Symmetry collapse due to the presence of multiple local aromaticity in Ge244−

Understanding the structural changes taking place during the assembly of single atoms leading to the formation of atomic clusters and bulk materials remains challenging. The isolation and theoretical characterization of medium-sized clusters can shed light on the processes that occur during the transition to a solid-state structure. In this work, we synthesize and isolate a continuous 24-atom cluster Ge244−, which is characterized by X-ray diffraction analysis and Energy-dispersive X-ray spectroscopy, showing an elongated structural characteristic. Theoretical analysis reveals that electron delocalization plays a vital role in the formation and stabilization of the prolate cluster. In contrast with carbon atoms, 4 s orbitals of Ge-atoms do not easily hybridize with 4p orbitals and s-type lone-pairs can be localized with high occupancy. Thus, there are not enough electrons to form a stable symmetrical fullerene-like structure such as C24 fullerene. Three aromatic units with two [Ge9] and one [Ge6] species, connected by classical 2c-2e Ge-Ge σ-bonds, are aligned together forming three independent shielding cones and eventually causing a collapse of the global symmetry of the Ge244− cluster.

U nderstanding how the addition of atoms one by one leads to the transition from a single atom to a diatomic molecule to atomic clusters and finally to the formations of bulk solid-state allotropes is a dream of many chemists. This understanding will help us to design tailorable materials with ever unusual structures and other physical and chemical properties. Today we still do not understand how such evolution is happening. A striking example is carbon-one of the most investigated elements. Although it is known that the transition from diatomic C 2 to larger carbon clusters goes through the formation of linear chains 1 , cyclic structures 2 , and cage-like fullerenes 3 , we still do not completely know how fullerenes will transform upon further addition of atoms and finally form bulk graphite or diamond. For other elements, our knowledge of this evolution is less clear. Even for the most similar isoelectronic elements of the IV group of the Periodic Table (Ge and Si), computational studies showed that atomic clusters' structures behave differently upon growth [4][5][6] . Thus, the smallest fullerene-like structure for carbon atom occurs at 20 atoms 7 and continues to evolve beyond. However, according to the computational results, Si and Ge tend to form prolate structures for medium-sized clusters rather than spherical-like fullerenes. The experimental evidence of such behavior so far was limited to ion mobility experiments 8 and 2D electron microscopy experiments 9 . Although theory can propose some trustworthy candidates for low energy structures, one of the most reliable pieces of experimental evidence-a solid state X-Ray characterization, is still lacking for large continuous Ge clusters. Hence the isolation of medium-sized pure germanium species as a key intermediate to understand the structural transition is of greatest importance. The isolated ligand-free germanium clusters with over 10 atoms known to date always exhibited a sole coupling model of small clusters [10][11][12] , which should be better regarded as polymerization tendency. In addition, although the silyl-protected Ge 18 [Si(SiMe 3 ) 3 ] 6 cluster cannot be seen as polymers like [Ge 9 -Ge 9 ] 6− , the outer ligands may dramatically affect the structures of cluster cores and thus it cannot represent the real structure of pure germanium cluster with 18 atoms 13,14 .
Here, we show the successful isolation and structural characterization of a germanium cluster Ge 24 4− (1a) featuring an extended prolate structure with fused three-fold faces. Our theoretical calculations show that Ge 24 4− consists of three independent local sigma-aromatic fragments, which is the reason for the collapse of the symmetry and the formation of a prolate structure. This result helps us understand why carbon structures are so different from silicon and germanium ones. Such a model of Ge 24 4− reveals the structural features of medium-sized germanium clusters providing solid prospects for further rationalization of larger species.

Results
Preparation of the anionic Ge 24 4− cluster. The title complex [K(2,2,2-crypt)] 4 Ge 24 (1) was synthesized by mild oxidation of K 12 Ge 17 using excess Co(dppe)Cl 2 in ethylenediamine solution at 55°C. After being layered with toluene for 5 weeks, black block-like crystals occurred on the wall of a reaction test tube in an approximate 25% yield based on K 12 Ge 17 . The structure of 1 was characterized by X-ray diffraction analysis, in which some restraints (SIMU, ISOR and/or DFIX for one K atom and related C, N, O atoms on 2,2,2-crypt) were used in the refined process for better building the model of corresponding [K(2,2,2-crypt)] + fragment. The Co(II) complex of Co(dppe)Cl 2 was used as a mild oxidizing agent here, which played a crucial role in the formation of a large title cluster. Similarly, the oxidation reactions of Zintl ions could be observed in the previous cluster formation, such as ten-vertex closo-E 10 2− (E = Ge/Pb) 15 6 14 and coupling [Ge 9 = Ge 9 = Ge 9 ] 6− 11 in which Fe(II) salt and organic reagent like PPh 3 serve as oxidizing agents, respectively. Furthermore, the redox chemistry involving Co(dppe)Cl 2 was presented in the synthesis of silylprotected [Co(dppe) 2   As shown in Fig. 1a, the overall structure of Ge 24 4− is prolate with an aspect ratio of nearly 3:1 and can be divided into four different polyhedron sections, including a D 3h -symmetric Ge 9 cage (unit-1, Ge1-9), distorted prism (unit-2, Ge7-12), second peculiar Ge 9 cage (unit-3, Ge10-18) and the third distorted C 4vsymmetric Ge 9 cage (unit-4, Ge16-24). This prolate geometry is similar to the ligand-protected tin cluster Sn 20 (Si t Bu 3 ) 10 Cl 2 with raspberry-like arrangement of smaller Sn 10 units, which is formed by the disproportionation reaction of a Sn(I) halide 25 . In light of the structural feature, cluster 1a exhibits a larger prolate structure compared with previous ten-vertex closo-E 10 2− (E = Ge/Pb) 15,16 and [Ge 10 Mn(CO) 4 ] 3− 17 which are formed by similar soft oxidation from basic E 9 (E = Ge/Pb) units. Such atomic arrangement in 1a is different from the oxidative coupling forms of (Ge 9 ) n 10-13 . In this sense, Ge 24 4− may undergo a more complex growth pattern. The attempt using the K 4 Ge 9 as a precursor failed to obtain the title compound under parallel experimental conditions. In contrast to smaller Ge 10 species, the formation of the title cluster 1a may require a downsizing and further combination of additional Ge 9 units. The effect of Ge 4 units from K 12 Ge 17 is still unclear in the formation of cluster Ge 24 4− . Compared with the binary [Au 3 Ge 45 ] 9− 26 , the Ge 24 4− cluster represents a medium-sized Ge cluster without doped transition metals. Furthermore, except for the similar structural characteristic from one Ge 9 of unit 4 and central Ge 6 fragment, the Ge 24 4− cluster exhibits another type of coordinated Ge 9 unit to the central Ge 6 fragment, which is different from the [Au 3 Ge 45 ] 9− due to the effect of Au atoms.
From another perspective, the Ge 24 4− cluster could also be described as two-terminal Ge 9 -units bridged via a Ge 6 central fragment along exo-bonds to triangular faces. In this sense, the central bowl-shaped Ge 6 fragment plays a crucial role in the formation of 1a, and it is suggested as a growth-trigger in the evolution towards larger species. Furthermore, it is also likely to affect the shapes of two terminal Ge 9 -cages by the different coordination fashions. The whole structure can be also viewed as three connected Ge 9 -units involving a terminal cage and fused nine-membered cages sharing three atoms, providing many flavors of the Ge Zintl-ion chemistry in a single molecular structure, able to coincide under similar experimental conditions. Apart from the K 4 Ge 9 , the K 12 Ge 17 was also used as the source of Ge 9 unit and related examples have been reported, such as [Ge 9 -Ge 9 ] 6− (with ZnCp* 2 , Cp*= pentamethylcyclopentadienyl) 27  The bowl-shaped Ge 6 fragment ( Fig. 1b) is reminiscent of similar organic molecules corannulene (C 20 H 10 ) 30 or sumanene (C 21 H 12 ) 31 , a fullerene fragment, with a curved molecular surface. In contrast, the bowl depth of the Ge 6 fragment is 0.93 Å, which is close to corannulene (~0.88 Å) 32 . As shown in Fig. 1c, the central triangle (dotted lines) in the Ge 6 fragment has elongated Ge-Ge distances of av. 2.813 Å like in [Au 3 Ge 45 ] 9− 26 , which is remarkably longer than other Ge-Ge bonds with an average length of 2.487 Å. Furthermore, the Ge 6 bowl combines with a neighboring Ge 3 face from unit-4 by three Ge-Ge bonds (2.471-2.495 Å) to form an interesting nine-atom cage (Fig. 1d) in which two staggered Ge 3 faces lead to three almost identical edge-sharing pentagons. In unit-1, the Ge-Ge distances  34 . Additionally, the extended bottom face of the central Ge 6 fragment coordinates to the triangle face of unit-1 through three exo Ge-Ge bonds (av. 2.581 Å) forming a distorted triangular prism (Fig. 1e). In contrast to D 3h -unit-1, unit-4 exhibits a largely distorted C 4v -structure with a broader range of Ge-Ge contacts (2.4960(14)-2.8598(15) Å).
Computational studies. To understand the reason for the stability and geometrical features of the Ge 24 4− cluster we performed density functional theory (DFT) calculations 35,36 . The details of theoretical calculations are given in the methods section of this manuscript. The optimized geometry resembles all structural features that were found in the X-Ray experiment. The average Ge-Ge distance of the optimized structure is 0.07 Å longer than the experimental one, which is a common deviation for the calculation of highly charged Zintl ions with DFT methods. A high HOMO-LUMO gap (2.67 eV) was found for the optimized cluster indicating its remarkably high stability, while shapes of three lowest-lying valence molecular orbitals show certain lack of global aromaticity as the extent of electron delocalization is restricted to three disjoint fragments, D 3h -Ge 9 (HOMO-49), C 4v -Ge 9 (HOMO-48), and Ge 6 (HOMO-47) (Fig. 2a). To evaluate whether and to what extent these characteristic delocalization patterns survive the interference with all the remaining valence molecular orbitals, we performed the Electron Density of Delocalized Bonds (EDDB) analysis 37 . The EDDB is a part of the state-of-the-art theoretical method combining different quantum-chemistry and information-theory techniques to decompose the valence-electron density of a molecule into density layers representing chemical entities such as lone pairs, localized (Lewis-type) bonds, and delocalized ('resonating') bonds 38 . The results of the EDDB analysis clearly show that 28.5% of the valence-shell electrons do not participate in chemical bonding giving rise to fifteen (4s-type) lone-pairs, about 39.2% of the valence-shell electrons is involved in the Lewis-type Ge-Ge σ-bonding, while the remaining electrons are delocalized in full accordance with topology of HOMO-49, HOMO-48, and HOMO-47, thus marking three independent locally aromatic units: two 3D-aromatic Ge 9 cages and a single σaromatic Ge 6 fragment (Fig. 2b, Supplementary Movie 1). We note that the presented case is different from cylindrical aromaticity 39 , or organic cages with antiaromatic circuits stacked to each other 40 since three independent aromatic fragments are aligned together, preserving their individual aromatic properties.

ARTICLE
The average contribution of each germanium atom in the Ge 24 4− cluster to the electron delocalization is 1.43 |e| , 1.42 | e | , and 1.10 | e| in units D 3h -Ge 9 , C 4v -Ge 9 , and Ge 6 , respectively, which is even higher than in the archetypical aromatic system-benzene, where each of the sp 2 -hybridized carbon atoms contributes to the aromatic ring 0.89 | e| and 0.10 | e| through πand σ-channel, respectively 37 . All this may account for crucial role of the composite aromatic stabilization in the Ge 24 4− cluster, and the lack of effective s-p atomic-orbital hybridization, especially in the Ge 9 3D-cages, seems to significantly increase the ability to charge delocalization.
For a more in-depth and systematic study of the chemical bonding in the synthesized cluster, we performed the Adaptive Natural Density Partitioning (AdNDP) analysis 41,42 . The AdNDP is an electron-localization technique that partitions the natural density of the system and reproduces the most occupied localized bonding elements. The results of the analysis are shown in Fig. 3. Considering one-center two-electron (1c-2e) elements, AdNDP found fifteen s-type lone-pairs with high occupation number values (ON = 1.90-1.87 | e | ) on Ge atoms. Chemical bonding of the middle part of the cluster majorly consists of classical 2c-2e Ge-Ge σ-bonds with ON = 1.95-1.91 | e| and describes a bonding between Ge 6 and two Ge 9 fragments. Highly occupied delocalized 3c-2e σ-bond (ON = 1.96 | e | ) governs the bonding within the Ge 6 fragment and stabilizes the bowl-like Ge 6 structure. Chemical bonding of the D 3h -Ge 9 fragment consists of two 3c-2e σ-bonds with ON = 1.97 | e| and nine 5c-2e σ-bonds (three bonds per each Ge 5 cap) with ON = 1.91-1.79 | e | . The collection of such delocalized bonding elements possesses spherical-like shielding cones as was shown in our previous studies 43,44 . Analogically, the chemical bonding of the C 4v -Ge 9 fragment consists of three delocalized bonding regions resulting in three 5c-2e bonding elements within the Ge 5 cap (ON = 1.98-1.93 | e | ), three 4c-2e bonding elements within the Ge 4 square (ON = 1.95-1.62 | e | ), and five 8c-2e bonding elements within the Ge 8 antiprism (1.99-1.87 | e | ). We note that the low occupation number of 4c-2e bonding element could be increased up to 1.94 | e| with the inclusion of all atoms of Ge 8 antiprism ( Supplementary Fig. 12). A similar situation was earlier described for the isolated C 4v -Ge 9 4− cluster 45 . That assignment does not change the overall chemical bonding picture. Shapes of the found bonds and numbers of electrons on the fragments that agree with the Hückel's (4n + 2) electron counting rule render two Ge 9 fragments locally σ-aromatic 45 . From the chemical bonding analysis described above, we can expect the presence of three independent aromatic regions from the C 4v -Ge 9 , Ge 6 , and D 3h -Ge 9 fragments, in full agreement with theoretical results obtained by the EDDB method.  In order to further explore the aromatic characteristics of 1a, the magnetic criteria of aromaticity was employed (Fig. 4a) [46][47][48] . The isotropic term, given by NICS iso three-dimensional grids, similar to isochemical shielding surface (ICSS) maps, shows a continuous shielding region along with the entire structure. Significantly, under different orientations of the applied field, the shielding cone characteristics were found. In contrast to planar aromatic species for which shielding cones are enabled only when the field is oriented perpendicular to the ring 49 , we found the presence of three cones merged together for any direction of the applied field 48,50 . With the field-oriented along the axis containing all the three cluster fragments (i.e. external field oriented along with the z-axis, B z ind ), a formation of three-overlapped shielding cones centered at each Ge-fragment is observed. For perpendicular orientations (i.e. y-and x-axis, B y ind and B x ind respectively), the three shielding cones are aligned similar to the anthracene molecule, which features three fused aromatic rings as depicted in previous works ( Supplementary  Fig. 10) 51,52 . Such features are retained under arbitrary orientations of the applied field, denoting how the three adjacent shielding cones evolve under rotation ( Supplementary Fig. 11).
Next, we explore the characteristics of each aromatic unit. To represent Ge 6 bowl-like structure, a Ge 9 cluster with a shared triangular face of C 4v -Ge 9 was chosen. Interestingly, despite of fragments' different shapes, each isolated fragment exhibits similar characteristics to spherical aromatic species with a continuous shielding region from NICS iso , and shielding cone characteristics under different orientations of the field (Fig. 4b) 49 . Noteworthy, the overlap between the aromatic characteristics of the three isolated Ge 9 4− clusters largely resembles the behavior of the overall Ge 24 4− cluster supporting that after aggregation involving both exo-bonds and face-fusion schemes, each Ge 9 unit meets the electronic distribution requirements to behave as spherical aromatics. Hence, Ge 24 4− can be viewed as a linear trimer built-up by related aromatic clusters, exhibiting different shapes and aggregation schemes.

Discussion
The synthesis and characterization of Ge 24 4− cluster in a solidstate is a missing chain link between small germanium clusters and bulk solid-state germanium. It confirms the prolate structure that was predicted computationally in a gas phase for neutral germanium species 4-6 , providing an explicit structural characteristic of a medium-sized Ge cluster. High symmetry collapse in Ge 24 4− occurs due to the presence of multiple local aromaticity and lack of s-p hybridization in Ge. The formation of three independent aromatic units shed light on the reason for the formation of low-symmetric prolate structure. We expect that this kind of aromatic units' aggregation will be found in many cluster chemical compounds made in the future. We believe that further investigation of the transition from atomic clusters to bulk materials will bring an understanding and a significant advancement for materials design with a target physical property. X-ray diffraction. Suitable crystal from 1 was selected for X-ray diffraction analysis. Crystallographic data was collected on Rigaku XtalAB Pro MM007 DW diffractometer with graphite monochromated Mo Kα radiation (λ = 0.71073 Å). The structure of crystal 1 was solved using direct methods and then refined using SHELXL-2014 and Olex2 [54][55][56] . All the non-hydrogen atoms were refined anisotropically. All hydrogen atoms of organic groups were rationally placed by geometrical considerations. We used the PLATON SQUEEZE procedure to remove the solvent molecules which could not be modeled properly 57 . We refined the structure by using the rational restraints of anisotropy (SIMU, ISOR, DFIX for K-crypt fragments) and omitted the most disagreeable reflections. Energy dispersive X-ray (EDX). EDX analysis on the title cluster 1 was performed using a scanning electron microscope (FE-SEM, JEOL JSM-7800F, Japan). Data acquisition was performed with an acceleration voltage of 20 kV and an accumulation time of 60 s.

Methods
Powder X-ray diffraction. Powder X-ray diffraction (PXRD) data were collected on a Rigaku diffractometer using Cu Ka radiation (λ = 1.5418 Å). The sealed samples were scanned for every 0.01°increment over the Bragg angle range of 10 − 80°.

Quantum chemical calculations
Magnetic response analysis: Geometry optimizations and subsequent calculations were performed using scalar relativistic DFT methods employing the ADF code with the all-electron triple-ζ Slater basis set plus the double-polarization (STO-TZ2P) basis set in conjunction with the PBE0 functional 36,58,59 . In order to evaluate the induced field (B ind ) upon an external magnetic field (B ext ) at the molecular surroundings, according to B i ind = −σ ij B j ext46,60-63 , the nucleus-independent shielding tensors (σ ij ) 46,63,64 were calculated within the GIAO formalism, employing the OPBE 59,65,66 functional and the all-electron triple-ζ Slater basis set plus the double-polarization (STO-TZ2P), placed in a three-dimensional grid. Relativistic effects were considered through the ZORA Hamiltonian 67 , ensuring an equal footing treatment of different clusters. For convenience, the I and j suffixes are related to the x-, y-and z-axes of the molecule-fixed Cartesian system (i, j = x, y, z). The values of B ind are given in ppm in relation to B ext .
Chemical bonding analysis: Geometry optimization and frequency calculations were performed using Gaussian 16 software at the PBE0/Def2-QZVP level of theory 36,59,68 . To analyze the extent of electron delocalization in the investigated species, we performed the electron density of delocalized bonds (EDDB) calculations 37,38 ; to identify and characterize the chemical bonding, we carried out adaptive natural density partitioning (AdNDP) analysis as implemented in the AdNDP 2.0 code 41,42 . The EDDB and AdNDP analyses were performed at PBE0/ Def2-TZVP level of theory; previously, the results by both methods have been shown to be insensitive to the size of the basis set used 38,69 .

Data availability
The additional data that support the findings of this study are available from the corresponding authors on a request. The X-ray crystallographic coordinates for structure reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition number 2072965.