Fe–Fe bonding in the rhombic Fe4 cores of the Zintl clusters [Fe4E18]4− (E = Sn and Pb)

We report here the synthesis and characterization of two endohedral Zintl-ion clusters, [Fe4Sn18]4− and [Fe4Pb18]4−, which contain rhombic Fe4 cores. The Fe–Fe bond lengths are all below 2.5 Å, distinctly shorter than in the corresponding Cu clusters, indicating the presence of Fe–Fe bonding. Subtle differences in the structure of the Fe4 core between the two clusters suggest that the change in tetrel element causes a change in electronic ground state, with a very short Fe–Fe bond length of 2.328 Å present across the diagonal of the rhombus in the lead case.


Introduction
2][3][4][5][6] Some of the earliest examples, such as icosahedral [M@Pb 12 ] 2− , 7,8 are relatively simple from an electronic perspective because the endohedral metal has a closedshell (d 10 ) conguration, and the core-like nature of the d orbitals limits the degree of interaction with the cage.The incorporation of earlier transition metals with fewer d electrons raises the possibility of paramagnetism, as is observed in [Mn@Pb 12 ] 3− ((ref.9) (a triplet)) and [Fe@Ge 10 ] 3− ((ref.10) (a doublet)). 11,12][15][16] The extension of these principles to larger clusters containing two or more open-shell transition metal ions opens up a further range of possibilities.If the encapsulated metal ions are dilute, cooperative magnetic phenomena (ferro-and anti-ferromagnetism) may emerge, while a closer approach brings covalent metal-metal bonding into play.In the latter scenario, metal-metal and metal-cage bonding may be complementary: overlap between the metals will destabilise antibonding orbitals, potentially to the extent that electrons may be driven onto the cage.Opportunities to explore this landscape of possibilities have, up until now, been restricted by the relatively small number of well-characterized examples containing two or more endohedral metals.Amongst the very few Zintl-ion clusters with direct covalent metal-metal bonds, the Fe-Fe bond length in [Fe 2 Ge 16 ] 4− (ref.17) (Fig. 1(a)) is 2.636(3) Å whilst in [Fe 2 -Sn 4 Bi 8 ] 3− , 18 it is remarkably short, at 2.396(4) Å. Very recently, we have also reported the tri-iron cluster [Fe 3 Sn 18 ] 4− (Fig. 1(b)) which contains a linear array of Fe centres, again with a very short Fe-Fe bond length of 2.4300(9) Å. 19 These Zintl clusters are members of a wider family of iron clusters with direct covalent Fe-Fe bonds, which includes the Fe 1 Fe 1 paddlewheel complex with ultra-short Fe-Fe bonds (2.127 Å), linear Fe 3 chains (Fig. 1(b)) 20,21 and triangular Fe 3 (ref.5][26][27] Ohki has also reported a series of hydride bridged Fe 4 and Fe 6 clusters based on a rhombic Fe 4 core, with Fe-Fe distances between 2.5 and 2.7 Å (Fig. 1(e)).Neidig and co-workers have also recently characterized the structure of the previously elusive 'Kochi cluster', a [Fe 8 Me 12 ] − (Fig. 1(f)), a distorted cube with a doublet ground state and averaged Fe-Fe bonds lengths of 2.43 Å. 28,29 Paramagnetism is ubiquitous in the clusters shown in Fig. 1, and their electronic structure has typically been interpreted in terms of a delocalized manifold of Fe-based orbitals, occupied to maximise the multiplicity ('Hund's coupling'). 30n a previous paper we have reported the structures of the copper-containing clusters, [Cu 4 Sn 18 ] 4− and [Cu 4 Pb 18 ] 4− . 31We now extend that work to the earlier transition metals by reporting the properties of two new Zintl clusters, [Fe 4 Sn 18 ] 4− and [Fe 4 Pb 18 ] 4− , both of which contain rhombic Fe 4 cores, isostructural with the Cu analogues.The Fe-Fe separations (2.328 Å to 2.498 Å) are, however, shorter than those in [Cu 4 E 18 ] 4− (2.52-2.55Å), consistent with the presence of Fe-Fe bonding.The Fe 4 cores are supercially very similar, but subtle differences suggest that the nature of the Fe-Fe bonding may be different in the Sn 18 and Pb 18 clusters.This observation motivates a detailed survey of the electronic structure using density functional theory, where we draw on comparisons both between the Sn and Pb species and also between the Fe and Cu analogues.] 4− , appear not to interconvert, even in the presence of excess Fe. 1 crystallizes in the monoclinic space group P2 1 /n and contains a single anionic stannaspherene unit [Fe 4 Sn 18 ] 4− along with four [K(2.2.2-crypt)] + cations and four pyridine molecules in the asymmetric unit (Fig. 2(a)).The [Fe 4 Pb 18 ] 4− unit 2 is isostructural with 1 (Fig. 2(b)), both having approximate D 2h symmetry, as do their copper analogues, [Cu 4 Sn 18 ] 4− and [Cu 4 Pb 18 ] 4− . 31Two of the Fe atoms (Fe1 and Fe1 0 ) are encapsulated in 8-vertex E 8 polyhedra while Fe2 and Fe2 0 sit in approximately trigonal prismatic sites either side of the waist of the cluster.Averaged bond lengths for all four clusters are collected together in Table 1 for comparison.The gross features of the E 18 cage are largely unaffected by the change from Cu to Fe, with E-E bond lengths deviating by less than 0.05 Å in all cases.There are, however, subtle changes in M-M distances that reect the emergence of metal-metal bonding in the iron clusters.As we have noted above, the d 10 conguration of the Cu + ions limits direct Cu-Cu bonding to the cuprophilic type, and so the short Cu1-Cu2 distances of ∼2.53 Å must reect, at least to some extent, the constraints imposed by the E 18 framework.Irrespective of whether the main-group element is Sn or Pb, the Fe1-Fe2 bond lengths are shorter than the Cu1-Cu2 analogues by approximately 0.1 Å. Differences in the M2-M2 0 distances are, in contrast, rather more variable: in the Sn clusters, the Fe2-Fe2 0 is shorter than Cu2-Cu2 0 by 0.135 Å, but this difference increases to 0.233 Å for the Pb pair.Indeed the Fe2-Fe2 0 distance of 2.328 Å in [Fe 4 Pb 18 ] 4− is comparable to the shortest Fe-Fe bonds shown in Fig. 1.The correlation of bond length and bond strength is not always straightforward in clusters with bridging ligands, but we note that for a given oxidation state the radius of Fe is intrinsically larger than that of Cu, so the shorter Fe-Fe distances within a constant E 18 framework are a strong a priori indication of direct Fe-Fe bonding.Moreover, the wider variation in the M2-M2 0 bond lengths is probably a reection of the fact that these atoms are not fully encapsulated by the cluster, and are therefore more free to move in response to subtle changes in Fe-Fe bonding.We explore the origins of these structural differences as part of a detailed analysis of electronic structure presented in the following sections.

Results and discussion
Electrospray ionization mass spectra (ESI-MS) of freshly prepared samples of 1 and 2, measured in negative-ion mode, are shown in Fig. S9-15.† For 1, the spectrum shows an intense feature due to the dianion [Fe 4 Sn 18 ] 2− , as well as smaller features due to the monoanion, [Fe 4 Sn 18 ] − and the dianion paired with a single [K(2.2.2-crypt)] + cation, [K(2.2.2-crypt) Fe 4 Sn 18 ] − .The corresponding spectrum for 2, in contrast, shows a single dominant peak due to the decomposition product [FePb 12 ] − , most likely an endohedrally encapsulated icosahedron, similar in structure to the known [Mn@Pb 12 ] 3− cluster.The only possible trace of the intact cluster is a very small peak, just above the baseline, centreed at m/z = 1977: it is clear that the parent cluster does not survive in any signicant quantities under ESI-MS conditions.The magnetic susceptibility of 1 was measured between 2 and 300 K using a superconducting quantum interference device (SQUID), Fig. 3.The measured magnetic moments (m eff ) decreases with decreasing temperature from a value of 9.37 m B (c M T = 10.97 cm 3 K mol −1 ) at 300 K to ∼9 m B at 100 K, before dropping to 8.6 m B at 10 K, and, nally, to much lower values below this temperature.The drop off below 10 K may be the result of zero-eld splitting and/or weak antiferromagnetic coupling between cluster units.Limiting spin-only (g = 2) values of m eff for S = 4, S = 5 and S = 6 are 8.94 m B , 10.95 m B and 12.96 m B , respectively, and the absence of a plateau at 300 K suggests that the ground spin state is not isolated.Despite multiple attempts on freshly prepared samples, we were not able to make reproducible magnetic measurements on the lead analogue, 2: this probably reect the difficulties in separating crystals of 2 from other side products of the reaction while preparing the sample for magnetic measurements and/or rapid decomposition of the sample, as is apparent in the ESI-MS experiment.

Electronic structure
The electronic structure of the two Cu clusters, [Cu 4 Sn 18 ] 4− and [Cu 4 Pb 18 ] 4− , was the subject of a previous study 31 where we concluded that the ground states were singlets, with Cu + ions in a d 10 conguration and no direct Cu-Cu interactions.In contrast, the open-shell Fe centres generate several closelyspaced electronic states that differ both in multiplicity and spatial symmetry, and the energies of the lowest-lying states Table 1 Selected bond lengths from crystallographic and DFT-optimized structures (M06-L functional) for the [M 4 E 18 ] 4− family (all distances in Å)  1).In the ground states of the two clusters with 2S + 1 = 11, ( 11 B 1g and 11 B 3g ) the highest of these 20 linear combinations, 7b 1g , is vacant in both spin-a and spin-b manifolds, leaving 9 doubly-occupied and 10 singly-occupied orbitals.The doubly-occupied levels are largely Fe1-Fe2 and Fe2-Fe2 0 bonding while the singly-occupied levels are largely antibonding, giving rise to net Fe-Fe bonding, in contrast to the Cu analogues where all bonding and antibonding combinations are lled (see the discussion of the PDOS and OPDOS in the ESI † for more details).We can identify three distinct bonding/ antibonding orbital pairs that make substantial contributions to the Fe2-Fe2 0 bonding in both the 11 B 1g and 11 B 3g states: the 8a g 2 8b 2u 1 conguration (Fe2-Fe2 0 s), the 4b 1u 2 5b 3g 1 conguration (p op ) and the 7b 3u 2 7b 1g 0 conguration (p ip ).The key difference between the 11 B 1g and 11 B 3g states lies in the reversal of the 6b 1g and 4b 3g orbitals (highlighted in red and blue, respectively, in Fig. 4) the rst of which has signicant Fe2-Fe2 0 p ip * character while the second is localised largely on the Fe1 centres with little amplitude on the central Fe2-Fe2 0 unit.The in-plane component of the Fe2-Fe2 0 bond is therefore stronger in the 11     degenerate states with S = 5 as the most stable (M06-L functional), with very different Fe2-Fe2 0 bond lengths that map onto the differences seen in the crystallography.On that basis we believe that the two clusters adopt ground states with the same multiplicity but different spatial symmetry, with Fe-Fe p bonding more developed in the [Fe 4 Pb 18 ] 4− case.
4 Materials and methods  (1).In a 10 mL vial, K 4 Sn 9 (122 mg, 0.1 mmol) and 2.2.2-crypt (115 mg, 0.3 mmol) were dissolved in en (ca. 3 mL) and stirred for 30 min, resulting a dark brown solution.Then FeCp 2 (30 mg, 0.161 mmol) was dispersed in toluene (0.5 mL), producing a light pink suspension, and then added dropwise to the above mixture.The mixture was stirred for 3 h at room temperature yielding a brown solution.All volatiles were removed at 60 °C under vacuum to obtain a black solid which was dissolved in 3 mL pyridine.The resulting green-black solution was stirred for 2 h at room temperature and ltered with glass wool.The ltrate was layered with 3 mL toluene.Block-shaped crystals of 1 were obtained (20% yield based on the used precursor K 4 Sn 9 ) aer six weeks.

[K(2.2.2-crypt)] 4 [Fe 4
Pb 18 ]$4Py(2).In a 10 mL vial, K 4 Pb 9 (120 mg, 0.059 mmol), 2.2.2-crypt (88 mg, 0.234 mmol) and FeCp 2 (22 mg, 0.118 mmol) were dissolved in 3 mL en yielding a black solution.The mixture was stirred for 3 h at room temperature yielding a brown solution.All volatiles were removed at 60 °C under vacuum to obtain a dark-brown solid which was dissolved in 3 mL pyridine.The resulting green-black solution was stirred for 1 h at room temperature and ltered with glass wool.The ltrate was layered with 3 mL toluene.Black rod-like crystals of 2 were obtained (13% yield based on the used precursor K 4 Pb 9 ) aer one week.

Experimental analysis
4.3.1 X-ray diffraction.Suitable single crystals were selected for X-ray diffraction analyses.Crystallographic data were collected on Rigaku XtalAB Pro MM007 DW diffractometer with graphite monochromated Cu Ka radiation (l = 1.54184Å).  6230).The spray voltage was 5.48 kV and the capillary temperature was kept at 300 °C.The capillary voltage was 30 V. The samples were made up inside a glovebox under a nitrogen atmosphere and rapidly transferred to the spectrometer in an airtight syringe by direct infusion with a Harvard syringe pump at 0.2 mL min −1 .
4.3.3Energy dispersive X-ray (EDX) spectroscopic analysis.EDX analysis on the title clusters were performed using a scanning electron microscope (FE-SEM, JEOL JSM-7800F, Japan).Data acquisition was performed with an acceleration voltage of 15 kV and an accumulation time of 60 s.
4.3.4Superconducting quantum interference devices (SQUID).Magnetic measurements were performed using a Quantum Design SQUID MPMS-3 magnetometer in the 2.0 to 300 K temperature range with an applied eld of 1000 Oe.

Computational details
All calculations are performed using density functional theory as implemented in the ADF 2021.104package. 43The local functional of Minnesota 06 family (M06-L) functionals 44,45 was used and triple-zeta basis sets included with two polarization functions are used for all atoms. 46All electrons are treated as valence in the calculations.Relativistic effect was considered with The Zeroth-Order Regular Approximation (ZORA). 47The numerical quality was set to 'verygood'. 48A Conductor-like Screening Model (COSMO) with dielectric constant of 78.39 was used to simulate the conning environment of the ionic lattice. 49Optimized structures were conrmed to be minima through the absence of imaginary frequencies. 50The sensitivity of the results to choice of functional was also explored by repeating the calculations using the PBE and PBE0 functionals. 51,52
B 1g state, leading to compressed bond in [Fe 4 Pb 18 ] 4− .The differences between Cu and Fe, and between [Fe 4 Sn 18 ] 4− and [Fe 4 Pb 18 ] 4− , are captured in the Mayer bond orders (MBO), 41 delocalization indices (DI) 42 and bond critical point ellipticities (3) shown in the ESI, Table S6.† The Mayer bond orders of 0.51 and 0.91 for the Fe2-Fe2 0 bonds of [Fe 4 Sn 18 ] 4− and [Fe 4 Pb 18 ] 4− in their respective ground states are a clear indication of the stronger bond in the latter while the Fe1-Fe2 bonds show the opposite trend (0.85 and 0.69).The corresponding values are, on average, less than 0.2 for the Cu clusters, where formal Cu-Cu bond orders are zero.The ellipticity at the critical point, 3, provides a measure of the balance between s, p ip and p op character: values close to 0 are indicative of a cylindrically symmetric environment while larger values indicate an anisotropic p component to the bond.The values of 3 ∼0.2 for the Cu

Fig. 3
Fig. 3 Effective magnetic moment, m eff , as a function of temperature for 1.

Fig. 4
Fig. 4 Kohn-Sham molecular orbitals for the 11 B 3g of [Fe 4 Sn 18 ] 4− and the 11 B 1g state of [Fe 4 Pb 18 ] 4− .The eigenvalues correspond to the spinb manifold in both cases, and they are shifted such that E = 0 is defined as the mid-point between the eigenvalues of HOMO and LUMO.The orbitals highlighted in red and blue are those whose occupations differ in the 11 B 3g and 11 B 1g states.The isosurfaces shown correspond to the spin-b set of [Fe 4 Pb 18 ] 4− .

4. 3 . 2
Electrospray ionization mass spectrometry (ESI-MS) investigations.Negative ion mode ESI-MS of the DMF solutions of the single crystal and reaction solution were measured on an LTQ linear ion trap spectrometer by Agilent Technologies ESI-TOF-MS ( Sn 18 ] 4− cluster only in the source of Fe: ferrocene here but [K(thf)Fe(O t Bu) 3 ] 2 (thf = tetrahydrofuran).The two clusters, [Fe 3 Sn 18 ] 4− and [Fe 4 Sn 18 31e measured magnetic moment of 9.37 m B for [Fe 4 Sn 18 ] 4− at 300 K lies considerably below the spinonly value for S = 5 (10.95 m B ), and in fact is more consistent with a ground-state with S = 4.The apparent discrepancy between computed and experimental values may be a consequence of the well-known sensitivity of ground-state multiplicity to choice of density functional or, alternatively, may indicate the presence of diamagnetic impurities in the sample that serve to depress the measured moment.Of the two states with 2S + 1 = 11, 11 B 1g is the most stable for both [Fe 4 Pb 18 ] 4− and [Fe 4 Sn 18 ] 4− , although the energetic difference is too small to allow a condent assignment of the ground state, particularly in the Sn cluster where the two differ by only 0.05 eV.However, a comparison of optimized and measured bond lengths offers important clues to the identity of the electronic ground states.Sn 18 ] 4− and [Fe 4 Pb 18 ] 4− in their respective11B 3g and 11 B 1g states is shown in Fig.4, and a full analysis of the orbitals, projected densities of states (PDOS), and overlap-projected densities of states (OPDOS) is presented in the ESI.†The interpretation of the electronic structure is a complex challenge due to the open-shell character, and a consideration from a symmetry-based perspective is a useful starting point.The rhombic Fe 4 4+ unit has a total of 4 × 5 = 20 linear combinations of Fe 3d orbitals, which can be separated into in-plane (a g , b 1g , b 2u , b 3u symmetries) and out-of-plane (a u , b 1u , b 2g and b 3g ) subsets.The in-plane set support Fe-Fe interactions of local s and p ip symmetry, while the out-of-plane set have local Fe-Fe p op and d symmetry.§Theformaloxidationstate,and therefore the number of electrons occupying the Fe 3d manifold, is not straightfoward due to the multiple redox states available to Fe.However, the structures of the E 18 units in 1 and 2 and also the Sn/Pb densities of states (ESI, Fig.S22 †) are striking similar to those in the [Cu 4 E 18 ] 4− cases, where the charge state of the E 18 unit was assigned as 8-.31The relationship between structure and charge in the family of 18-vertex tetrel clusters has been discussed by us and others in the recent literature, 19,36-40 and we provide further justication for the assignment of an 8-charge state in the ESI.† Assuming the same 8-charge for the E 18 unit in [Fe 4 E 18 ] 4− , we then have a net 4+ charge for the Fe 4 unit and hence 28 valence electrons in the Fe 3d manifold.Distributing these 28 valence electrons across the 20 orbitals generates a maximum possible spin of S = 6 (the 13 B 2g state identied in Table © 2024 The Author(s).Published by the Royal Society of Chemistry Chem.Sci., 2024, 15, 4981-4988 | 4983 Edge Article Chemical Science with 2S + 1 = 9, 11 and 13, calculated with the M06-L functional, are summarized in Table 1.Amongst these, the two lowest share a common spin, S = 5, but have different spatial symmetries, 11 B 1g and 11 B 3g : the lowest-lying state with S = 4 lies more than 0.5 eV higher in energy.

3
Summary and conclusionsIn this paper we have reported the synthesis and characterization of two new Fe-based Zintl clusters, [Fe 4 Sn 18 ] 4− , [Fe 4 Pb 18 ] 4− , both of which have rhombic Fe 4 cores.The clusters are isostructutal with the previously-reported Cu analogues, but the Fe-Fe bonds, all of which are below 2.5 Å, are substantially shorter than the corresponding Cu-Cu distances, indicating the presence of Fe-Fe bonding.There are also signicant differences between the Fe 4 cores in the Sn and Pb clusters, with the Fe2-Fe2 0 bond across the diagonal of the rhombus being notably shorter in the latter (2.328 Å vs. 2.498 Å).Magnetic susceptibility measurements for [Fe 4 Sn 18 ] 4− indicate a highspin ground state, with limiting values of m eff consistent with either S = 5 or S = 6.A survey of the potential energy surface using density functional theory identies two almost