Armin R Eulenstein

A romaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by inherent delocalization of 4n + 2 π-electrons over the atoms of a highly symmetric ring 1 . This electron delocalization allows a ring current to be sustained in an external magnetic field. In addition to structural and energetic features, as well as specific reactivity patterns, ring currents are used as another aromaticity criterion [2][3][4] , which can be probed experimentally via NMR shifts or calculated by means of quantum chemistry. The latter is possible either directly 5 or indirectly via nucleus-independent chemical shifts (NICSs) 6 . Hückel postulated that all planar monocyclic molecules with 4n + 2 π-electrons fulfil the preconditions for aromaticity, while 4n π-electrons lead to antiaromaticity. These rules were then applied to organic monocycles with the general formula C n R n (R = H, organic substituent), to heteroaromatic compounds comprising one or more non-carbon atoms in the cycle, as well as to a small number of accessible purely inorganic compounds. The list of experimentally accessible π-aromatic molecules comprising exclusively metal atoms is considerably shorter, although metal atoms should allow for strong electron delocalization of any kind due to their preference for metallic bonding. Yet, only a few planar cyclic compounds with notable ring currents have been reported so far, with a maximum number of five metal atoms, as metal atoms tend to form polyhedral structures rather than cycles. The challenge hence is to overcome these two contradicting preconditions and find a way of stabilizing larger metal cycles, not only to expand the knowledge of this highly uncommon class of compounds, but also to explore and further shape such molecules' exceptional electronic properties and eventually reactivities. Figure 1 provides an overview of the classes of π-aromatic molecules that have been verified experimentally, along with their calculated NICS values (in ppm) and ring current strengths (in nA T -1 ), thereby indicating all experimentally secured types of molecules exhibiting all-metal π-aromaticity.

In contrast to the large number and diversity of typical π-aromatic C n H n cycles (Fig. 1a; including Li 2 [(Me 3 SiC) 4 ] as a rare example of four-membered cycles 7 ) and heteroaromatic analogues (Fig. 1b; including derivatives like K[(B t Bu) 2 CCH(SiMe 3 ) 2 ] (ref. 8 ) or [(Ar*Ga) 2 (CH) 2 (CPh) 2 ] 2-with Ar* = C 6 H 3 -2,6-(C 6 H 3 -2,6i Pr 2 ) 2 (ref. 9 )), the formation of planar cycles that exhibit ring currents indicative of π-aromaticity has been reported for considerably fewer examples in purely inorganic systems. As shown in Fig. 1c, several aromatic molecules with up to 10 atoms have been experimentally realized that exhibit 4n + 2 π-aromaticity 10 . The smallest examples are borane derivatives based on B 3 and B 4 moieties with two π-electrons [START_REF] Ahlrichs | Electronic structure calculations on workstation computers: The program system turbomole[END_REF][12][START_REF] Balasubramani | Modular program suite for ab initio quantum-chemical and condensed-matter simulations[END_REF][14] . Most species exhibit six π-electrons: '[(RSi) 4 ] 2-' in [{η 4 -(RSi) 4 }Ru(CO) 3 ] (R = SiMe t Bu 2 ) 15 , the carbon-free rings S 2 N 2 (ref. 16 ), Ch 4 2+ (Ch = S, Se, Te) 17,18 and Pn 4 2-(Pn = P, As (refs. 19,20 ); note that Sb 4 2-and Bi 4 2-are weakly π-antiaromatic 21,22 ) and the (C 5 H 5 ) -and C 6 H 6 analogues P 2 N 3 -(refs. 23 ), Pn 5 -(Pn = P, As) 24 and Pn 6 (Pn = P, As) 24 ) 16 . Some of these cycles show similarities to their organic analogues, for example as ligands in sandwich complexes like [(Cp*Mo) 2 Pn n ] (Cp* = C 5 Me 5 or C 5 Me 4 Et; Pn = P, As; n = 5, 6) 24 . However, they usually exhibit lower stabilities, and their reactivities differ from the typical substitution chemistry of their organic cousins because of their varied electronic structures, all of which is of general interest for synthetic chemistry and the development of new compounds from such species.

The fewest examples are found in the family of all-metal π-aromatic compounds (Fig. 1d), with the ring size limited to five atoms and the number of π-electrons being two or six in all reported cases. It was first suggested in 1995 that a cyclic trigallane cluster anion, [(RGa) 3 ] 2-(R = C 6 H 3 -2,6-(C 6 H 2 -2,4,6-Me 3 ) 2 ) 25,26 , the Al analogue of which was reported 10 years later 27 , behaves electronically like the isoelectronic cyclopropenyl cation (C 3 H 3 ) + with two π-electrons. In 2001, the square planar 'Tr The concept of aromaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by the inherent delocalization of 4n + 2 π-electrons over the ring atoms. Since then, π-aromaticity has been observed for a large variety of organic and inorganic non-metal compounds, yet, for molecules consisting only of metal atoms, it has remained restricted to systems with three to five atoms. Here, we present the straightforward synthesis of a metal 12-ring that exhibits 2π-aromaticity and has a ring current much stronger than that of benzene (6π) and equivalent to that of porphine (26π), despite these organic molecules having (much) larger numbers of π-electrons. Highly reducing reaction conditions allowed access to the heterometallic anion [Th@Bi 12 ] 4-, with interstitial Th 4+ stabilizing a Bi 12 8-moiety. Our results show that it is possible to design and generate substantial π-aromaticity in large metal rings, and we hope that such π-aromatic heavy-metal cycles will eventually find use in cluster-based reactions.

A romaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by inherent delocalization of 4n + 2 π-electrons over the atoms of a highly symmetric ring 1 . This electron delocalization allows a ring current to be sustained in an external magnetic field. In addition to structural and energetic features, as well as specific reactivity patterns, ring currents are used as another aromaticity criterion [2][3][4] , which can be probed experimentally via NMR shifts or calculated by means of quantum chemistry. The latter is possible either directly 5 or indirectly via nucleus-independent chemical shifts (NICSs) 6 . Hückel postulated that all planar monocyclic molecules with 4n + 2 π-electrons fulfil the preconditions for aromaticity, while 4n π-electrons lead to antiaromaticity. These rules were then applied to organic monocycles with the general formula C n R n (R = H, organic substituent), to heteroaromatic compounds comprising one or more non-carbon atoms in the cycle, as well as to a small number of accessible purely inorganic compounds. The list of experimentally accessible π-aromatic molecules comprising exclusively metal atoms is considerably shorter, although metal atoms should allow for strong electron delocalization of any kind due to their preference for metallic bonding. Yet, only a few planar cyclic compounds with notable ring currents have been reported so far, with a maximum number of five metal atoms, as metal atoms tend to form polyhedral structures rather than cycles. The challenge hence is to overcome these two contradicting preconditions and find a way of stabilizing larger metal cycles, not only to expand the knowledge of this highly uncommon class of compounds, but also to explore and further shape such molecules' exceptional electronic properties and eventually reactivities. Figure 1 provides an overview of the classes of π-aromatic molecules that have been verified experimentally, along with their calculated NICS values (in ppm) and ring current strengths (in nA T -1 ), thereby indicating all experimentally secured types of molecules exhibiting all-metal π-aromaticity.

In contrast to the large number and diversity of typical π-aromatic C n H n cycles (Fig. 1a; including Li 2 [(Me 3 SiC) 4 ] as a rare example of four-membered cycles 7 ) and heteroaromatic analogues (Fig. 1b; including derivatives like K[(B t Bu) 2 CCH(SiMe 3 ) 2 ] (ref. 8 ) 9 )), the formation of planar cycles that exhibit ring currents indicative of π-aromaticity has been reported for considerably fewer examples in purely inorganic systems. As shown in Fig. 1c, several aromatic molecules with up to 10 atoms have been experimentally realized that exhibit 4n + 2 π-aromaticity 10 . The smallest examples are borane derivatives based on B 3 and B 4 moieties with two π-electrons [START_REF] Ahlrichs | Electronic structure calculations on workstation computers: The program system turbomole[END_REF][12][START_REF] Balasubramani | Modular program suite for ab initio quantum-chemical and condensed-matter simulations[END_REF][14] . Most species exhibit six π-electrons: 15 , the carbon-free rings S 2 N 2 (ref. 16 ), Ch 4 2+ (Ch = S, Se, Te) 17,18 and Pn 4 2-(Pn = P, As (refs. 19,20 ); note that Sb 4 2-and Bi 4 2-are weakly π-antiaromatic 21,22 ) and the (C 5 H 5 ) -and C 6 H 6 analogues P 2 N 3 -(refs. 23 ), Pn 5 -(Pn = P, As) 24 and Pn 6 (Pn = P, As) 24 ) 16 . Some of these cycles show similarities to their organic analogues, for example as ligands in sandwich complexes like [(Cp*Mo) 2 Pn n ] (Cp* = C 5 Me 5 or C 5 Me 4 Et; Pn = P, As; n = 5, 6) 24 . However, they usually exhibit lower stabilities, and their reactivities differ from the typical substitution chemistry of their organic cousins because of their varied electronic structures, all of which is of general interest for synthetic chemistry and the development of new compounds from such species.

or [(Ar*Ga) 2 (CH) 2 (CPh) 2 ] 2-with Ar* = C 6 H 3 -2,6-(C 6 H 3 -2,6-i Pr 2 ) 2 (ref.
'[(RSi) 4 ] 2-' in [{η 4 -(RSi) 4 }Ru(CO) 3 ] (R = SiMe t Bu 2 )
The fewest examples are found in the family of all-metal π-aromatic compounds (Fig. 1d), with the ring size limited to five atoms and the number of π-electrons being two or six in all reported cases. It was first suggested in 1995 that a cyclic trigallane cluster anion, [(RGa 25,26 , the Al analogue of which was reported 10 years later 27 , behaves electronically like the isoelectronic cyclopropenyl cation (C 3 H 3 ) + with two π-electrons. In 2001, the square planar 'Tr The concept of aromaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by the inherent delocalization of 4n + 2 π-electrons over the ring atoms. Since then, π-aromaticity has been observed for a large variety of organic and inorganic non-metal compounds, yet, for molecules consisting only of metal atoms, it has remained restricted to systems with three to five atoms. Here, we present the straightforward synthesis of a metal 12-ring that exhibits 2π-aromaticity and has a ring current much stronger than that of benzene (6π) and equivalent to that of porphine (26π), despite these organic molecules having (much) larger numbers of π-electrons. Highly reducing reaction conditions allowed access to the heterometallic anion [Th@Bi 12 ] 4-, with interstitial Th 4+ stabilizing a Bi 12 8-moiety. Our results show that it is possible to design and generate substantial π-aromaticity in large metal rings, and we hope that such π-aromatic heavy-metal cycles will eventually find use in cluster-based reactions.

) 3 ] 2-(R = C 6 H 3 -2,6-(C 6 H 2 -2,4,6-Me 3 ) 2 )
[MTr 4 ] -anions produced in gas-phase experiments (M/Tr = Li/Al, Na/Al, Cu/Al, Na/Ga, Na/In) 28,29 were classified as aromatic molecules with two completely delocalized π-electrons, which led to the introduction of the term 'all-metal aromaticity' 30 . The series of experimentally accessible species has expanded to include some further three-membered, four-membered and five-membered metal cycles: 32 , Hg 4 6-(ref. 33 ), Pn 5 -(Pn = Sb, Bi; gas phase only) 34 and Tt 5 6-(Tt = Sn, Pb) 35 with six π-electrons, as well as Pb 5

'Sb 3 3- ' (in [(Sb 3 ) 2 Au 3 ] 3-) 31 , '[Ga 4 ] 4-' (in [(Ar*Ga) 2 Ga 2 ] 2-; Ar* = C 6 H 3 - 2,6-(C 6 H 2 -2,4,6-iPr 3 ) 2 )

2-

(in [Pb 5 {Mo(CO) 3 } 2 ] 4-) 36 with two π-electrons. Further cycles bearing π-aromaticity, like M 3 q (M/q = Zn/2-, Cd/2-, Hg/2-, Ta/1-, Hf/0) 37 or Mg 3 2-(ref. 38 ), have been theoretically predicted, yet have not proved detectable so far in this form. It is worth noting that several other species were identified to show effective σ delocalization [39][40][41][42] , which cannot easily be discriminated from the classical superatom model that is related to the Jellium model for spherical metal NICS values (in ppm, grey) and ring currents (in nA T -1 , black) were calculated at the PBE/def2-TZVP/grid3 level of theory [48][49][50][51][52][53]59 , with the conductor-like screening model (COSMO) applied for anions 54 . Simplifications of the molecules for the calculations are shown. From left to right: molecules with three to eight atoms and examples with more than eight atoms (rightmost) contributing to the 4n + 2 π-aromatic system. Missing entries indicate that no example has been reported for the respective class. a, Representatives of C-H aromatic molecules (with Li 2 [(Me 3 SiC) 4 ] (ref. 7 ) as a rare example of a four-membered cycle). b, Representatives of heteroaromatic molecules (with K[(B t Bu) 2 CCH(SiMe 3 ) 2 ] as a rare example of a three-membered cycle 8 and [(Ar*Ga) 2 (CH 2 )(CPh) 2 ] 2-as a representative of metallaaromatic molecules; Ar* = C 6 H 3 -2,6-(C 6 H 3 -2,6i Pr 2 ) 2 ; ref. 9 ). c, Examples of purely inorganic, non-metal aromatic molecules (with the gas-phase species [B 3 (CO) 3 ] + as a rare example of a three-membered cycle) [START_REF] Ahlrichs | Electronic structure calculations on workstation computers: The program system turbomole[END_REF] . d, Survey of all known types of molecules exhibiting all-metal π-aromaticity, with their stabilizing atoms or groups: [25][26][27] ); M/Tr = Li/Al, Na/Al, Cu/Al, Na/In, Na/Ga in gas-phase species [MTr 4 ] -(refs. 28,29 ); 32 ); Tt = Sn, Pb (ref. 36 ); Pn = Sb, Bi in gas-phase species Pn 5 -(ref. 34 ). NICS values and ring currents are given for one homologue only, as numbers within the homologous series are similar. Note that the numbers refer to total ring currents unless noted otherwise. This may include additional contributions of σ-aromaticity. Weakly π-antiaromatic Pn 4

Tr = Al, Ga and R = C 6 H 3 -2,6-(C 6 H 2 -2,4,6-Me 3 ) 2 in [(RTr) 3 ] 2-(refs.
Ar* = C 6 H 3 -2,6-(C 6 H 2 -2,4,6-i Pr 3 ) 2 ] in [(Ar*Ga) 2 Ga 2 ] 2-(ref.
2-(Pn = Sb, Bi) 21,22 are not listed here. For further references, see the text. Further details of the NICS and ring current calculations are provided in the Supplementary Information.

clusters 43 . The relatively small number of species quoted above highlights the current limits of the all-metal π-aromatic systems experimentally secured so far. On the other hand, the ring currents shown in Fig. 1 indicate that these can indeed surmount those of organic systems, which suggests fundamentally different electronic and chemical properties are to be expected from such species. However, up to now, all isolable all-metal aromatic rings have been stabilized from 'outside'-by incorporation into a neat intermetallic solid or by attachment of protective organic groups, metal ions or transition metal complex fragments. This largely reduces the accessibility of the cycles, and thus the possibility of studying reactions involving the aromatic ring.

An approach for the formation of accessible all-metal aromatic molecules would be the stabilization of distinctly larger cycles from 'inside' , which previously allowed the formation of spherical intermetalloid clusters only 44 . Very recently, Sun and others synthesized lanthanide ion-centred polystibide clusters of the type [Ln@Sb 12 ] 3- (Ln = La, Y, Ho, Er, Lu), which were described as a combination of three π-antiaromatic Sb 4

2-moieties that are connected to form an 'Sb 12 6-' belt embedding an Ln 3+ ion 45 . At the same time, we presented the topologically related, yet more highly charged, polybismuthide substructure in [U@Bi 12 ] 3-(ref. 46 ). An inspection of the aromaticity in this system was inhibited by the open-shell situation (due to an unpaired f electron), but the highest occupied molecular orbital (HOMO) suggested inherent π-electron delocalization.

Hence, our straightforward idea of how to (1) generate and ( 2) verify an all-metal π-aromatic cluster was to replace U with an earlier actinide that would not bear an unpaired electron, while still allowing the high charge to remain on the ring. This approach was explored successfully by using Th 4+ as the central ion, with no pronounced tendency of withdrawing electrons from the polymetallide ring due to the high stability of the +4 oxidation state of thorium. Here, we present the synthesis and crystal structure of [K(crypt-222)] 4 [Th@Bi 12 ]•2en (where en is ethane-1,2-diamine), comprising the anionic cluster [Th@Bi 12 ] 4-. Magnetic measurements and quantum chemical studies confirm the formal assignment as Th 4+ and 'Bi 12 8-' . Structural features and calculated ring currents as well as NICS values indicate the latter to be aromatic, with two π-electrons causing a remarkably strong ring current that is similar to the one in porphine (26π), despite a much smaller number of π-electrons to be delocalized over the uncommon polymetallide architecture. This anion is an all-metal π-aromatic molecule that exists without additional (external) coordination in the crystal and in solution. It even survives the transfer into the gas phase in the given composition under mass spectrometry conditions.

Results and discussion

Synthesis and structure of [K(crypt-222)] 4 [Th@Bi 12 ]•2en (2).

The reaction of [ThCp #

3 Cl] (1; Cp # = C 5 Me 4 H) with K 5 Ga 2 Bi 4 (A), as an in situ source of (GaBi 3 ) 2-and Bi 4

2-(refs. 21,47 ) was performed in ethane-1,2-diamine (en) in the presence of the cation sequestration agent 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo [8.8.8] hexacosane (crypt-222). Following filtration, layering of the filtrate with toluene and storage at 5 °C, the formation of black, prismatic crystals was obtained after 10 days (for further details of the synthesis, see Methods). Using single-crystal X-ray diffraction (Supplementary Table 1), the composition of the crystals was determined to be [K(crypt-222)] 4 [Th@Bi 12 ]•2en (2), and the Th:Bi ratio of 2 was verified by micro-X-ray fluorescence spectroscopy (µ-XFS; Supplementary Fig. 6 and Supplementary Table 2). Compound 2 comprises the novel Th-centred intermetalloid cluster anion [Th@ Bi 12 ] 4-(2A), the composition of which was additionally confirmed by electrospray ionization mass spectrometry (ESI-MS; Supplementary Fig. 9). The molecular structure of 2A is illustrated in Fig. 2.

According to single-crystal X-ray structure analysis, cluster 2A adopts the same overall architecture as [U@Bi 12 ] 3-. Three four-membered, folded {Bi 4 } rings are connected at opposing corners to create a doughnut-shaped {Bi 12 } ring enclosing the actinide ion in its centre. Two different types of Bi-Bi bond are observed, with those between the four-membered rings (d A ) being slightly shorter, on average, than those within the rings (d B ). This is like the situation in [U@Bi 12 ] 3-, but it is in striking contrast to the structural properties of the [Ln@Sb 12 ] 3-series mentioned above. As discussed in the following, this structural detail informs us about the frontier orbital situation (and hence the situation near the energy level of the highest and lowest molecular orbitals, HOMO and LUMO), and as such provides a strong indication of the successful generation of an all-metal π-aromatic cluster in 2A. This can be qualitatively connected to the symmetry criterion for aromatic molecules: first, the {Bi 12 } subunit exhibits an overall much narrower range of bond lengths in 2A (Bi-Bi 3.0420(14)-3.132(1) Å) as compared to the range reported for the {Sb 12 } subunit in [La@Sb 12 ] 3-(2.8088(5)-3.0517(5) Å). Second, the relatively small Bi A -Bi A ′ distances (3.0420(14)-3.0785(13) Å) indicate a strengthening of the respective bonds and the presence of π interactions in 2A, as compared to the relatively large Sb-Sb distances between the corresponding {Sb 4 } units in [La@Sb 12 ] 3-(3.0179(6)-3.0517(5) Å). Although it is difficult to comment on the relative stability of the aromatic molecule (as a third criterion), because no related system is known so far for the given elemental composition, it is notable that anion 2A exhibits a considerable (thermal) stability both in the condensed phase (crystal and solution) and even in the gas phase (cf. the mass spectra), without the presence of externally stabilizing ligands or additional cations. It might therefore be a good candidate to eventually study the reactivity of all-metal π-aromatic molecules in solution for the first time.

Quantum chemical study of the geometric and electronic structure of [Th@Bi 12 ] 4-(2A).

To verify the success of our concept, density functional theory (DFT) calculations were carried out with the program system Turbomole 48,49 , using the PBE functional (developed by Perdew, Burke, and Ernzerhof) 50 . For Th, an effective core potential covering the 78 inner electrons (ECP-78) 51 was employed together with a triple-zeta basis 51 , and for Bi an ECP-60 52 with a triple-zeta basis 53 . The negative charge was compensated by employing the conductor-like screening model (COSMO) with default parameters 54 . The geometric structure of 2A is well reproduced by the calculated distances (deviations amount to ~0.01 Å). In particular, as in the experiment, d A is shorter than d B by 0.03 Å, like in [U@Bi 12 ] 3-. Note that the inverse trend applies for the hypothetical '[La@Bi 12 ] 3-' , which behaves like the experimentally determined [La@Sb 12 ] 3-mentioned above. To place the electronic situation in 2A in the context of related (hypothetical or known) anions based on 12-atomic polybismuthide rings, we also calculated 'Bi 12 6-' , '[La@Bi 12 ] 3-' , [U@Bi 12 ] 3-, and 'Bi 12 8-' . Figure 3a presents the calculated molecular structures of these species and 2A, while the frontier orbital regions of their molecular orbitals are given in Fig. 3b (the complete set of valence molecular orbitals is provided in Supplementary Fig. 16), with the respective molecular orbitals of 2A illustrated in Fig. 3c.

Owing to the different total electron counts, 66 in 'Bi 12 6-' and '[La@Bi 12 ] 3-' , 69 in [U@Bi 12 ] 3-, and 68 in 2A and 'Bi 12 8-' , the molecular orbital denoted as the irreducible representation 14a 2 ″ in 2A is the LUMO in '[La@Bi 12 ] 3-' , while it is the HOMO in [U@Bi 12 ] 3-and 2A. The occupation of this a 2 ″ molecular orbital is directly correlated with d A being shorter than d B , as this orbital is bonding in d A but anti-bonding in d B . As is evident from Fig. 3b, the most obvious difference in the electronic structures of [Th@Bi 12 ] 4-(2A) and [U@Bi 12 ] 3-is one unpaired electron residing in the HOMO-1 (a 1 ′) of [U@Bi 12 ] 3-, leading to a doublet state, while 2A represents the desired closed-shell case. In contrast to [U@Bi 12 ] 3-, none of the molecular orbitals in [Th@Bi 12 ] 4-shows any notable 5f contribution (results of a Mulliken population analysis are shown in Fig. 3c and Supplementary Table 11) 55 . This is in perfect agreement with the measurement of the magnetic susceptibility, which reveals the diamagnetic nature of compound 2 (Supplementary Fig. 12). Overall, the situation in 2A is indeed described best as Th 4+ residing in a cyclic Bi 12 8-unit.

A comparison of the frontier orbitals of all five species, 'Bi 12 6-' , '[La@Bi 12 ] 3-' , [U@Bi 12 ] 3-, [Th@Bi 12 ] 4-(2A), and 'Bi 12 8-' , indicates the following major characteristics: the central ion strongly influences the molecular-orbital energy levels with regard to the empty {Bi 12 } rings, mostly as a consequence of electrostatic interactions. Somewhat larger stabilizations are found for the molecular orbitals that are denoted as 18a 1 ′ and 19e″ in 2A, which exhibit some d-orbital contribution of the inner metal atom (for example, 0.33 e -and 0.69 e -for 2A, according to the Mulliken analysis; Supplementary Tables 89101112). The most important feature regarding aromaticity, however, is the occupation or non-occupation of the molecular orbital denoted as 14a 2 ″ in 2A, as discussed in the following.

Quantum chemical investigation of the π-aromaticity in [Th@Bi 12 ] 4-(2A).

As already known, π-aromatic compounds gain stability by inherent delocalization of 4n + 2 π-electrons over the ring system. To probe whether 2A exhibits this kind of delocalization, as suggested by the shape of the HOMO (14a 2 ″, Fig. 4a), we carried out a localization procedure for the 34 valence molecular orbitals using the Boys method 56 (Fig. 4b-g) and further calculated the intrinsic bond orbitals (IBOs; Supplementary Fig. 13) 57 . From both procedures, we obtained 33 localized orbitals representing either two-centre bonds (nonpolar Bi-Bi bonds, Fig. 4c,d) slightly polarized towards Th and strongly polar Th-Bi bonds (Fig. 4e) or lone pairs (one per Bi atom, Fig. 4f,g). One orbital is remaining, ' (Supplementary Fig. 14), indicating the π delocalization of the respective two electrons in the 12-membered ring.

All experimental and quantum chemical findings described so far are strong indications for a π-aromatic situation within this cyclic polybismuthide. Thus, we calculated the magnetically induced current density to study the aromaticity based on the magnetic criterion [2][3][4][5] and the electron delocalization pathways of the cluster. This was done with the gauge-including magnetically induced currents (GIMIC) method 59 . A plot of the magnetically induced current density is provided in Fig. 5. The torus-shaped current density is similar to that in planar rings, despite the perpendicularly oriented Bi B atoms (Fig. 2). Hence, the π-aromatic system is indeed best described as a cycle (or a 'belt'). By numerical integration along a plane perpendicular to the Bi A -Bi A ′ bond and parallel to the magnetic field direction, a diatropic net ring current of 22.7 nA T -1 was found. When using more sophisticated scalar-relativistic all-electron approaches (X2C) [60][61][62][63] , the value is even increased to 24.8 nA T -1 . These values are roughly twice the ring current of 6π-aromatic benzene (11.4 nA T -1 ) and close to that of 26π-aromatic porphine, which is often simplified to an 18π-aromatic compound (25.3 nA T -1 ) 64 . Therefore, [Th@Bi 12 ] 4-is clearly proven to be π-aromatic based on the structural and magnetic criteria.

Notably, the (hypothetical) 'Bi Information). So, the Th 4+ ion is indeed mainly required to enable its synthetic access by stabilizing the cycle. Another frequently used quantity for the quantum chemical indication of aromaticity is NICS 6 , which indirectly probes the magnetically induced current density. This method also suggests aromaticity because of NICS values of approximately -17 ppm (ECPs) and -16 ppm (X2C) for the hypothetical 'Bi 12 8-' (Supplementary Table 4). For comparison, the ring currents and NICS values of Al 4 2-are 27.6 nA T -1 and -31.8 ppm, respectively (Fig. 1). Although the two π-electrons are delocalized over four atoms in ' Al 4 2-' , the delocalization involves 12 atoms in 2A, without a drop in the ring current strength.

Finally, to probe the applicability of the 4n + 2 π rule to this class of compounds, we also studied the next (hypothetical) cousins in this series, 'Bi ' , indicating notable π-aromaticity. However, it is unlikely that a polybismuthide of this charge could be synthesized from solution.

To summarize, we have presented the targeted synthesis of [K(crypt-222)] 4 [Th@Bi 12 ]•2en (2) with a [Th@Bi 12 ] 4-anion (2A), which is best described as a highly symmetric 'Bi 12 8-' ring embedding a central Th 4+ ion. The entire anion can be transferred into solution, and it stays intact under ESI-MS conditions, indicating considerable thermodynamic stability. The HOMO of the anion shows π delocalization and, in contrast to all other molecular orbitals, it is inherently not localizable. This renders 2A, in particular the {Bi 12 } moiety in it, a new type of a 4n + 2 π-aromatic system (with n = 0), which is based on an uncommon cyclic molecular structure that is neither planar nor spherical. Quantum chemical studies further indicate a remarkable ring current strength of 24.8 nA T -1 for [Th@Bi 12 ] 4-(and 23.7 nA T -1 for 'Bi 12 8-'), which is much larger than in 6π-aromatic benzene (11.4 nA T -1 ). It is indeed similar to that in 26π-aromatic porphine (25.3 nA T -1 ), in spite of the notably lower number of π-electrons involved, and to that in ' Al 4 2-' (27.6 nA T -1 ), in spite of the much larger number of metal atoms involved. The central Th 4+ ion mainly serves to help the formation of the cycle and to stabilize it 'from inside' , like a very uncommon type of metal complex with an aromatic ligand. This way, the molecule is generally accessible for post-synthetic chemistry in the condensed phase, which is unprecedented in the field of all-metal π-aromaticity.

The formation and isolation of compound 2 has hence opened a new chapter in this field, which may be expanded in future work by extension to other main group metals and other highly charged inner metal ions to fine-tune the electronic properties. We hope that our findings will help towards the targeted construction of even more complex heavy-metal cycles displaying all-metal π-aromaticity, and in turn new prospects for cluster-based chemistry.

ARTICLES

NATURE CHEMISTRY

Methods

General methods. All manipulations and reactions were performed under a dry argon atmosphere using standard Schlenk or glovebox techniques with freshly dried and distilled solvents. Elements were used as received: K lumps, Acros Organics, 98%; Ga pellets, Alfa Aesar, 99,9999% (metals basis); Bi powder, ChemPur Karlsruhe, 99%. Ethane-1,2-diamine (en) and N,N-dimethylformamide (DMF; Aldrich, 99.8%) were distilled from CaH 2 and stored over 3-Å molecular sieves. Toluene (Acros Organics, 99%) was distilled from sodium-potassium alloy and stored over 4-Å molecular sieves. Kryptofix 222 (crypt-222, Merck) was dried under vacuum overnight. K 5 Ga 2 Bi 4 (A) 47 , known as a source of [K(crypt-222)] 2 (GaBi 3 ) (B) 47 and [K(crypt-222)]Bi 4 (C) 21 , was synthesized by combining K, Ga and Bi in stoichiometric amounts in a niobium ampoule. The ampoule was sealed by arc-welding, placed in an oven and kept at 900 °C for 48 h. The same steps were applied to synthesize a phase with the nominal composition 'K 2 Tl 1 Bi 3 ' . Upon extraction of 'K 2 Tl 1 Bi 3 ' with en/crypt-222, filtration and subsequent removal of the solvent, [K(crypt-222)] 2 (TlBi 3 )•0.5en (D) was obtained in crystalline form 65 . A similar procedure employing a solid mixture of the nominal composition 'K 1 Pb 1 Bi 1 ' yielded crystalline [K(crypt-222)] 2 (Pb 2 Bi 2 )•en (E) 66 . ThCl 4 was synthesized according to the literature procedure 67 . Samples were shielded from ambient light throughout cluster syntheses. Note that all compounds comprising cluster anions 1-4 are air-sensitive. 3 Cl] (19 mg, 30 µmol). The components were combined in a Schlenk tube and dissolved in 4 ml of en. An intense green solution formed initially, indicating the formation of bluish-green Bi 42-(ref. 21 ). After stirring for 2 h, the solution was filtered through densely packed glass wool, carefully layered with toluene (5 ml) and stored for crystallization at 5 °C. After 10 days, crystals of 2 suitable for single-crystal X-ray diffraction formed at the wall of the Schlenk tube in ~20% yield. Identified by-products are [K(crypt-222)] 2 (GaBi 3 ) (B) and [K(crypt-222)]Bi 4 (C) in some cases, in varying yields. Single-crystal X-ray diffraction data. The data for the X-ray structural analyses were collected at 100(2) K with Cu-Kα radiation (λ = 1.54186 Å) on an area detector system (STOE StadiVari; compounds 1, 2 and 3) or with Mo-Kα radiation (λ = 0.7107 Å) on an imaging plate detector system (STOE IPDS II; compound 4). The structures were solved by dual space methods (SHELXT) 68 . The refinement was done by full-matrix least-squares methods against F 2 with the program SHELXL 69 . The crystal data and experimental parameters of the structure determination are collected in Supplementary Table 1. Unit cell plots of the crystal structures are provided in Supplementary Fig. 1 (compound 1), Supplementary Fig. 2 (compound 2), Supplementary Fig. 3 (compound 3) and Supplementary Fig. 4 (compound 4). Powder X-ray diffraction. The powder X-ray diffraction pattern of the crystalline material obtained at the synthesis of 2 was measured on a STOE StadiMP diffractometer system equipped with a Mythen 1K silicon strip detector and a Cu-Kα radiation source (λ = 1.54056 Å). An as-prepared sample of 1 was filled into a glass capillary (0.5-mm diameter), which was then sealed air-tight with soft wax. The tube was then mounted onto the goniometer head using wax (horizontal set-up) and rotated throughout the measurements. The diffraction diagram is shown in Supplementary Fig. 5. It exhibits compound 2 together with a related crystalline phase, most probably upon loss of crystal solvent in situ. µ-XFS. All µ-XFS measurements were performed with a Bruker M4 Tornado, equipped with a Rh-target X-ray tube and a silicon drift detector. The emitted fluorescence photons were detected with an acquisition time of 100 s. Quantification of the elements was achieved through deconvolution of the spectra. The results are shown in Supplementary Figs. 678and summarized in Supplementary Table 2.

Synthesis of [ThCp

Synthetic protocol of further

ESI-MS.

ESI mass spectra (Supplementary Figs. 9-11) were recorded with a Thermo Fisher Scientific Finnigan LTQ-FT spectrometer in negative ion mode. Single crystals of compounds 2-4 were dissolved in freshly distilled DMF inside a glovebox. The solutions were injected into the spectrometer with gas-tight 250-µl Hamilton syringes by syringe pump infusion. All capillaries within the system were washed with dry DMF for 2 h before and at least 10 min in between measurements to inhibit decomposition reactions and consequent clogging. The spectra are shown in Supplementary Figs. 9-11.

Magnetic measurements.

The magnetic measurements on compound 2 were carried out with the use of a Quantum Design MPMS-XL SQUID magnetometer, which operates between 1.8 and 400 K with magnetic field up to 7 T. Measurements were performed on polycrystalline samples of 2 (29.1 and 11.9 mg) sealed in a polyethylene bag (29.7 and 31.4 mg) and prepared under a nitrogen atmosphere. Before the experiments, the field-dependent magnetization was measured at 100 K to confirm the absence of any bulk ferromagnetic impurities. The magnetic data were corrected for the sample holder. As shown in the χ versus T plot in Supplementary Fig. 12, compound 2 is reproducibly diamagnetic over the whole range of temperature between 1.85 and 300 K. The susceptibility at room temperature, -0.0019 cm 3 mol -1 , is close to the expected diamagnetic value of -0.5 × MW × 10 -6 = -0.0023 cm 3 mol -1 intrinsic to the constituting atoms (MW, molecular weight). The small increase of the susceptibility below 10 K is compatible with a Curie law for 0.5% of an S = 1/2 spin (considering the MW of 2). This type of Curie law, usually above 1%, is quasi-systematically observed in diamagnetic compounds and is the signature of defects or impurities that are easy to observe at low temperatures.

Quantum chemical calculations.

Calculations were done with TURBOMOLE 48,49 , both employing ECPs and scalar-relativistic all-electron approaches within the one-component local variant of the X2C Hamiltonian [60][61][62][63] . For details, see Supplementary Information. Magnetically induced current densities were obtained with the GIMIC) code 59 using the perturbed density 70 from TURBOMOLE.

The TURBOMOLE quantum program suite is available from https://www. turbomole.org (retrieved 29 August 2020), and the GIMIC code can be obtained from the GitHub repository at https://github.com/qmcurrents/gimic (retrieved 29 August 2020; open-source; see also ref. 69 ). The GitHub repository also includes a sample input for GIMIC.

Further details are provided in the Supplementary Information, as well as a short note on the use of GIMIC with Python version 2.

Supplementary Discussion on the Formation of Compound 2

We suggest that the reaction that led to the formation of compound 2 took place according to the following reaction schemes starting out from compound K5Ga2Bi4 (A). 1 The latter has been known as a precursor for the formation and isolation of the Zintl salt [K(crypt-222)]2(GaBi3)•en (B), but notably, the use of isolated B alone does not lead to the formation of any isolable cluster compounds. When A is employed instead, we observe not only the formation of compound 2, but also the intermediate formation of bluish-green Bi4 2-. 2 Therefore, we assume that A served as a source of both Bi4 2-and (GaBi3) 2-anions to form in situ upon extraction with en [equations ( 1) and ( 2)], hence allowing for compound 2 to form under the given reaction conditions from these two reactants and compound [ThCp # 3Cl] (1) [equation ( 3)] (note that all compounds are given without crypt-222 or crystal solvent en for simplification):

K5Ga2Bi4 + 3 H2N(CH2)2NH2 → K2Bi4 + 2 Ga 0 ↓ + 3 KHN(CH2)2NH2 + 3 /2 H2↑
(1)

K5Ga2Bi4 + 3 H2N(CH2)2NH2 → K2(GaBi3) + Ga 0 ↓ + Bi 0 ↓ + 3 KHN(CH2)2NH2 + 3 /2 H2↑ (2) 3 K2Bi4 + K2(GaBi3) + [ThCp # 3Cl] (1) → K4[Th@Bi12] (2) + 3 KCp # + KCl + Ga 0 ↓ + 3 Bi 0 ↓ (3)
Compound 1 was previously prepared from ThCl4 3 and KCp # (Cp # = 2,3,4,5-tetramethyl cyclopentadienyl, C5Me4H) as described in the main document. To demonstrate the particular role of the Ga/Bi elemental combination in this synthetic route, we performed analogous reactions of [ThCp # 3Cl] (1) with [K(crypt-222)]2(TlBi3)•en (C) 4 and [K(crypt-222)]2(Pb2Bi2)•en (D) 5 under otherwise identical reaction conditions. This resulted in the formation of the actinide-centred clusters [Th@Tl2Bi11] 3-(3A) and [Th@Pb4Bi9] 3-(4A), in their corresponding [K(crypt-222)] + salts 3 and 4. Both compounds are isostructural with previously reported uranium analogues, with no significant differences in bond lengths or cluster geometries due to similar ionic radii of the central uranium and thorium atoms in a formal +IV oxidation state. We note that in the reaction of 1 with D, we did not observe the formation of a 14-vertex cluster, such as "[Th@Pb7Bi7] 3-" or "[Th@Pb8Bi6] 4-"; this stands in contrast to the corresponding reaction with the [UCp # 3Cl], where 13-vertex and 14-vertext clusters co-crystallized. We attribute this to the smaller ionic radius of Th 4+ relative to U 3+ , which leads to a distinct preference for the smaller 13-atom cluster shell. [6][7][8] 2. Supplementary Information on X-Ray Diffraction

Powder X-Ray Diffraction of Compound 2

Deviations between the measured diffraction pattern and the pattern simulated based on the singlecrystal data can be attributed to two major reasons. First, grinding of the crystals leads to a smeary solid, indicating that the crystals readily release solvent molecules (an observation that is often made for Zintl salts comprising crystal solvent), which commonly leads to the formation of related compounds with fewer crystal solvent, even in situ

Supplementary Information on Micro-X-Ray Fluorescence Spectroscopy (µ-XFS)

Results of the µ-XFS measurements are summarized in Supplementary Table 2, corresponding spectra are shown in Supplementary Figs. 6,7, and 8. The data of compound 2 was collected on the same crystal from which single crystal X-ray diffraction data was collected. Several measurements produced unreasonable deviation of the K versus Bi amounts. We assume that this is due to beginning corrosion on the crystal surface upon exposure during sample preparation. This is frequently observed for air-sensitive compounds, and also affects the data obtained for the other elements.

Supplementary Table 2 | µ-XFS analysis of 2 (K, Bi, Th), 3 (K, Tl, Bi, Th), and 4 (K, Pb, Bi, Th).

Element Element wt %

Weight % err.

( The magnetically induced current density was studied with the above ECPs, basis sets, and COSMO employing the BP86, 45,46 PBE, 14 TPSS, 47 and TPSSh 48 functional. Medium sized grids 17 (gridsize 3) were utilized for the numerical integration of the exchange correlation potential. Tight SCF convergence thresholds of 10 -8 Eh were used and a threshold of 10 -7 a.u. was used for the response of the orbitals in the coupled-perturbed Kohn-Sham equations to calculate the perturbed density as part of a NMR shielding calculation. 32 To study the effect of the relativistic Hamiltonian and the contribution of the core electrons to the ring current, the scalar-relativistic X2C Hamiltonian [23][24][25] was employed in its local variant 26 (DLU-X2C) within the finite nucleus model (parameters taken from Ref. 27) together with the segmented contracted Jorge-TZP-DKH, 49,50 taken from the basis set exchange library 51,52 and the decontracted Dyall-VTZ [53][54][55][56] basis set. Tailored grids 28 (gridsize 3a) were selected. Here, the RI-J approximation was not applied in the DLU-X2C calculations. The gauge-including magnetically induced current (GIMIC) code [57][58][59] was utilized to calculate the magnetically induced current density based on the derivative of the electron density with respect to the magnetic field and the Biot-Savart expressions of the NMR shielding constant. A diatropic current flow indicates an aromatic system whereas a paratropic current flow characterizes an antiaromatic compound according to the magnetic criterion of aromaticity. [59][60][61] The used version of GIMIC utilizes Python 3. For Python 2, the line 'from__future__import print_function' must be added to the header of the build version of turbo2gimic.py, which converts TURBOMOLE's (un)perturbed density matrices, structure, and basis set data to the GIMIC input. This allows Python 2.6 and 2.7 to interpret the Python 3 syntax of the print function.

The net current flow strength was obtained by numerical integration. Therefore, an integration plane was placed through the BiA-BiA′ bond parallel to the magnetic field, which is perpendicular to the molecular plane consisting of the BiA atoms and Th, as shown in Supplementary Fig. 15.

Supplementary Fig. 15 | Integration plane to calculate the current strength in order to quantify the degree of aromaticity. The integration plane was determined based on the magnetically induced current density profile for each level of theory.

The total net ring currents in Supplementary Table 3 indicate aromaticity. A diatropic ring current of ca. 22 to 24 nA/T was found in the ECP calculations. This is roughly twice the ring current of benzene (11.4 nA/T at the PBE level) and close to the ring current of porphine and zinc porphyrin (25.3 and 25.0 nA/T at the PBE level). The application of the DLU-X2C Hamiltonian results in a slight increase of the net ring current by ca. 2-3 nA/T with the Jorge-TZP-DKH basis set. Therefore, [Th@Bi12] 4-is clearly aromatic based on the magnetic criterion. The Bi12 8-ring sustains a net current flow of 23.4 nA/T at the ECP/BP86 level. Here, the integration plane starts at the centre of the ring. Similar to porphine, 62 all valence electrons of the Bi12 8-framework are involved in the current flow. Thus, Th 4+ is mainly required to stabilize the cluster, and of minor importance for the degree of aromaticity as it only changes the net ring current by ca. 3%. The ring current depends on the number of electrons and the molecular structure. Hence, it is not a direct measure of aromaticity. But has proven to be a useful tool in numerous studies 60,[62][63][64][65] and the ring current is a justification of aromaticity according to the International Union of Pure and Applied Chemistry 61 (IUPAC). Furthermore, we calculated the nucleus-independent chemical shifts 35 of the hypothetically "Bi12 8-" at the centre of the cluster. The NICS and current strengths are reported in Supplementary Table 4. These results also indicate aromaticity. GIMIC and NICS were also used to study and confirm the aromaticity of Al4 2-with Li + counter ions at the coupled-cluster level. 66 In our work, we calculated the NICS and ring current strength at the same level of theory as above (def2-TZVP/PBE/COSMO). This yields a NICS of -31.8 ppm and net ring current of 27.6 nA/T. The hypothetical "[Th@Bi12] ±0 " possess a diatropic net ring current of 6.9 nA/T (PBE).

Supplementary

To study the applicability of the 4n+2 rule, we considered the hypothetical "Bi12 10-" and "Bi12 12-" clusters. For the first, anti-aromaticity would be expected. The closed-shell singlet state is not the electron ground state, the triplet state is lower in energy: 9.76 kJ/mol (BP86), 8.54 kJ/mol (PBE), 8.01 kJ/mol (TPSS), and 9.74 kJ/mol (TPSSh). The triplet ground state is further confirmed by the fractional occupation number approach 67 and optimizing the number of unpaired electrons starting at a high damping level (9 a.u.). In contrast, the closed-shell "Bi12 12-" cluster is expected to be aromatic again. This is confirmed by computational studies based on the magnetic criterion. The ring current strength and the NICS values are listed in Supplementary Table 5. Here, the cluster sustains a global net ring current of more than 40 nA/T and the NICS about -33 ppm also indicates aromaticity. Furthermore, we calculated the NICS and current strengths of "Bi12 8-" and "Bi12 12-" with our NMR-tailored x2c-SVPall-s, 28 x2c-TZVPall-s, 28 and x2c-QVZPall-s basis sets 68 and proper auxiliary basis sets 29,68 for the RI-J approximation, which are listed in Supplementary Table 6 and Supplementary Table 7, respectively. Here, we also used the B3LYP, 69,70 CAM-B3LYP, [START_REF] Yanai | A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)[END_REF] and the PBE0 33 hybrid functional.

The optimized structure (Cartesian coordinates) of [Th@Bi12] 4-and the four reference compounds (Al4 2-, benzene, porphine, and zinc porphyrin) are listed in a separate file as part of the supplementary material (OptimizedStructures.txt) along with those of all other species shown in Fig. 3 in the main document and in Supplementary Figure 16. The structures of the reference compounds were optimized with grid 3. In addition, Supplementary Tables 8-12 provide atomic orbital contributions to molecular valence orbitals of all species shown in Fig. 4 of the main document and in Supplementary Figure 16.

Supplementary

Atomic Orbital Contributions to Molecular Orbitals

The contributions of atomic orbitals to valence orbitals of the species shown in Supplementary Fig. 16 and Fig. 4 of the main document according to Mulliken population analyses 10 are summarized in Supplementary Tables 8-12. Note that "ε" denotes the eigenvalue of the Kohn-Sham Fock matrix.

Supplementary Table 8 | Mulliken contributions of atomic orbitals (AOs) to valence molecular orbitals (MOs) of "Bi12 6-" (Supplementary Fig. 16 and Fig. 4 in the main document). The atom labelling scheme corresponds with that in Fig. 2 in the main document.

Mulliken contributions of Bi(A), and Bi(B) to the valence MOs of "Bi12 16 and Fig. 4 in the main document). The atom labelling scheme corresponds with that in Fig. 2 in the main document.

Mulliken contributions of La, Bi(A), and Bi(B) to the valence MOs of [La@Bi12] 16 and Fig. 4 in the main document). The atom labelling scheme corresponds with that in Fig. 2 in the main document. 16 and Fig. 4 in the main document). The atom labelling scheme corresponds with that in Fig. 2 in the main document. 16 and Fig. 4 in the main document). The atom labelling scheme corresponds with that in Fig. 2 in the main document.

Mulliken contributions of Bi(A) and Bi(B) to the valence MOs of Bi12

3 -

 3 . Larger S-N rings possess 10 π-electrons (S 4 N 2 , S 3 N

3 -

 3 . Larger S-N rings possess 10 π-electrons (S 4 N 2 , S 3 N

Fig. 1 |

 1 Fig.1| Survey of different classes of experimentally secured molecules exhibiting 4n + 2 π-aromaticity. NICS values (in ppm, grey) and ring currents (in nA T -1 , black) were calculated at the PBE/def2-TZVP/grid3 level of theory[48][49][50][51][52][53]59 , with the conductor-like screening model (COSMO) applied for anions54 . Simplifications of the molecules for the calculations are shown. From left to right: molecules with three to eight atoms and examples with more than eight atoms (rightmost) contributing to the 4n + 2 π-aromatic system. Missing entries indicate that no example has been reported for the respective class. a, Representatives of C-H aromatic molecules (with Li 2 [(Me 3 SiC) 4 ] (ref.7 ) as a rare example of a four-membered cycle). b, Representatives of heteroaromatic molecules (with K[(B t Bu) 2 CCH(SiMe 3 ) 2 ] as a rare example of a three-membered cycle8 and [(Ar*Ga) 2 (CH 2 )(CPh) 2 ] 2-as a representative of metallaaromatic molecules; Ar* = C 6 H 3 -2,6-(C 6 H 3 -2,6i Pr 2 ) 2 ; ref.9 ). c, Examples of purely inorganic, non-metal aromatic molecules (with the gas-phase species [B 3 (CO) 3 ] + as a rare example of a three-membered cycle)[START_REF] Ahlrichs | Electronic structure calculations on workstation computers: The program system turbomole[END_REF] . d, Survey of all known types of molecules exhibiting all-metal π-aromaticity, with their stabilizing atoms or groups:Tr = Al, Ga and R = C 6 H 3 -2,6-(C 6 H 2 -2,4,6-Me 3 ) 2 in [(RTr) 3 ] 2-(refs.[25][26][27] ); M/Tr = Li/Al, Na/Al, Cu/Al, Na/In, Na/Ga in gas-phase species [MTr 4 ] -(refs.28,29 );Ar* = C 6 H 3 -2,6-(C 6 H 2 -2,4,6i Pr 3 ) 2 ] in [(Ar*Ga) 2 Ga 2 ] 2-(ref.32 ); Tt = Sn, Pb (ref.36 ); Pn = Sb, Bi in gas-phase species Pn 5 -(ref.34 ). NICS values and ring currents are given for one homologue only, as numbers within the homologous series are similar. Note that the numbers refer to total ring currents unless noted otherwise. This may include additional contributions of σ-aromaticity. Weakly π-antiaromatic Pn 42-(Pn = Sb, Bi)21,22 are not listed here. For further references, see the text. Further details of the NICS and ring current calculations are provided in the Supplementary Information.

Fig. 2 | 2 .

 22 Fig. 2 | Molecular structure of the cluster anion [Th@Bi 12 ] 4-in compound 2. The molecule is shown in two different orientations with displacement ellipsoids drawn at the 50% probability level at 100(2) K. Ranges of selected distances (in Å): Bi A -Bi A ′ = d A 3.0420(14)-3.0785(13), Bi A -Bi B = d B 3.0440(11)-3.132(1), Th-Bi B = d c 3.2104(11)-3.2571(9), Th-Bi A 3.5251(13)-3.5908(9).

Fig. 3 |

 3 Fig. 3 | Frontier orbital region of the molecular orbital schemes of anions based on 12-atomic polybismuthide rings. a, Structure images of the calculated molecules (D 3h symmetry; Bi-Bi distances in Å). Atomic coordinates and contributions to all valence molecular orbitals are given in a separate file as part of the Supplementary Information and in Supplementary Tables 8-12, respectively. b, Frontier orbitals of the respective molecules: different irreducible representations are shown in different colours for clarity (molecular orbital levels drawn in grey are those that lie within the chosen energy range for the empty polybismuthide cycles only). The dashed lines serve as a guide to the eye to denote changes in the corresponding molecular-orbital energies. The energy of the HOMO is indicated by a filled circle and the lowest unoccupied molecular orbital (LUMO) by an open circle for each species; the singly occupied f orbital (HOMO-1, a 1 ′) of [U@Bi 12 ] 4-is indicated by a half-filled circle. c, Illustration of molecular orbitals of [Th@Bi 12 ] 4-(2A) in side view, with contours drawn at isovalues of ±0.02 a.u. in blue and red. Contributions from atomic orbitals to all valence molecular orbitals are provided in Supplementary Tables 8-12.

12 8 -Fig. 4 |

 84 Fig. 4 | HOMO of the cluster anion [Th@Bi 12 ] 4-and localized molecular orbitals (LMOs) from a Boys localization procedure in top and side views. a, The HOMO (character a 2 ′′ in D 3h symmetry). b, The LMO with the highest energy expectation value shows contributions from all 12 Bi atoms and has almost the same shape as the HOMO, which indicates intrinsic electron delocalization. c, Two-centre LMO representing a Bi-Bi bond within a Bi 4 ring. d, Two-centre LMO representing a Bi-Bi bond between two Bi 4 rings. e, Two-centre LMO representing a Bi-Th bond. f, One-centre LMO representing a lone pair at a Bi atom above/below the equatorial plane of the molecule. g, One-centre LMO representing a lone pair at a Bi atom within the equatorial plane of the molecule. Contours are drawn at isovalues of ±0.02 a.u. in blue and red, for approximately the same orientation of the molecule as shown in Fig. 2.

  four or six π-electrons, respectively. Although 'Bi 12 10-' possesses a triplet ground state (like the famous antiaromatic square planar cyclobutadiene), we calculate a ring current of 42.9 nA T -1 and a NICS value of -34 ppm for 'Bi12 12-

, As 5 - 3 +.Fig. 5 |

 535 Fig. 5 | Calculated ring currents in [Th@Bi 12 ] 4-. a, Plot of the magnetically induced current density (in atomic units), 2 bohr above the molecular plane of [Th@Bi 12 ] 4-. The magnetic field is perpendicular to the molecular plane. b, Profile of the magnetically induced current density to determine the boundaries for the numerical integration. The origin is at the zero point of the induced current density between the Bi A -Bi A′ bond and the Th atom (see Supplementary Information for details).

  # 3 Cl] (1). Compound 1 was prepared by metathesis reaction of ThCl 4 with KCp # (Cp # = 2,3,4,5-tetramethyl cyclopentadienyl, C 5 Me 4 H). ThCl 4 (3.065 g, 8.20 mmol) and KCp # (4.00 g, 25 mmol) were suspended in 300 ml of tetrahydrofuran at -78 °C. The mixture was allowed to reflux for a few hours. Soxhlet extraction of the crude, slightly yellow solid led to the extraction of 1.421 g (27.5%) of single-crystalline compound 1. Synthetic protocol of [K(crypt-222)] 4 [Th@Bi 12 ]•2en (2). The reactants for 2 were K 5 Ga 2 Bi 4 (A, 70 mg, 60 µmol), crypt-222 (113 mg, 300 µmol) and [ThCp #

  Th-centred clusters. To demonstrate the particular role of the Ga/Bi elemental combination in this synthetic route, we performed analogous reactions of [K(crypt-222)] 2 (TlBi 3 )•en (D, 200 mg 118 µmol) and [K(crypt-222)] 2 (Pb 2 Bi 2 )•en (E, 224 mg, 130 µmol) with [ThCp # 3 Cl] (37 mg, 59 µmol or 20 mg, 30 µmol) under otherwise identical reaction conditions. This resulted in the formation of the actinide-centred clusters [Th@Tl 2 Bi 11 ] 3- (3A) and [Th@Pb 4 Bi 9 ] 3-(4A), in their corresponding [K(crypt-222)] + salts [K(crypt-222)] 3 [Th@Tl 2 Bi 11 ]•tol (3) and [K(crypt-222)] 3 [Th@Pb 4 Bi 9 ] (4), both of which are known spherical cluster topologies. Compound 3 formed in 80% yield, and compound 4 formed as a minor product alongside re-crystallized precursor [K(crypt-222)] 2 (Pb 2 Bi 2 )•en and crystals of [K(crypt-222)] 2 (Pb 7 Bi 2 )•en 66 .

  (a famous example for the co-existence of such compounds 6[In4Bi5][In4Bi5]•1.5en•0.5tol). 1 Second, this procedure at the same time enhances the background, and it changes the relative intensities in addition to inherent texture effects. Cocrystallization of the interim precursors [K(crypt-222)]2(GaBi3) 1 and [K(crypt)]2Bi4 5 is sometimes observed under the given reaction conditions (see Methods section in the main document), yet in this sample, the reflections were not detected. Supplementary Fig. 5 | Powder X-ray diffraction diagram of compound 2. The black line shows the measured diffraction pattern, the red line represents the diffraction pattern simulated from the single-crystals X-ray diffraction data.

Supplementary Fig. 13 |

 13 Illustration of representative localized molecular orbitals of [Th@Bi12] 4-generated with the intrinsic bond orbital (IBO) method. a, IBO representing a non-localizable orbital of highest energy that is responsible for the π-aromaticity of compound 2 (side view). b, IBO representing a 2-center-2-electron (2c2e) Bi-Bi bond within a Bi4 ring (top view). c, IBO representing a 2c2e Bi-Bi bond between two Bi4 rings (top view). d, IBO representing a 2c2e Bi-Th bond (top view). e, IBO representing a lone pair at a Bi atom above/below the equatorial plane of the molecule (top view). f, IBO representing a lone pair found at a Bi atom within the equatorial plane of the molecule (top view). Contours are drawn at isovalues of ±0.021 a.u. in blue and red colour in each panel.

2.1. Supplementary Information on the Single-Crystal X-Ray Diffraction Studies

	All hydrogen atoms were kept riding on calculated positions with isotropic displacement
	parameters U = 1.2 Ueq (or 1.5 Ueq for methyl groups) of the bonding partners. Crystallographic
	data for the three structures reported in this paper have been deposited with the Cambridge
	Crystallographic Data Centre as supplementary publications nos. CCDC-1983070 (1), CCDC-
	1983072 (2), CCDC-1983073 (3), CCDC-1983071 (4). The crystal data and experimental
	parameters of the structure determinations are collected in Supplementary

Table 1 . Supplementary Table 1 | Crystal data and details of the structure determinations of 1-4.

 1

	Compound	1	2	3	4
	empirical formula	C27H39ClTh	C76H156Bi12K4N12O24Th	C42N4O12K3Tl2Bi11Th	C43N4O12K3Pb4Bi9Th
	nominal formula	C27H39ClTh	C76H156Bi12K4N12O24Th C61H116N6O18K3Tl2Bi11Th C61H116N6O18K3Pb4Bi9Th
	formula weight [g mol -1 ]	631.07	4257.50	3809.32	4188.38
	crystal colour, shape	colourless, plate	black, prism	black, block	black, block
	crystal size [mm 3 ]	0.03×0.03×0.06	0.17×0.09×0.015	0.15×0.16×0.010	0.12×0.10×0.08
	crystal system	cubic	triclinic	monoclinic	monoclinic
	space group	I-43d	P1	P21/m	P21/m
	a [Å]	21.3159(3)	14.5025(2)	14.6434(1)	14.6520(3)
	b [Å]		16.4157(2)	21.801(2)	21.970(4)
	c [Å]		27.2255(4)	16.3934(2)	16.468(3)
	α [°]		81.1720(10)
	β [°]		86.0500(10)	107.135(1)	107.80(3)
	γ [°]		6 7 . 1 6 0 0 ( 1 0 )
	V [Å 3 ]	9685.3(4)	5902.27(15)	5001.15(9)	5047.4(19)
	Z / ρcalc [g cm -3 ]	16 / 1.731	2 / 2.540	2 / 2.530	2 / 2.511
	µ [mm -1 ]	(CuKα) 20.93	(CuKα) 40.064	(CuKα) 49.285	(MoKα) 23.908
	absorption correction	numerical	numerical	numerical	numerical
	θ range [°]	5.1 -69.9	2.9 -68.0	2.8 -67.5	1.3 -25.4
	total reflns	20014	170346	150785	45407
	unique reflns / [Rint]	1529 / 0.047	21314/ 0.109	9272/ 0.095	9511/ 0.179
	obs. Reflns [I > 2σ(I)]	1389	14722	8068	6108
	Parameters	92	1171	213	213
	wR2 (all data) / R1 [I > 2σ(I)]	0.0247 / 0.0129	0.2324/ 0.0759	0.2312 / 0.0774	0.2395/ 0.0831
	GooF (all data)	1.04	1.01	1.06	1.05
	max peak/hole [e Å -3 ]	0.23/ -0.31	4.80/ -3.64	7.56/ -3.54	3.81/ -4.20

Table 3 | Current strength of [Th@Bi12] 4-in nA/T at various levels of theory.

 3

	Functional	ECP/def(2)-TZVP	DLU-X2C/Jorge-TZP-DKH	DLU-X2C/Dyall-VTZ
	BP86	22.4	24.7	23.2
	PBE	22.7	24.8	23.4
	TPSS	22.9	24.8	23.3
	TPSSh	24.0	25.5	24.2
	Supplementary

Table 4 | Current strength in nA/T and NICS values in ppm of "Bi12 8-".

 4

	Functional	ECP/def(2)-TZVP	DLU-X2C/Jorge-TZP-DKH	DLU-X2C/Dyall-VTZ
		R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S
	BP86	23.4	-16.8	23.0	-15.3	23.3	-17.6
	PBE	23.7	-17.1	23.2	-15.4	23.4	-17.8
	TPSS	23.4	-17.1	22.8	-15.7	23.1	-17.7
	TPSSh	23.7	-17.5	23.0	-16.3	23.4	-18.0

Table 5 | Current strength in nA/T and NICS values in ppm of "Bi12 12-".

 5

	Functional	ECP/def(2)-TZVP	DLU-X2C/Jorge-TZP-DKH	DLU-X2C/Dyall-VTZ
	R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S
	BP86	42.0	-33.4	41.0	-32.1	41.1	-34.2
	PBE	42.9	-34.0	41.8	-32.7	41.9	-34.8
	TPSS	42.6	-33.9	41.6	-33.0	41.7	-34.7
	TPSSh	42.8	-34.3	41.8	-33.5	41.6	-35.1
	Supplementary

Table 6 | Current strength in nA/T and NICS values in ppm of "Bi12 8-" using the NMR-tailored basis sets and the DLU-X2C Hamiltonian.

 6

	Functional	x2c-SVPall-s	x2c-TZVPall-s	x2c-QZVPall-s
		R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S
	BP86	21.0	-15.5	21.8	-16.3	23.0	-18.0
	B3LYP	20.8	-16.3	21.9	-16.6	23.1	-17.9
	CAM-B3LYP	20.2	-16.4	21.4	-16.5	22.8	-17.5
	PBE	21.1	-15.6	22.0	-16.5	23.1	-18.2
	PBE0	21.2	-16.7	22.3	-17.3	23.6	-18.7
	TPSS	20.8	-15.7	21.7	-16.5	22.8	-18.0
	TPSSh	20.9	-16.2	21.9	-16.9	23.1	-18.3

Supplementary Table 7 | Current strength in nA/T and NICS values in ppm of "Bi12 12-" using the NMR-tailored basis sets and the DLU-X2C Hamiltonian.

	Functional	x2c-SVPall-s	x2c-TZVPall-s	x2c-QZVPall-s
		R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S	R i n g C u r r e n t	N I C S
	BP86	36.2	-31.2	37.9	-32.6	40.4	-34.7
	B3LYP	35.1	-30.9	36.6	-32.3	38.9	-34.3
	CAM-B3LYP	32.3	-29.3	33.7	-30.9	37.0	-33.8
	PBE	36.9	-31.7	38.7	-33.2	41.1	-35.2
	PBE0	36.7	-32.2	38.7	-33.9	41.0	-36.1
	TPSS	36.5	-31.6	38.6	-33.1	40.9	-35.2
	TPSSh	36.5	-31.9	38.6	-33.5	40.9	-35.6

Table 9 | Mulliken contributions of atomic orbitals (AOs) to valence molecular orbitals (MOs) of [La@Bi12] 3-(Supplementary Fig.

 9

	6-" at the ECP/def(2)-TZVP/PBE level using COSMO

Table 10 | Mulliken contributions of atomic orbitals (AOs) to valence molecular orbitals (MOs) of [U@Bi12] 4-(Supplementary Fig.

 10

	3-at the ECP/def(2)-TZVP/PBE level using COSMO

Table 10 (continued).

 10

	Mulliken contributions of U, Bi(A), and Bi(B) to the valence MOs of [U@Bi12] 4-at the ECP/def(2)-TZVP/PBE level using COSMO
	16a1' α (ε = -0.2397690 a.u.)
	atom	total	s	p	d	f
	U	0.07663	0.00217	0.00000	0.07135	0.00311
	Bi(B)	0.06633	0.00068	0.06355	0.00203	0.00007
	Bi(A)	0.08757	0.00019	0.08613	0.00121	0.00004
	17a1' α (ε = -0.2324428 a.u.)
	U	0.08697	0.08490	0.00000	0.00202	0.00006
	Bi(B)	0.07925	0.00403	0.07361	0.00155	0.00005
	Bi(A)	0.07292	0.00225	0.06756	0.00302	0.00010
	18a1' α (ε = -0.1631745 a.u.)
	U	0.19740	0.02305	0.00000	0.16861	0.00573
	Bi(B)	0.06008	0.00159	0.05575	0.00222	0.00052
	Bi(A)	0.07368	0.00243	0.07069	0.00031	0.00026
	11a2' α (ε = -0.1392247 a.u.)
	U	0.07656	0.00000	0.00000	0.00000	0.07656
	Bi(B)	0.05448	0.00000	0.05251	0.00137	0.00060
	Bi(A)	0.09943	0.00186	0.09721	-0.00016	0.00052
	26e' α (ε = -0.2045006 a.u.)
	U	0.25341	0.00000	0.00005	0.25017	0.00319
	Bi(B)	0.09549	0.00360	0.08608	0.00529	0.00052
	Bi(A)	0.19561	0.01017	0.18180	0.00332	0.00032
	27e' α (ε = -0.1942777 a.u.)
	U	0.05164	0.00000	0.02710	0.02073	0.00381
	Bi(B)	0.11032	0.00291	0.10383	0.00297	0.00062
	Bi(A)	0.21440	0.00426	0.20547	0.00430	0.00037
	28e' α (ε = -0.1762217 a.u.)
	U	0.10593	0.00000	0.00656	0.09833	0.00104
	Bi(B)	0.08752	0.00064	0.08343	0.00272	0.00073
	Bi(A)	0.22816	0.00324	0.22005	0.00397	0.00089
	29e' α (ε = -0.1309009 a.u.)
	U	0.28890	0.00000	-0.00030	0.10707	0.18213
	Bi(B)	0.22197	-0.00132	0.22107	0.00135	0.00087
	Bi(A)	0.06322	-0.00053	0.05781	0.00479	0.00114
	30e' α (ε = -0.0794484 a.u.) LUMO (α spin)
	Bi(B)	0.19658	-0.00185	0.19238	0.00487	0.00118
	Bi(A)	0.13651	-0.00751	0.13374	0.00967	0.00061
	7a1" α (ε = -0.1708066 a.u.)
	Bi(B)	0.08181	0.00000	0.07855	0.00308	0.00017
	Bi(A)	0.08486	0.00000	0.08342	0.00109	0.00035
	12a2" α (ε = -0.1959519 a.u.)
	U	0.01748	0.00000	0.00356	0.00000	0.01392
	Bi(B)	0.10264	0.00096	0.09982	0.00166	0.00020
	Bi(A)	0.06111	0.00000	0.06060	0.00027	0.00024
	13a2" α (ε = -0.1500130 a.u.)
	U	0.02367	0.00000	0.01757	0.00000	0.00610
	Bi(B)	0.14236	0.00212	0.13990	0.00016	0.00017
	Bi(A)	0.02036	0.00000	0.01686	0.00309	0.00040
	14a2" α (ε = -0.1005623 a.u.) HOMO (α spin)
	U	0.04634	0.00000	-0.00089	0.00000	0.04723
	Bi(B)	0.06815	-0.00466	0.07014	0.00243	0.00024
	Bi(A)	0.09079	0.00000	0.08348	0.00654	0.00078
	17e" α (ε = -0.2219263 a.u.)
	U	0.18025	0.00000	0.00000	0.16790	0.01234
	Bi(B)	0.15548	0.00205	0.15132	0.00206	0.00004
	Bi(A)	0.14781	0.00000	0.14387	0.00373	0.00021
	18e" α (ε = -0.1576063 a.u.)
	U	0.36239	0.00000	0.00000	0.29502	0.06737
	Bi(B)	0.23172	0.00516	0.22598	0.00009	0.00049
	Bi(A)	0.04122	0.00000	0.03814	0.00203	0.00105

Table 10 (continued).

 10

	19e" β (ε = -0.1517744 a.u.)
	U	0.10094	0.00000	0.00000	0.09876	0.00218
	Bi(B)	0.15876	0.00303	0.15032	0.00441	0.00101
	Bi(A)	0.15775	0.00000	0.15380	0.00333	0.00062
	Supplementary

Table 11 | Mulliken contributions of atomic orbitals (AOs) to valence molecular orbitals (MOs) of [Th@Bi12] 4-(Supplementary Fig.

 11

Table 11 (continued).

 11 Mulliken contributions of Th, Bi(A), and Bi(B) to the valence MOs of [Th@Bi12] 4-at the ECP/def(2)-TZVP/PBE level using COSMO

	16a1' (ε = -0.2263257 a.u.)
	atom	total	s	p	d	f
	Th	0.11326	0.01674	0.00000	0.09063	0.00585
	Bi(B)	0.13357	0.00457	0.12481	0.00403	0.00016
	Bi(A)	0.18089	0.00056	0.17766	0.00256	0.00011
	17a1' (ε = -0.2223264 a.u.)
	Th	0.21972	0.21299	0.00000	0.00653	0.00020
	Bi(B)	0.13507	0.00423	0.12816	0.00251	0.00017
	Bi(A)	0.16164	0.00411	0.15282	0.00458	0.00013
	18a1' (ε = -0.1449244 a.u.)
	Th	0.40042	0.06606	0.00000	0.32621	0.00788
	Bi(B)	0.14210	0.00144	0.13653	0.00339	0.00075
	Bi(A)	0.12449	0.00309	0.12021	0.00063	0.00057
	11a2' (ε = -0.1364050 a.u.)
	Th	0.04784	0.00000	0.00000	0.00000	0.04784
	Bi(B)	0.12266	0.00000	0.11975	0.00197	0.00094
	Bi(A)	0.20269	0.00435	0.19668	0.00069	0.00098
	26e' (ε = -0.1985834 a.u.)
	Th	0.41579	0.00000	0.00459	0.40757	0.00325
	Bi(B)	0.22110	0.01062	0.20075	0.00882	0.00090
	Bi(A)	0.37627	0.01293	0.35614	0.00660	0.00060
	27e' (ε = -0.1846237 a.u.)
	Th	0.16342	0.00000	0.05896	0.10264	0.00166
	Bi(B)	0.17503	0.00226	0.16680	0.00480	0.00117
	Bi(A)	0.46440	0.01157	0.44634	0.00600	0.00049
	28e' (ε = -0.1723174 a.u.)
	Th	0.25737	0.00000	0.01335	0.24276	0.00011
	Bi(B)	0.18915	0.00142	0.18052	0.00587	0.00135
	Bi(A)	0.43462	0.00411	0.42159	0.00738	0.00155
	29e' (ε = -0.1253780 a.u.)
	Th	0.27128	0.00000	0.00875	0.19529	0.06720
	Bi(B)	0.44999	-0.00083	0.44707	0.00267	0.00108
	Bi(A)	0.17146	0.00216	0.15498	0.01205	0.00228
	30e' (ε = -0.0779870 a.u.) LUMO
	Th	-0.01413	0.00000	0.00250	-0.02220	0.00332
	Bi(B)	0.41541	-0.00216	0.40475	0.01064	0.00218
	Bi(A)	0.25361	-0.01461	0.24957	0.01745	0.00121
	7a1" (ε = -0.1737260 a.u.)
	Bi(B)	0.16637	0.00000	0.16185	0.00425	0.00027
	Bi(A)	0.16674	0.00000	0.16389	0.00227	0.00058
	12a2" (ε = -0.1774834 a.u.)
	Th	0.02484	0.00000	0.01377	0.00000	0.01107
	Bi(B)	0.18850	0.00384	0.18203	0.00220	0.00044
	Bi(A)	0.14069	0.00000	0.13989	0.00030	0.00050
	13a2" (ε = -0.1404908 a.u.)
	Th	0.05272	0.00000	0.04862	0.00000	0.00400
	Bi(B)	0.29026	0.00215	0.28755	0.00032	0.00024
	Bi(A)	0.03428	0.00000	0.02702	0.00654	0.00072
	14a2" (ε = -0.0920928 a.u.) HOMO
	Th	0.01848	0.00000	0.00386	0.00000	0.01325
	Bi(B)	0.15803	-0.00976	0.16380	0.00374	0.00025
	Bi(A)	0.17223	0.00000	0.15824	0.01252	0.00148

Table 12 | Mulliken contributions of atomic orbitals (AOs) to valence molecular orbitals (MOs) of "Bi12 8-" (Supplementary Fig.

 12

  8-at the ECP/def(2)-TZVP/PBE level using COSMO

	18e" (ε = -0.1202864 a.u.)
	Bi(B)	0.32469	0.00000	0.31732	0.00625	0.00112
	Bi(A)	0.34198	0.01114	0.32224	0.00704	0.00156
	19e" (ε = -0.0796599 a.u.) HOMO
	Bi(B)	0.02733	0.00000	0.01920	0.00594	0.00219
	Bi(A)	0.63934	-0.00063	0.63386	0.00582	0.00029
	15a1' (ε = -0.2004016 a.u.)
	atom	total	s	p	d	f
	Bi(B)	0.19462	0.00003	0.19339	0.00112	0.00008
	Bi(A)	0.13871	0.00357	0.13342	0.00156	0.00017
	16a1' (ε = -0.1749722 a.u.)
	Bi(B)	0.18776	0.00225	0.18264	0.00275	0.00011
	Bi(A)	0.14558	-0.00046	0.14712	-0.00130	0.00021
	17a1' (ε = -0.0992400 a.u.)
	Bi(B)	0.11237	0.00280	0.10408	0.00450	0.00099
	Bi(A)	0.22096	-0.00028	0.21973	0.00144	0.00007
	11a2' (ε = -0.1129345 a.u.)
	Bi(B)	0.21023	0.00321	0.20293	0.00298	0.00112
	Bi(A)	0.12310	0.00000	0.12073	0.00153	0.00084
	25e' (ε = -0.1705667 a.u.)
	Bi(B)	0.42599	0.00300	0.41549	0.00691	0.00058
	Bi(A)	0.24068	0.00826	0.22499	0.00657	0.00087
	26e' (ε = -0.1607234 a.u.)
	Bi(B)	0.51719	0.00939	0.50628	0.00106	0.00045
	Bi(A)	0.14948	-0.00007	0.14611	0.00254	0.00090
	27e' (ε = -0.1439596 a.u.)
	Bi(B)	0.35455	0.00652	0.33621	0.01015	0.00166
	Bi(A)	0.31212	0.00160	0.30853	0.00099	0.00100
	28e' (ε = -0.0913007 a.u.)
	Bi(B)	0.27122	-0.00154	0.26034	0.01048	0.00194
	Bi(A)	0.39545	0.00060	0.38643	0.00725	0.00118
	29e' (ε = -0.0563593 a.u.) LUMO
	Bi(B)	0.24318	-0.02551	0.25303	0.01461	0.00105
	Bi(A)	0.42349	-0.00219	0.40795	0.01584	0.00188
	7a1" (ε = -0.1500247 a.u.)
	Bi(B)	0.17600	0.00000	0.17287	0.00247	0.00066
	Bi(A)	0.15733	0.00000	0.15251	0.00452	0.00031
	11a2" (ε = -0.1541818 a.u.)
	Bi(B)	0.14442	0.00000	0.14373	0.00014	0.00055
	Bi(A)	0.18891	0.00333	0.18361	0.00151	0.00047
	12a2" (ε = -0.1125620 a.u.)
	Bi(B)	0.04967	0.00000	0.04327	0.00582	0.00058
	Bi(A)	0.28366	-0.00109	0.28143	0.00295	0.00036
	13a2" (ε = -0.0810022 a.u.)
	Bi(B)	0.15102	0.00000	0.13891	0.01075	0.00136
	Bi(A)	0.18232	-0.00709	0.18784	0.00148	0.00008
	17e" (ε = -0.1863270 a.u.)
	Bi(B)	0.36827	0.00000	0.36361	0.00440	0.00026
	Bi(A)	0.29840	0.00110	0.29496	0.00191	0.00042

Acknowledgements

We thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for financial support within the framework of GRK 1782. We thank J.L. Vasco and M. Pyschik for help with the synthesis, S. Ivlev, B. Weinert, M. Marsch and R. Riedel for help with the diffraction experiments, and M. Hellwig for measuring the EDX spectra of 1. We also thank K. Reiter and F. Dehnen for discussions. N.L. acknowledges a grant from Marburg University Research Academy (MARA). Y.J.F. is grateful to Fonds der Chemischen Industrie for general support of his PhD. studies (Kekulé fellowship), to the German Academic Exchange Service (Deutscher Akademischer Austauschdienst, DAAD) for a fellowship (grant no. 57438025) and to F. Furche for hosting. R.C. acknowledges support from the University of Bordeaux, the CNRS, the Region Nouvelle Aquitaine, the MOLSPIN COST action CA15128 and the GdR MCM-2.

Data availability

All data generated or analysed during this study are included in this Article and its Supplementary Information files. The structures of compounds 1-4 were determined by single-crystal X-ray diffraction. The crystallographic data have been deposited with the Cambridge Crystallographic Data Centre under CCDC numbers 1983070 (1), 1983072 (2), 1983073 (3) and 1983071 (4). The optimized structures of all studied compounds are part of the Supplementary Information (separate zip file 'Supplementary-Computational-Data.zip'): the coordinates of the optimized structures shown in Fig. 1, as well as their NICS values and ring current strengths, are provided in the Supplementary File 'Fig1-OptimizedStructures-GIMIC-NICS.txt' . All calculated coordinates of the optimized structures of 2A and the compounds mentioned explicitly in the main text or Supplementary Information are provided in a Supplementary File 'OptimizedStructures.txt' . The files comprise all necessary data for reproducing the values. All non-default parameters for the computational studies are given in the Supplementary Information together with the corresponding references of the used methods. For the default parameters of TURBOMOLE, such as the convergence criteria for structure optimizations, please see the manual at https://www.turbomole.org (retrieved 29 August 2020).

Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41557-020-00592-z.

Author contributions

A.R.E., N.L., R.J.W. and H.L.D. conceived and performed the synthetic experiments, collected single-crystal X-ray crystallographic data, solved and refined the structures, performed ESI-MS and prepared samples for further analyses. R.C. performed and analysed the magnetic measurements. F.W. performed the computational structure optimization and orbital analysis, and Y.J.F. studied the aromaticity and performed the TD-DFT calculations as well as the structure optimizations for Fig. 1. S.D., F.K. and F.W. supervised the work. All authors co-wrote the paper.

Competing interests

The authors declare no competing interests.

Supplementary Information

Substantial π-aromaticity of the anionic heavy-metal cluster [Th@Bi12] 4- Armin R. Eulenstein, 1,2 Yannick J. Franzke, 3, † Niels Lichtenberger, 1,2 Robert J. Wilson, 1,2 H. Lars Deubner, 1 Florian Kraus, 1 Rodolphe Clérac, 4 Florian Weigend, 1 * and Stefanie Dehnen 1,2 * 1 Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany. E-Mail: dehnen@chemie.uni-marburg.de; florian.weigend@chemie.uni-marburg.de 2 Wissenschaftliches Zentrum für Materialwissenschaften (WZMW), Philipps-Universität Marburg, Hans-Meerwein-Str. 6, 35032 Marburg, Germany. 3 Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131 Karlsruhe, Germany.

Details of the Structure Determinations

Structure Determination of Compounds [ThCp # 3Cl] (1) and [K(crypt-222)]4[Th@Bi12]•2en (2)

Supplementary Fig. 1 provides the view of a section of the crystal structure of compound 1, and Supplementary Fig. 2 provides the view of a section of the crystal structure of compound 2. The structure of 2 could be solved in the centrosymmetric triclinic space group P1 . It revealed one independent [Th@Bi12] 4-anion with pseudo-symmetry D3h (see Fig. 2 in the main document). Remaining electron density is mainly located in close proximity to the heavily absorbing Th and Bi atoms and is an effect of absorption that could not be resolved by different absorption correction techniques (µ = 40mm -1 ), in addition to termination effects near the heavy atoms.

Structural Models of Compounds [K(crypt-222)]3[Th@Tl2Bi11]•tol (3) and [K(crypt-222)]3[Th@Pb4Bi9]•tol (4)

Supplementary Fig. 3 provides the view of a section of the crystal structure of compound 3, and Supplementary Fig. 4 provides the view of a section of the crystal structure of compound 4. For compounds 3 and 4, the solvent mask as implemented in Olex 2-1.3 was applied for one not localizable crypt-222 molecule per compound. 9 For compound 3, the total solvent accessible volume / cell amounts to 1673.3 Å 3 [33.5%], the total electron count / cell is 196.8. For compound 4, the total solvent accessible volume / cell amounts to 1684.1 Å 3 [33.4%], the total electron count / cell is 97.7.

Supplementary

Responses to A-Level and B-Level Alerts in the CIFs of Compounds 2, 3, and 4

Responses to A-level and B-level alerts in the CIF of compound [K(crypt-222)]4[Th@Bi12]•2en (2)

PROBLEM: Large Hirshfeld Difference C8DA--C7DA 0.32 Ang. RESPONSE: This is due to heavy disorder of the organic molecules in the crystal structure, which was modelled by split positions that produce small distances between (non-bonded) atoms on these disorder positions.

Supplementary Fig. 6 | µ-XFS spectrum of 2 (line) with the results of the deconvolution algorithm (solid, coloured).

Colours are used as follows: K (yellow), Bi (turquoise), Th (orange). Note, that the intensity is displayed on a square root scale to allow for a better visibility of small features in the spectrum.

Supplementary Fig. 7 | µ-XFS spectrum of 3 (line) with the results of the deconvolution algorithm (solid, coloured).

Colours are used as follows: K (green), Bi (turquoise), Th (orange), Tl (yellow). Note, that the intensity is displayed on a square root scale to allow for a better visibility of small features in the spectrum.

Supplementary Fig. 8 | µ-XFS spectrum of 4 (line) with the results of the deconvolution algorithm (solid, coloured).

Colours are used as follows: K (green), Bi (turquoise), Th (orange), Pb (red). Note, that the intensity is displayed on a square root scale to allow for a better visibility of small features in the spectrum.

Supplementary Information on Electrospray Ionization (ESI) Mass Spectrometry

ESI Mass Spectrum of [K(crypt-222)]3[Th@Tl2Bi11]•tol (3)

Supplementary Fig. 10 |

ESI Mass Spectrum of [K(crypt-222)]3[Th@Pb4Bi9]•tol (4)

Supplementary Fig. 11 |

Supplementary Information on Magnetic Measurements of Compound 2

Supplementary Fig. 12 | Temperature dependence of the magnetic susceptibility, χ, at 0.1 and 1 T between 1.85 and 300 K. The susceptibility χ is defined as magnetic susceptibility equal to M/H per mole of the complex).

Supplementary Details on Quantum Chemical Investigations

Methods and Supplementary Results

Calculations were carried out with TURBOMOLE. [10][START_REF] Ahlrichs | Electronic structure calculations on workstation computers: The program system turbomole[END_REF][12][START_REF] Balasubramani | Modular program suite for ab initio quantum-chemical and condensed-matter simulations[END_REF] The structures of the molecules displayed in Fig. 1 of the main text and related compounds were optimized with the PBE 14 functional. For molecules featuring light elements (up to Kr) only, the def2-TZVP basis 15 together the corresponding auxiliary basis sets 16 for the resolution of the identity approximation (RI-J). Medium sized grids 17 (gridsize 3) were used for the numerical integration of the exchange-correlation terms. The conductor-like screening model 18,19 (COSMO) was applied for charge compensation of the cations and anions with the default parameters. The dispersion corrections D3 20 and D4 21,22 were applied to the diborallyl cation due to the tert-butyl groups. Structures of molecules containing heavier elements were optimized with the scalar-relativistic exact two-component (X2C) Hamiltonian [23][24][25] in its local variant 26 (DLU-X2C) within the finite nucleus model (parameters taken from Ref. 27) using tailored grids 28 (gridsize 3a) and the x2c-TZVPall-s basis set 28 with the corresponding auxiliary basis. 29 Additionally, single point calculations of these compounds were carried out with the def2-TZVP (auxiliary) basis set and effective core potentials. 30,31 Tight selfconsistent field (SCF) convergence thresholds of 10 -8 Eh were used for all calculations and a threshold of 10 -7 a.u. was used for the response of the orbitals (norm of the residuum) in the coupled-perturbed Kohn-Sham equations to calculate the perturbed density as part of a nuclear magnetic resonance (NMR) shielding calculation. 32 For Sb4 2-and Bi4 2-, calculations were further performed with the PBE0 hybrid functional 33 and also with the def2-TZVPPD basis set. 34 Ring currents and nucleus-independent chemical shifts 35 (NICS) were calculated analogously as outlined below for [Th@Bi12] 4-. However, for S2N2, Se4 2+ , and Te4 2+ NICS(1) to NICS (5) were additionally calculated in line with Ref. 36. The results are listed in an additional supplementary file (Fig1-OptimizedStructures-GIMIC-NICS.txt).

The structure of [Th@Bi12] 4-was optimized with the following parameters. For Th, an effective core potential covering the 78 inner electrons (ECP-78) 37 was used together with a triple-zeta basis 37 (def-TZVP), for Bi an ECP-60 30 also with a triple-zeta basis 15 (def2-TZVP). COSMO 18,19 was applied for charge compensation with the default parameters. Structures were optimized using the PBE 14 functional and medium sized modified grids 17 (gridsize m3) together with a selfconsistent field (SCF) convergence threshold of 10 -7 Eh. The RI-J approximation was applied with the corresponding auxiliary basis sets. 16 The lowest triplet excitation energy based on timedependent density functional theory [38][39][40] (TD-DFT) is 0.351 eV. A norm of the residuum of 10 -6 a.u. ensures well-converged excitation vectors. Thus, no triplet instability is encountered.

Orbital localization was carried out with the Boys procedure 41 and the intrinsic bond orbital (IBO) method, 42 representative localized orbitals are shown in Fig. 4b-4g in the main document, and Supplementary Fig. 13. Atomic charge contributions to molecular orbitals were calculated with a Mulliken population analysis. 43 A comparison of the electron localization function 44 (ELF) of "[Bi12] 6-" and "[Bi12] 8-" is shown in Supplementary Fig. 14. Supplementary Fig. 14 | .