A family of lead clusters with precious metal cores

Gold nanoparticles have been used for centuries, both for decoration and in medical applications. More recently, many of the major advances in cluster chemistry have involved well-defined clusters containing tens or hundreds of atoms, either with or without a ligand shell. In this paper we report the synthesis of two gold/lead clusters, [Au8Pb33]6− and [Au12Pb44]8−, both of which contain nido [Au@Pb11]3− icosahedra surrounding a core of Au atoms. Analogues of these large clusters are not found in the corresponding Ag chemistry: instead, the Ag-centered nido icosahedron, [Ag@Pb11]3−, is the only isolated product. The structural chemistry, along with the mass spectrometry which shows the existence of [Au2Pb11]2− but not [Ag2Pb11]2−, leads us to propose that the former species is the key intermediate in the growth of the larger clusters. Density functional theory indicates that secondary π-type interactions between the [Au@Pb11]3− ligands and the gold core play a significant part in stabilizing the larger clusters. Many Zintl ions with a single endohedrally encapsulated transition metal ion are known, but relatively few where clusters of two or more metals are present. Here, the authors report the synthesis and characterization of two clusters, [Au8Pb33]6− and [Au12Pb44]12−, which contain Au8 and Au12 cores surrounded by Pb shells.

G old clusters have long held the attention of chemists, in part because of their often spectacular highly symmetric geometries but also because they have recently found applications in medicine and nanotechnology 1,2 . At one extreme are the naked clusters [Au x ] +/0/− which have been studied using a variety of gas-phase spectroscopies 3 while at the other, thiolatesupported clusters with ever-increasing dimensions continue to emerge. Amongst these, Kornberg's Au 102 (S-C 6 H 4 -COOH) 44 and the recently reported Au 279 (S-C 6 H 4 -t Bu) 84 "Faradaurate-279" are particularly striking examples of how a spherical core of gold atoms can be stabilized by di-, tri-and tetrameric anionic 'staple ligands', RS(AuSR) n (n = 1, 2, 3) which constitute a protective 'mantle' around the cluster 4,5 . Häkkinen and colleagues have coined the term 'divide and protect' to describe the way that the gold content is separated into a zero-valent Au 0 core and monovalent Au + -containing thiolate 'staples', formally anionic 4electron donor ligands that bind to two atoms of the core via lone pairs on the terminal sulfur atoms 6 . At the core of many of these clusters, it is possible to identify high-symmetry Au x units, perhaps the most prominent being the 8-electron [Au 13 ] 5+ icosahedron, found, for example, in [Au 25 (S-C 6 H 4 -COOH) 18 ] − and also in phosphine-ligated systems such as [Au 13 Cl 2 (PMe 2 Ph) 10 ] 3+ 7,8 . Mingos' theoretical work has shown that the relationship between structure and electron count in these and other gold clusters can be understood in terms of overlap of radially directed s/d z 2 hybrids on each gold atom 9,10 . This model accounts elegantly for the approximately spherical geometries of [Au 4 (P t Bu 3 ) 4 ] 2+ (1S 2 ) and [Au 13 Cl 2 (PMe 2 Ph) 10 ] 3+ (1S 2 1P 6 ) as well as the prolate and oblate distortions found in [Au 6 (PPh 3 ) 6 ] 2+ (1S 2 1P 2 ) and [Au 7 (PPh 3 ) 7 ] + (1S 2 1P 4 ), respectively [11][12][13] . Clusters with 8 gold atoms, in contrast, tend to adopt rather less symmetric structures, such as the 'core + exo' geometries of [Au 8 (dppp) 4 ] 2+ and [Au 8 (dppp) 4 X 2 ] 2+ , X=Cl − , PhC≡C − (Fig. 1) where an octahedral Au 6 core is capped by two 'exo' gold atoms 14,15 , or the highly distorted cube reported recently for [Au 8 (PPh 3 ) 8 ] 2+ 13 .
In contrast to the well-established chemistry of gold clusters with thiolate or phosphine ligands, there has been only one previous report of a Zintl-ion cluster containing gold, that being the approximately icosahedral 62-electron [Au@Pb 12 ] 3− reported by some of us in 2017 16 . The wider family of endohedral lead clusters also includes 60-electron [M@Pb 12 ] q− (M=Ni, Pd, Pt, q = 2, M=Co, Rh, Ir, q = 3) and 58-electron [Mn@Pb 12 ] 3−17-21 . The 60electron count has 'magic' status in this family, and also in the analogous clusters of Sn, simply because it corresponds to closedshell configurations at both M (d 10 ) and the closo [Pb 12 ] 2− cage (4n + 2 = 50 where n is the number of vertices), and indeed the empty [Pb 12 ] 2− cage has itself been identified as a stable entity in the gas phase. Smaller lead cages are also known; for example homometallic [Pb 10 ] 2− and its nickel-centered analogue [Ni@Pb 10 ] 2− have both been isolated in the solid state while the heavier group 10 analogues [M@Pb 10 ] 2− (M=Pd, Pt) have been detected in gas-phase experiments 17,22,23 Fig. 2, is an approximately C 5v -symmetric nido-icosahedron, with the Ag center encapsulated by the Pb 11 cluster (the encapsulation is indicated by the "@" in [Ag@Pb 11 ] 3− ). The Ag-Pb bond lengths to the apical Pb (Pb1 in Fig. 2) and the five Pb atoms of the open face (Pb7-11 in Fig. 2) are all~3.01 Å while the distances to Pb2-6 are somewhat longer at 3.09 Å. The Pb-Pb bond lengths vary between 3.15 and 3.30 Å, and are very similar to those reported for the closo clusters [M@Pb 10 ] 2− and [M@Pb 12 ] 2−/3− discussed in the introduction [16][17][18][19][20][21][22][23] . The characteristic valence electron count of 48 (4n + 4) for a nido 11-vertex polyhedron 28 demands a charge of 4-on the Pb 11 cluster, consistent with the presence of an Ag ion in the +1 oxidation state (i.e., d 10 ). Whilst 1 is the only crystalline product obtained from this reaction, the ESI mass spectrum of the reaction mixture ( Supplementary  Fig. 12 Fig. 3. It is immediately striking that the Au and Pb content of the clusters is segregated, with an inner Au x core surrounded by an outer Pb y shell, an observation that is consistent with the low miscibility of the two metals. A closer inspection shows that the two clusters share many common features: both are constructed from Au-centered Pb 11 nido-icosahedra (Au@Pb 11 ) similar to those found in 1, surrounding a core of Au atoms, Au 5 [3,5] and [4,8] members, respectively. The four Au@Pb 11 nido-icosahedra in 3 are remarkably similar to each other, and also to the isolated [Ag@Pb 11 ] 3− cluster: the Pb-Pb bond lengths vary between 3.149 (2) and 3.340(2) Å, slightly longer, on average, than those in typical [M@Pb 12 ] n− units (3.10-3.20 Å) and the eleven Au-Pb distances vary between 2.969(2) and 3.174(2) Å. Corresponding values in [Au@Pb 12 ] 3− lie in the range 3.030(9)-3.093(4) Å 16 . The approximately cubic Au 8 core in [Au 12 Pb 44 ] 8− is shown from two perspectives in Fig. 4a. The Au-Au bond lengths are in the range 2.8941(19)-2.943(2) Å, broadly comparable to those in   (2)-2.821(2) Å between the endohedral Au (Au1-4) and the Au atom that completes the icosahedral surface (Au5-8). We refer to these four Au atoms as the 'surface' Au for this reason. The interactions between the Au 8 cube and the nido-icosahedra are not, however, restricted to the four surface Au atoms directly bound to the open pentagonal faces of the nido icosahedra. There are also numerous secondary contacts between the Pb atoms of the icosahedra and the four Au atoms of the Au 8 cube that are not bonded directly to the open faces (Au9-12 in Fig. 4-we refer to these as the 'capping' Au atoms). These secondary interactions are shown as dashed red lines in Fig. 4b. The precise bond lengths depend critically on the conformation of the icosahedra, but it is clear that each capping Au atom has secondary contacts at~3.6 Å with Pb centers on all three neighboring icosahedra and also that each icosahedron has secondary contacts with all three adjacent capping Au atoms (Fig. 4, lower panel). Whilst these secondary interactions are~0.5 Å longer than the Au-Pb bonds within the icosahedra, they are sufficiently short and sufficiently numerous to play a significant part in maintaining the integrity of the cluster, as we will show in the subsequent analysis of the electronic structure.
The [Au 8 Pb 33 ] 6− cluster in 2 is rather less symmetric than 3, but the icosahedral Au@Pb 11 units in the two clusters are very similar. Moreover, the structure of the Au 6 Pb 22 fragment (containing Au1,3,4,6,7 and 8 in Figs. 3 and 4) resembles very closely one half of the [Au 12 Pb 44 ] 8− cluster found in 3: the Au-Au distances are in the region of 2.9 Å and the secondary interactions between the Pb atoms and the two bridging Au atoms are again apparent. This structural relationship suggests that [Au 8 Pb 33 ] 6− can be formulated as a "dimer + monomer" wherein an ([Au@Pb 11 ] 2 )(Au 4 ) unit (the [2,4] member of the [m,n] series) coalesces with an additional icosahedral Au@AuPb 11 cluster (the [1, 1] member) to form the [3,5] cluster. The Au@AuPb 11 icosahedron bridges the Au 4 unit of the [2,4] fragment in an η 2 fashion, via both the surface Au atom, Au5, and one of the adjacent Pb atoms, Pb20. The Au4-Au5 bond is, at 2.7609(12) Å, the shortest Au-Au bond in either 2 or 3, while the Pb20-Au6 distance of 3.4098(12) Å is shorter than any of the other secondary interactions. As a result of this strong secondary interaction, Pb20 is pulled out of the icosahedral surface, leading to four unusually long Pb-Pb bonds between 3.30 and 3.40 Å.
The ESI mass spectrum of the solution from which 3 is isolated ( Supplementary Fig. 9) offers some support for the proposal that an Au 2 Pb 11 cluster is a common intermediate in the coalescence of the larger clusters. The parent ions of 2 and 3 lie outside the accessible window for ESI mass spectrometry, but the low-mass region (below m/z = 3200) shows prominent peaks due to a number of smaller fragments, the most intense of which are [AuPb 10    Based on a combination of the structural and ESI mass spectroscopic data, we can speculate on possible mechanistic pathways that control cluster growth (Fig. 5). The nidoicosahedron [M@Pb 11 ] 3− has been structurally characterized for M = Ag and a cluster with the same composition has been observed as a prominent peak in the mass spectrum for M = Au. It seems reasonable, therefore, to propose [Au@Pb 11 3,5]). In support of this hypothesis, we have observed that heating an isolated sample of 2 for 3 h at 60°C leads to the formation of 3, presumably via de-coordination of the bridging icosahedron followed by coalescence of two dimer units ( Supplementary Fig. 8). A plausible alternative cluster growth pathway might involve the bonding of multiple copies of the fundamental ligand unit, [Au@Pb 11 ] 3− , to pre-formed [Au 5 ] 3+ and [Au 8 ] 4+ clusters to generate 2 and 3, respectively. We have, however, found no evidence to support the formation of such large naked gold clusters under the prevailing reaction conditions, so we favor the simpler scheme below where the Au@AuPb 11 unit, for which there is experimental evidence, is the common intermediate. In either case, the identity of the dominant isolated product will necessarily be very sensitive to the concentrations of free Au, and so, inevitably, to subtle variations in temperature and solvent polarity.
Electronic structure analysis. In order to gain further insight into the bonding in the anionic clusters in 1, 2 and 3, and the possible pathways that lead to their formation, we have turned to density functional theory. In  where the relatively high symmetry simplifies the interpretation of the electronic structure. The cluster in the crystal is approximately D 2d symmetric, but small deviations inevitably arise due to the low symmetry of the crystalline environment. We have, therefore, adjusted the coordinates to impose strict D 2d symmetry in a structure that is closest, in a least-squares sense, to the geometry of the cluster in the crystal (see Supplementary  Fig. 16 for details). Given the overestimation of Pb-Pb bond lengths that we encountered for the tri-anionic [Ag@Pb 11 ] 3− cluster, we have made no attempt to further optimize the structure of [Au 12 Pb 44 ] 8− . Single point calculations on the D 2dsymmetrized structure indicate the presence of a near degenerate triplet of orbitals, e + b 2 , in the frontier region, over which two electrons are distributed (Fig. 7). The near degeneracy arises because the Au 8 core is not strongly distorted from a perfect tetrahedron, in which limit the e + b 2 manifold correlates with triply degenerate t 2 . By distributing two electrons over these three orbitals we can converge on two triplet states, 3 A 2 and 3 E, (e 2 and e 1 b 1 configurations, respectively) and a closed-shell singlet ( 1 A 1 , b 2 2 ), all of which lie within 0.03 eV. Given the well-documented limitations of DFT in identifying ground-state multiplicities 33,34 , these energies are too close to allow for a definitive conclusion on the ground spin state of [Au 12 Pb 44 ] 8− . The following analysis is based on the singlet, although very similar features emerge in the other two low-lying states. The bond orders for the Au-Au and Au-Pb bonds within the individual icosahedra are very similar to those in the isolated [Au@AuPb 11 ] 2− fragment (~0.06 and 0.13-0.16, respectively). Perhaps more surprisingly, bond orders for the Au-Au bonds within the Au 8 cube are also small (0.09-0.13), and in fact are of similar magnitude to the secondary Au-Pb interactions between the icosahedra and the capping Au atoms alluded to previously (0.08-0.11). Given the large number of these secondary interactions (on average, 3 per capping Au atom, 3 per icosahedron, Fig. 4), it seems likely that they are more influential in determining the structure than direct Au-Au bonding. This might account for the very different structure adopted by the [Au 8 ] 4+ core in 2 compared to the bicapped octahedral in [Au 8 (dppp) 4 X 2 ] 2+ 15 , where Au-Au bonding is clearly the dominant structural influence.
A schematic molecular orbital diagram where the cluster is decomposed into four nido [Au@Pb 11 ] 3− ligands and an approximately cubic [Au 8 ] 4+ core is presented in Fig. 7. The calculations were performed in D 2d symmetry, and a full analysis is presented in the Supplementary Figs. 16 and 17 and Supplementary Table 8, but for the sake of clarity we find it convenient here to adopt the symmetry labels of the higher T d point group. The frontier region for the [Au 8 ] 4+ fragment can be understood in terms of the interactions of 8 s/d z 2 hybrids, which generate bonding and antibonding linear combinations, a 1 /a 1 * and t 2 /t 2 *. The bonding a 1 orbital is strongly stabilized and doubly occupied, and this pair of electrons is primarily responsible for the integrity of the Au 8 unit in [Au 8 ] 4+ and also in 3 itself. The remaining two valence electrons then occupy the t 2 orbital, driving a first-order Jahn-Teller instability which accounts for the slight distortion of the Au 8 core in [Au 12 Pb 44 ] 8− from perfect tetrahedral symmetry. This distortion is, however, a minor feature that does not negate the value of presenting the analysis in the higher point group. When the four nido [Au@Pb 11 ] 3− ligands are introduced, we can identify two distinct types of interactions with the [Au 8 ] 4+ cluster (see inset in Fig. 7). First, the HOMO-4 of the ligands (a 1 in Fig. 6) generate linear combinations (a 1 + t 2 ) with local σ symmetry that can overlap directly with the corresponding linear combinations of s/d z 2 hybrids on the Au atoms bonded directly to the open Pb 5 faces, in precisely the same way as the s/ d z 2 hybrid on the single Au atom did in [Au 2 @Pb 11 ] 2− (see the cartoon representations of the 3a 1 and 4t 2 orbitals in Fig. 7). The second mechanism involves the doubly degenerate HOMO/ HOMO-1 of the ligand which has local π symmetry and generates linear combinations of e + t 1 + t 2 symmetry, the last of which can overlap with a t 2 -symmetric linear combinations of s/d z 2 hybrids on the three adjacent capping Au atoms. The π character of this pathway is shown in the cartoon representation of the 3t 2 orbital of [Au 12 Pb 44 ] 8− in Fig. 7, and the contours of the corresponding isosurface on the nido [Au@Pb 11 ] 3− ligands (highlighted in the red circles in Fig. 7), show the clear fingerprint of the HOMO/ HOMO-1. The bonding of the [Au@Pb 11 ] 3− ligand to the Au 8 core is therefore made up of two quite distinct components-σ bonding to the Au atoms that bind to the center of the Pb 5 faces and secondary π bonding to the three adjacent capping Au atoms. We can estimate the relative importance of the two components by performing an energy decomposition analysis, noting that the σ-type interactions are mediated primarily by the a 1 * and t 2 * orbitals of the Au 8 core while the π-type interactions involve primarily the partially occupied t 2 orbital. By successively removing virtual fragment orbitals from the basis (using the removefragorbitals option in ADF), we can therefore associate distinct energetic contributions to the σ and π pathways.
Eliminating the four virtual orbitals on [Au 8 ] 4+ that mediate the σ pathway (a 1 * and t 2 *) reduces the total interaction energy by 2.4 eV, while further closing down the secondary π pathway by eliminating the two unoccupied components of t 2 leads to an additional loss of 3.2 eV. By this measure, it appears, therefore, that the secondary π-type interactions make a dominant contribution to the overall stability of the cluster: they are particularly strong because they allow for electron transfer from the high-energy HOMO and HOMO-1 of the ligand to the Au 8 core.

Discussion
The   Fig. 5 allows us to speculate on what other members of the Au/Pb family might be accessible. The next obvious stages in cluster growth would be the [5,11] cluster, a hexa-capped trigonal bipyramid with overall composite [Au 16 Pb 55 ] 10− , and a [6,14] octa-capped octahedron, [Au 20 Pb 66 ] 12− . Whilst the progressive 2increase in anionic charge at each step will certainly terminate the series before very large gold cores can be reached, these larger clusters may be accessible under reducing conditions where Au is present in excess.  Pb 44 ] was obtained by layering with toluene (3 mL) (18% crystalline yield based on Pb). In a separate experiment, a crystalline sample of 3 was also obtained starting from an isolated sample (20 mg) of 2 dissolved in pyridine (1.0 mL) in an NMR tube. The resulting red-brown solution was heated at 60°C for 3 h and then layered by toluene (1.0 mL) to allow for crystallization. Black block-like crystals of [K([2.2.2]crypt)] 8 [Au 12 Pb 44 ] were isolated after two weeks (25% yield based on 2).

Methods
Single crystal X-ray diffraction data analyses. The available data for 1 and 2 were refined successfully against the structural models, as measured by R 1 and wR 2 values of less than 0.07 and 0.18, respectively. In contrast, all attempts to obtain the high-quality X-ray diffraction data for compound 3 were unsuccessful due to the absorption of the Cu light source (λ = 1.54184 Å) by the Au and Pb elements of the cluster and its large unit cell volume. Despite this, one data set of reasonable quality was obtained but still contains a relatively large final R value of 15.06%. All diffraction methods were carried out at 100 K. A summary of the crystallographic data for these complexes is listed in Supplementary Table 1, and selected bond distances  are given in Supplementary Tables 2-4 for compound 1, 2 and 3, respectively. Photographs of the crystals are shown in Supplementary Fig. 1, while unit cells and asymmetric units for 1, 2 and 3 are shown in Supplementary Figs. 2-7.
Computational details. All density functional calculations were performed using the Amsterdam Density Functional (ADF) software package, version 2017.11 [35][36][37] . The Perdew Burke Ernzerhof (PBE) functional 38 was used in conjunction with a polarized triple-zeta (TZP) basis on Ag, Au, and Pb 39 . Core orbitals up to and including 3d (Ag) and 4d (Au, Pb) were treated as core for both atoms ("small" core option in ADF). Scalar relativistic corrections were included using the Zero-Order relativistic approximation (ZORA) [40][41][42] . The confining effects of the cation environment was mimicked using a continuum solvent model with dielectric constant of 78.39 43 . Where geometries were optimized, the gradient algorithm of Versluis and Ziegler was employed 44