φ-Aromaticity in prismatic {Bi6}-based clusters

The occurrence of aromaticity in organic molecules is widely accepted, but its occurrence in purely metallic systems is less widespread. Molecules comprising only metal atoms (M) are known to be able to exhibit aromatic behaviour, sustaining ring currents inside an external magnetic field along M–M connection axes (σ-aromaticity) or above and below the plane (π-aromaticity) for cyclic or cage-type compounds. However, all-metal compounds provide an extension of the electrons’ mobility also in other directions. Here, we show that regular {Bi6} prisms exhibit a non-localizable molecular orbital of f-type symmetry and generate a strong ring current that leads to a behaviour referred to as φ-aromaticity. The experimentally observed heterometallic cluster [{CpRu}3Bi6]–, based on a regular prismatic {Bi6} unit, displays aromatic behaviour; according to quantum chemical calculations, the corresponding hypothetical Bi62− prism shows a similar behaviour. By contrast, [{(cod)Ir}3Bi6] features a distorted Bi6 moiety that inhibits φ-aromaticity.


Supplementary Discussion on the Formation of Compounds [K(crypt-222)]1·0.5tol and [K(crypt-222)]2·tol
The formation pathway of the anions 1and 2apparently follows a complicated redox cascade, as at some stage the Bi2 2− has to undergo a number of oxidation processes to account for the surprisingly low charge of the overall clusters in compounds [K(crypt-222)]1·0.5tol and [K(crypt-222)]2·tol.
Regarding the prismatic architecture of the {Bi6} in [{LM}3Bi6] − (LM = CpRu in 1 and (cod)Ir in 2) with a formal charge of 4-in combination with three formally 1+ charged {LM} units, two pathways seem to be plausible starting out from Bi2 2based on observations made in this study and in previous ones: (1) Formation of two 6π-aromatic species Bi3 3from three Bi2 2in the first step, potentially/in part with transition metal complex fragments attached, and a pairwise coplanar oxidative coupling.
(2) Formation of the known anion Bi4 2-(under 2-eoxidation) and linkage of the latter with the originally provided Bi2 2anion under assistance and attachment of transition metal complex fragments.
The formation of Bi4 2was reported in previous studies. The compound can be identified easily from the formation of a blueish-greenish color of the reaction solution shortly upon combination of the reactants. However, in the current case, such observations were not made, which seems to disfavor route (2).
Notably, a species [{(cod)Ir}3Bi3H] − is observed in the ESI-MS studies of the reaction solution yielding the cluster 1 -. A plausible reaction scheme for the final cluster thus accords with pathway (1) from the experimental data. We assume that upon combination of a Bi3 3unit with three [(cod)Ir] + fragments, this species actually carries no charge in solution, but takes up one negative charge during transfer into the gas phase in the ESI-MS experiment. Although a corresponding experimental proof is missing in the case of cluster 2as no other products have been experimentally identifiable (in agreement with the differently Lewis-acidic influence of the transition metal fragments), this does not exclude a corresponding mechanism to occur.
We therefore suggest the formation of the cluster via triangular units, their intermediate stabilization (and charge reduction) by attachment of three transition metal complex fragments, and subsequent combination of this heterometallic, hexanuclear cluster with another Bi3 3moiety under 2-eoxidation. An alternative scenario would include the preceding oxidation of Bi3 3to give Bi3and a combination of the latter with the {Ir3Bi3}-based unit, yet this seems to be less likely, as Bi3is an antiaromatic species and its formation is therefore less favorable.
The questions to be answered in future work addresses the details of the oxidation step. Based on preliminary findings, we suggest a concerted activity of the named intermediates with lower-charge polybismuthide-units that are further reduced to form higher-charge polybismuthide anions as byproducts. Given that we can obtain compounds [K(crypt-222)]1·0.5tol and [K(crypt-222)]2·tol in appreciable quantities, we suggest that their formation represents the first steps towards further investigation of the chemistry and reactivity of Bi-rich compounds in general.

Supplementary Information on X-Ray Diffraction
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 two structures reported in this paper have been deposited with the Cambridge Crystallographic Data Centre as supplementary publications nos. CCDC-2157676 ([K(crypt-222)]1·0.5tol) and CCDC-2157677 ([K(crypt-222)]2·tol). The crystal data and experimental parameters of the structure determinations are collected in Supplementary Table S1.

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 Figure 3 and Supplementary Figure 4. The data of both compounds were collected on crystals from the same reaction the crystal structures were obtained from. Several measurements produced a deviation of the K versus Bi amounts. This is frequently observed for air-sensitive compounds, and also affects the data obtained for the other elements. We assume that this is due to beginning corrosion on the crystal surface upon exposure during sample preparation.
The appearance of Rh in the measured spectrum is a consequence of the Rh X-ray source.

Supplementary Information on Electrospray Ionization (ESI) Mass Spectrometry
Results Overview spectrum between 200 and 3000 m/z with assigning of signals with a relative abundance higher than 5%. While the species at m/z = 1529.1 did not form an isolable product, single-crystals of [K(crypt-222)]2·tol were obtained from this solution that produce a pure mass spectrum of the peak at m/z = 2155.1 when re-dissolved in freshly distilled DMF (see main document).

Computational Methods and Details
Quantum chemical calculations were carried out with the TURBOMOLE program suite. [1][2][3][4] Structures were optimized with the TPSS density functional approximation 5 and the dhf-TZVP basis set 6 employing small-core Dirac-Fock effective core potentials (ECPs) for heavy elements. 7 In detail, an ECP-28 was applied for Ru, and an ECP-60 for Ir and Bi. The resolution of the identity approximation to the Coulomb integrals (RI-J) was employed with tailored auxiliary basis sets. 6 Fine grids were used for the numerical integration of the exchange-correlation terms (grid size 3a). 8-10 COSMO 11,12 was applied with the default parameters to compensate the negative charge and to model the counter ions. Thresholds of 10 −8 Eh for the energy and 10 −7 a.u. for the root mean square of the density matrix norm were chosen in the self-consistent field (SCF) procedure. For the structure optimizations, thresholds of 10 −6 Eh for the energy and 10 −3 Eh/bohr for the maximum gradient indicated convergence of the structure optimizations. The Cartesian coordinates of all optimized structures and the respective SCF energies are summarized in the supplementary document "optimized-structures.txt". The convergence of the ground-state configurations was validated with fractional occupation numbers and large damping factors of 5-8 a.u. during the SCF iterations. Orbitals were localized with the Boys method. 13 The chemical bonding was also studied with a self-consistent two-component formalism to treat spin-orbit coupling. 14 However, spinorbit coupling is of minor importance for the bonding situation and does not lead to qualitative changes for the studied molecules.
For the NMR shielding calculations, 15,16 the kinetic-energy density was generalized with the vector potential of the magnetic field 15,17 (TPSS) or the paramagnetic current density (cTPSS). 18-23 NMR calculations were carried out with both ECPs and the all-electron scalar-relativistic exact twocomponent (X2C) Hamiltonian in its local approximation (DLU-X2C). [24][25][26] The x2c-TZVPall-s basis sets 10 were used for the latter. A threshold of 10 −7 a.u. for the norm of the residuum was applied to indicate the convergence of the coupled-perturbed Kohn-Sham (CPKS) equations. Nucleus-independent chemical shifts 27 (NICS) were calculated at the center of mass of the complete molecule and the respective triangular units. The calculations are also corroborated with other density functional approximations, see Section 6.4.
Magnetically induced current densities and current strengths were obtained with the gaugeincluding magnetically induced current (GIMIC) method. 28

Canonical Frontier Molecular Orbitals
The canonical frontier molecular orbitals (MOs) of Bi6 2− and Bi6 4− are shown in Supplementary  Figure 10. The highest occupied molecular orbital (HOMO) of Bi6 2− and the HOMO-1 of Bi6 4− (D3h) show a φ-type cluster orbital, which is similar to an atomic fz3 orbital.
According to Supplementary Figure 11

Localized Molecular Orbitals of Bi6 2−
For a deeper understanding of the {Bi6} cluster and the electronic structure of 1 -, we carried out an orbital localization procedure according to the Boys method 13 for the parent Bi6 2− prism. The localized molecular orbitals (LMOs) are shown in Supplementary Figure 13. The shape of LMO 1 is similar to the canonical HOMO. According to the coefficients for the linear combinations, the HOMO also dominates this LMO with a contribution of 70%. The LMOs 2-4 describe the 2-center-2-electron (2c2e) Bi-Bi bonds between the triangles, whereas the LMOs 5-7 and 8-10 correspond to 2c2e bonds within the two triangles. Starting with LMO 10, the lone pairs at the Bi atoms are displayed. This shows that all canonical MOs except for the HOMO can be localized to describe 2c2e bonds or lone pairs. Based on the LMOs, the bond lengths and Wiberg bond indices can be rationalized. LMO 1 strengthens the Bi-Bi bonds in the triangles and thus shortens the bond lengths. The nodal plane between the triangles weakens the bonds between the triangles. Therefore, the WBI in the triangles is increased compared to the neutral Bi6 (1.14 for Bi6 2− vs. 0.99 for Bi6) and reveals a multi-bond character, while the WBI between the triangles is decreased (0.90 for Bi6 2− vs. 0.99 for Bi6).

Current Strengths and NICS of Bi6 q-Clusters and the Ru/Ir-Based Compounds
The ring current strengths of the Bi6 q prisms (q = 0 to 4-) and the Ru-based cluster 1as well as the Ir-based cluster 2are listed in Supplementary Table 3 and Supplementary Table 4 together with the respective NICS values. The integration planes are shown in Supplementary Figures 14-18. To compare with, we also added the π-aromatic benzene and the σ-aromatic Cu4Li2 with 6 delocalized electrons each as well as the parent all-metal aromatic Al4 2to these tables. The ring current was already studied with similar methods for some reference molecules, see, for instance, Ref. 31. However, we repeat the calculations with our computational settings for maximum consistency. Furthermore, we note in passing that the ring current of Cu4Li2 is caused by the energetically degenerate eu MOs, while the NICS value is mainly caused by the accumulation of electron density inside the {Cu4} ring due to the shape of the energetically lower a1g orbital. 32 To study the impact of the Li + cation, we also considered simplified derivatives Cu4 2and (Cu4Li) -. These are also σ-aromatic based on the magnetic criterion.
For TPSS and cTPSSh, the Ru-based cluster 1sustains a strong net diatropic ring current, and the Ir-based cluster 2features a similar net diatropic ring current. The NICS values are in line with these ring currents. Including the core electrons with X2C tends to increase the ring currents. We also performed calculations with hybrid density functional approximations. Therefore, we show the results with the TPSSh 5,33 as well as Becke's half and half (BH&HLYP) 34 Table 6 and Supplementary Table 7 Here, the relative deviation amounts to 23% and 29%. As evident by the current density plot in Sec. 6.11, there is also a σ-type contribution and φ-type contribution observed for 2 -.
The maximum diatropic current strength of the hypothetical Bi6 q prisms is found for the dianion, while a small ring current is observed for the tetraanion (singlet configuration) with all density functionals approximations. So, the trend of the current strengths is the same for all functionals, as the anion and the trianion represent intermediate cases. Again, the different results of Bi6 4between the functionals are caused by the response of the electron density, while the unperturbed density contributions to the shielding constants and NICS are very similar. The tetraanion is also a critical case for NICS, as the shielding of the ghost atom is not sufficient to properly describe the trend of the respective ring current of Bi6 4-. The ring current of the tetraanion is smaller than the ring current of the neutral Bi6 and Bi6 -, however, the NICS do not agree with this trend.
Notably, the neutral prism also sustains a ring current similar to the hypothetical neutral ThBi12 cluster, which is σ-aromatic. 41 According to the NICS values calculated at the center of mass of the entire cluster, the ring current flow of the neutral Bi6 prism differs from that of the dianion. A positive NICS value is found for the neutral Bi6, whereas a negative NICS value is computed for the dianion. The core electrons and an explicit treatment of scalar relativistic effects with the DLU-X2C Hamiltonian tend to increase the absolute values of the ring currents.

Current Profiles with Respect to the Height
The current profiles with respect to the height are shown in Supplementary Figures 19-22 for benzene (Supplementary Figure 19), Cu4Li2 (Supplementary Figure 20), Al4 2- (Supplementary  Figure 21), and the neutral, prismatic Bi6 as well as its dianion and tetraanion (all in Supplementary Figure 22). All current profiles start at the center of mass of the entire molecules. We partitioned the integration planes shown above into slices with a height 0.1 bohr and the full width.
The current profile of benzene clearly resembles the π-shape of the orbitals. The minimum of the current strength is in the molecular plane due to the nodal structure of the π-orbitals. In contrast, Cu4Li2 shows the maximum current strength in the molecular plane and a sharp peak caused by the contribution of the Li cation. The result herein is in line with high-level coupled-cluster studies. 31 Al4 2shows contributions of both σ-and π-type orbitals. The width of the peak at the center is notably increased due to the latter, while the maximum of the current strength is still in the molecular plane. This shows that the σ-contribution is larger than the π-contribution. According to previous ring current studies, 42-44 Al4 2is also both σ-aromatic and π-aromatic. The π-contribution amounts to 15-39%. [41][42][43][44] This synergy of σ-type and π-type contributions is a characteristic feature of many aromatic metal clusters. 45 In Supplementary Figure 22, Bi6 shows the maximum current strength in the Bi3 plane. The curve corresponds to that of known σ-aromatic systems such as {Cu4Li2}. 32 The dianion features a wider curve but retains the overall structure of the current profile of Bi6. The wider curve is in line with the shape of the HOMO. The current strength still features a minimum at the center of mass due to the nodal plane of this orbital. Therefore, Bi6 2is both σ-aromatic and φ-aromatic according to the magnetic criterion. The population of the φ-type cluster orbital in Bi6 2increases the ring current strength by about +5 nA/T. For the tetraanion in D3h symmetry, a substantial decrease of the ring current inside the {Bi3} plane is observed in line with the population of the HOMO in Supplementatry Figure 10. The HOMO of Bi6 4mainly affects the ring current inside the Bi triangles according to the nodal structure.
Based on the plots of the magnetically induced current density below (cf. Supplementary Figures  25-29), the σ-contribution is weakened for the clusters 1and 2 -. This can be rationalized by the population of the HOMO-2 of 1 -(see main text   Figure 31. Due to the degree of structural distortion, the numerical integration is less accurate than for the other clusters. The magnetically induced current density is illustrated in Supplementary Figure 32. Here, a σ-contribution and a φ-contribution can be seen. As the structure is highly distorted, the ring current strength is not directly comparable to the Rubased cluster and the regular {Bi6} prism. The ring current not only depends on the degree of electron delocalization and the number of delocalized electrons but also on the structure, the topology, and the chemical element. 45 Considering the core electrons with the scalar-relativistic X2C Hamiltonian leads to NICS values of -45.8 ppm at the center of mass as well as -59.9 and -62.5 ppm for the {Bi3} triangles, respectively. Therefore, this cluster also meets the magnetic criterion of aromaticity and shows a (structurally distorted) φ-type orbital. The degree of distortion indicates that more negative charge is accumulated at the {Bi6} core than for the Ru-based cluster. A natural bond orbital (NBO) analysis 47 leads to 0.90 exess electrons in the p orbitals. Here, the Ru-based and Ir-based clusters feature 0.22 and 0.65 excess electrons, respectively. Thus, this result is in line with the geometric structure and the increasing degree of distortion of the {Bi6} prism. This also supports the findings of Ref. 46, where a Bi6 4core was discussed. As shown in Supplementary Figure 10, the φ-type orbital is also present for Bi6 4-.

Comparison to [{(CO)3Mo}3Bi6] 4−
For completeness, we optimized the structure at the TPSS/dhf-TZVP level using COSMO with the default parameters. The structure is given in a separate file (optimized-structures.txt). Notably, this results in a more regular structure. However, the electronic structure is preserved, i.e., the NBO yields very similar results and also the φ-type orbital is still present. Furthermore, the NICS values are almost unchanged with -42.3 ppm at the center of mass and -58.1/-57.6 ppm for the triangles. Again, the very similar results are obtained with scalar-relativistic X2C. The cluster sustains a net diatropic ring current of about +37.0 nA/T.

Current Strengths of Prismane
The current strengths and NICS values of prismane are listed in Supplementary Table 8. Here, the integration plane is placed as was done for the Bi6 prisms, see Supplementary Figure 17. Supplementary Figure 33 shows the current profile. For this current profile, the integration plane was partitioned into slices with a width of 0.02 bohr and the full height. See also Figures 8 and 9 of Ref. 45 for theoretical details on this type of current profiles.
The NICS(1), NICS(2), and NICS(-1) values with respect to the upper C3 plane indicate that the current flows mainly above and below the complete molecule. The corresponding values are -23.4 ppm, -10.3 ppm, and -4.6 ppm. This is further confirmed by the ring current strength above the upper C3 triangle, which amounts to +5.4 nA/T. Extending the plane up to 0.5 bohr below the upper C3 plane yields a ring current of +7.1 nA/T. Therefore, the shape of the ring current flow is more similar to the neutral Bi6 prism. Molecular orbitals with an accumulation of electron density above the carbon triangle are shown in Supplementary Figure 34. Here, the close proximity of the three carbon atoms leads to the respective shape of the orbitals above the triangle. The similarity with the neutral Bi6 prism is further illustrated by the NICS values of +0.15 ppm at the C4 faces. Thus, there is only a local diatropic ring current in the C3 and Bi3 faces.