C1	−2191.80713	2.24	1.19
14c	C1	−2191.79908	2.22	0.62
14d	C1	−2191.79693	2.21	0.59
14e	C1	−2191.75525(img freq. = 1)	2.14	0.92
Au15	C1	−2038.17735	2.09	0.77
(Au15Si) 15a	C1	−2327.69106	2.23	1.13
15b	C1	−2327.67568	2.21	0.72
Au16	Cs	−2174.07615	2.13	1.25
(Au16Si) 16a	Cs	−2463.60072	2.28	1.06
16b	Cs	−2463.58702	2.25	0.79
16c	C1	−2463.58280	2.25	0.87
16d	C2	−2463.52569	2.16	0.84
Au16Si3	C2	−3042.51667	2.34	0.86

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The hetro-diatomic Au–Si has a bond length of 2.27 Å, smaller than that of Au₂ (2.56 Å) and in good agreement with the available experimental result (2.26 Å).³⁶ The lowest energy isomer of the Au₂Si cluster (2a) forms an isosceles triangle. The next highest-energy isomer, i.e. 2b, is a linear structure. The lowest energy structure of Au₃Si, 3a, is a capped triangle. The two other planar isomers, 3b and 3c, are 0.15 eV and 0.74 eV higher in energy than the lowest energy isomer. The most stable geometry of Au₄Si, 4a, has a tetrahedral configuration.³⁷ The other isomer that has been optimized, 4b, has a square pyramidal structure and is 0.21 eV higher in energy than the tetrahedral 4a. The Au₄Si cluster exhibits the highest binding energy among all the clusters. The lowest energy configuration of Au₅Si favors a top capped square prism with C_s symmetry. The lowest energy isomers of Au₆Si and Au₇Si prefer to have a tetra-coordinated Si atom and penta-coordinated Si for the low lying geometric isomers with higher energy. In contrast to this, the lowest energy isomers of Au_nSi (n = 8–13) exhibit hexa-coordinated silicon and tetra-coordinated Si for the low lying geometric isomers. All the lowest energy isomers, 8a–13a, of Au_nSi (n = 8–13) have the dangling Au–Si unit over a curved sheet of gold pentagons and are regarded as quasi-planar isomers. This structural preference is owing to the hypervalent character of silicon atoms. It is noteworthy that the recurring unit, hexa-coordinated Si with a gold pentagon, is not stable by itself and requires gold atoms in the neighbourhood for its existence. This view point is supported by the Au₆Si structures. In these clusters the gold pentagon with the Si–Au dangling unit could not be optimized as the lowest energy minima (the same is true for Au₇Si cluster) due to the lack of the neighbouring Au atoms required for its stability. In the case of Au₈Si, the structure 8a consisting of a gold pentagon with a Au–Si unit is the lowest energy structure in comparison to the other isomeric structures (8b and 8c, see Fig. 1). The preference for this geometrical pattern continues for all the larger sizes studied here. The higher stability of hypervalent isomers suggests that Au–Si interactions dominate the Au–Au interactions up to this size.

The caged structure of pure Au_n clusters beyond the size n = 13 is well reported. The exo and endohedral doping of Si in the Au₁₄ cage led to collapse of the gold cage with Si residing on the cluster surface (14a and 14b, see Fig. 1). Out of the five optimized geometries of Au₁₄Si, 14a–14d are confirmed as stable isomers, while 14e is a metastable geometry with an imaginary frequency. Quasi-planarity is clearly perceived in the 14c isomer, which has a Au–Si dangling unit with a gold pentagon surrounded by the neighbouring gold atoms.

In the case of Au₁₅Si, two optimized structures have been obtained. The input geometry for 15a is generated by the exohedral doping of Si in the Au₁₅ cage. This input geometry was optimized to a distorted cage with Si residing over the surface of the cluster. For 15b, the input was generated by adding one gold atom to the bridging gold site of 14c and on optimization a stable structure was obtained (see Fig. 1). It also has a dangling Au–Si unit on the surface of a fourteen gold atom cluster.

Four optimized structures have been obtained for the Au₁₆Si cluster. The structure 16c has a pentagonal unit of gold atoms with a Au–Si dangling unit surrounded by neighbouring gold atoms. Though this is one of the low energy isomers, the lowest energy structure has a distorted cage of Au₁₆ with Si residing over the surface of the cage. It is pertinent to mention here that for Au_nSi clusters beyond size n = 13, caged structures are the lowest energy structures on the energy scale. Nonetheless, the quasi-planar Si doped Au_nSi (n = 1–16) structures are permissible with the Au–Si unit on the top of a pentagonal Au₅ unit that needs to be supported by neighbouring gold atoms.

For n = 1–13, the lowest energy structures are quasi-planar isomers. This implies that Au–Si interactions are dominant over Au–Au interactions. However, beyond this size, i.e. for n = 14–16, it has been found that caged structures are the lowest energy structures in comparison to the quasi-planar isomers (low energy lying isomers). This implies that in large sized Au_nSi clusters (n = 14–16), Au–Au interactions dominate over the Au–Si interactions and the effect of the dopant atom decreases with increase in cluster size. In this context, it is interesting to see the effect of enhancing the number of silicon dopant atoms in the Au_n clusters. For this purpose, two symmetrically bent tips of 16d were doped with two Si atoms and the input geometry was designated as Au₁₆Si₃_initial (see Fig. 2). The optimized geometry, i.e. Au₁₆Si₃_final, shows that the silicon atoms lift the two bent tips of 16d and instead of inducing a curve in the planar geometry of the pure gold cluster, the silicon atoms make the cluster more planar. It is encouraging to notice that with a larger number of silicon atoms, the binding energy per atom (E_b/n) increased (see Table 1). Since the amount of Si doped is crucial to the curvature induced in the gold clusters, we limit the dopant concentration up to one Si atom in 16 atoms of gold.

Fig. 2 Initial and final geometry of the Au₁₆Si₃ cluster.

Following the trend of the lowest energy isomers of Au_nSi (n = 1–13), the low energy quasi planar isomers of Au_nSi (n = 14–16) also contain hexa-coordinated Si with a gold pentagon that is not stable by itself, as shown by stability analysis of the Au₆Si structures. These quasi-planar isomers are one of the local minima.

It is thus established that the Au–Si dangling unit plays an important role in stabilising a quasi-planar sheet of gold atoms and the pentagonal unit of Au must have some neighbouring gold atoms. The geometry of this quasi-planar configuration is reminiscent of curvature introduced in a hexagonal graphene sheet by the presence of a pentagon. Moreover, when such pentagons are repeated regularly, the resultant structure is a closed cage, e.g., C₆₀, C₈₀, C₁₂₀ etc. Encouraged by this observation we generated the coordinates of golden Bucky ball Au₉₂Si₁₂ (see Fig. 3) parallel to the structure of C₆₀ (consistent with the above stability criteria) and on optimization we obtained a stable geometry with a binding energy per atom (E_b/n) of 3.814 eV and a HOMO–LUMO gap (E_g) of 0.6 eV. This gold Bucky ball has a beautiful symmetric structure. In exception to the fullerene, this ball has twelve dangling units, which further enhance the stability of the ball structure. Consequently we can say that our results establish that gold Bucky ball Au₉₂Si₁₂ is one of the low lying energy isomers, if not the global minimum. The size of the system is prohibitive in exploring other structural arrangements of Au₉₂Si₁₂ clusters that may have some gold packed atoms. However our stability analysis confirms that this Bucky ball Au₉₂Si₁₂ is thermodynamically stable and this ball obeys the same rotational symmetries as the C₆₀ molecule (I₅). Similar to C₆₀, this molecule has no two pentagons sharing a bond. The diameter of the golden cage is 13.77 Å compared to 7.1 Å for C₆₀. The Au atom on any dangling unit may provide a site for functionalization by a variety of organic or inorganic units.

Fig. 3 Optimized geometry of the gold fullerene Au₉₂Si₁₂.

Energy and stability

Based on the lowest energy structures, the relative stabilities of Au_nSi and Au_n (n = 1–16) are discussed in terms of binding energies per atom, which are expressed as:

where E(Au_nSi), E(Au_n+1), E(Au) and E(Si) are the total energies of the ground state Au_nSi, Au_n+1, Au and Si, respectively. The binding energies of the Au_n+1 and Au_nSi clusters as a function of the total number of atoms present in the cluster are plotted in Fig. 4. This illustrates that as the cluster size grows, the contribution to E_b from Au–Si (Au–Au) interactions increases. The binding energy for Au_nSi is significantly higher than the binding energy of Au_n clusters (see Table 1). The additional energy is due to stronger interactions between the Au and Si atoms. Although the E_b/n of the Au_nSi clusters are higher than those of Au_n+1, the difference becomes smaller for larger sizes, indicating that the influence of impurity decreases as the number of gold atoms increases. It can be found that the E_b/n curves of the Au_nSi and Au_n+1 clusters increase noticeably from n = 1 to n = 4, then the values show a smooth growing tendency in the cluster size range of n = 5–16.

Fig. 4 The binding energies per atom (E_b/n) for Au_n and Au_nSi clusters are plotted against cluster size.

The relative stability order in a series of clusters can be illustrated more emphatically through the second-order energy difference as a function of cluster size, as shown in Fig. 5. The second difference in energy for clusters may be calculated as,

Δ₂E(n) = [E(n − 1) + E(n + 1) − 2E(n)]

Fig. 5 Second-order difference of energies for Au_nSi and Au_n clusters plotted against cluster size.

In cluster physics, the quantity Δ₂E(n) is commonly known to represent the relative stability of a cluster of size n with respect to its neighbour. Also Δ₂E(n) can be directly compared to the experimental relative abundance: the peaks in Δ₂E(n) are known to coincide with the discontinuities in the mass spectra.³¹ In view of second-order difference of energies, positive values of Δ₂E(n) mean that the clusters are particularly stable.

It is found that the stability patterns of Au_n and Au_nSi clusters follow a trend of odd–even oscillations. Au_n at even numbers and Au_nSi clusters at n = 4, 6, 10, and 14, correspond to a higher stability compared to the neighbour. Therefore we can conclude that even-numbered clusters are more stable than odd-numbered clusters. The particularly large positive values of Δ₂E(n) for Au₆ and Au₄Si further establish their particular stability in the series of clusters.

The stabilities of these clusters were also analyzed by examining fragmentation energies. Here, we consider two fragmentation channels involving either a Au atom or a Si atom. The fragmentation energies for a neutral Au_nSi cluster are calculated as

Δ²E(Au_nSi) = E(Au_nSi) − [E(Au_n−1Si) + E(Au)]

Fig. 6 shows the fragmentation energies for the Au_nSi clusters with respect to Au and Si atoms. It is found that Δ¹ ≥ Δ² for all n, thus implying that the interaction of Si atoms with the Au_n clusters is energetically more favorable than Au atoms, which is in agreement with the lower bond length of Au–Si than Au–Au. It is noticed that the curves have obvious even–odd oscillations, as previously seen in the binding energy plot.

Fig. 6 Size dependence of the fragmentation energy (eV) of Au_nSi (n = 1–16) clusters via loss of a Si atom and a Au atom.

The highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) gap is related to chemical reactivity, systems with larger HOMO–LUMO gaps being less reactive. The HOMO–LUMO gaps of the lowest energy structures of the Au_nSi and Au_n clusters versus cluster size is plotted in Fig. 7. Both Au_nSi and Au_n clusters follow the odd–even oscillatory trend. The particularly high HOMO–LUMO gaps for Au₄Si and Au₆ clusters establish the particular stability of these cluster sizes.

Fig. 7 Size dependence of the HOMO–LUMO gap of Au_nSi (n = 1–16) clusters.

Conclusions

We have reported the structural evolution of gold Bucky ball Au₉₂Si₁₂ via formation of a quasi-planar arrangement of Au_n−1 clusters with Au–Si dangling units. The structure, stability and effect of doping Si in gold Au_n (n = 1–16) clusters is investigated by DFT calculations. Doping of Au_n clusters by Si leads to an overall improvement in the binding of the Au_n clusters, as the energies of Si doped gold (Au_nSi) clusters are lower than those of pure gold Au_n clusters. In all the optimized geometries of Au_nSi (n > 7), a pentagon of gold atoms attached with a dangling Au–Si unit is present. Interestingly, this pentagonal unit with the Au–Si dangling unit cannot exist independently and requires the presence of neighbours to support quasi-planarity. We conclude that the Au–Si dangling unit on the planar sheet of Au_n−1 atoms plays a major role in stabilizing the quasi-planar gold cluster, and this led to the idea of optimization of a closed Si doped nanocluster, Au₉₂Si₁₂, that may be designated as a gold fullerene. The theoretical prediction of a Au₉₂Si₁₂ Bucky ball made in the present study paves the way for researchers for its experimental realization and further theoretical investigation.

Acknowledgements

SG is thankful to the Council of Scientific and Industrial Research (CSIR, New Delhi) with award ref. no. 20-6/2009(i) EU-IV dated 30.12.2009 for the Senior research fellowship.

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