An [FeIII34] molecular metal oxide.

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe 34 ] metal oxide molecule, structurally characterized by alternate layers of tetrahedral and octahedral Fe(III) ions connected by oxide and hydroxide ions. The outer shell of the cage is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe-O-Fe angles and Fe-O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe 34 ], bulk iron oxides, previous Fe(III)-oxo cages, and polyoxometalates (POMs), hints that much larger, molecular Fe(III) oxides can be made.

Compound 1 can also be prepared by replacing the HMTA in the above reaction with morpholine (4 mmol) or N-methylmorpholine (4 mmol).

X-ray crystallography
Diffraction data for 1 was collected using a Rigaku Oxford Diffraction SuperNova diffractometer with CuKα radiation, and is given in Table S1. An Oxford Cryosystems Cryostream 700+ low temperature device was used to maintain a crystal temperature of 120.0 K. The structure was solved using ShelXT and refined with version ShelXL interfaced through Olex2. [1], [2] All non-hydrogen atoms were refined using anisotropic displacement parameters. H atoms were placed in calculated positions geometrically and refined using the riding model. CCDC: 1900069.
A unit cell check of the crystals was performed prior to each of the following measurements.

Magnetic Susceptibility and Magnetisation (<7 T)
Dc susceptibility and magnetisation data were measured on powdered, polycrystalline samples of 1 in the T = 2-300 K and B = 0-7 T temperature and field ranges on a Quantum Design MPMS XL SQUID magnetometer equipped with a 7 T dc magnet. Diamagnetic corrections were applied to the data using Pascal's constants.

High Field Pulsed Magnetisation (<35 T)
Low-temperature magnetisation data was measured by the use of a conventional inductive probe in pulsedmagnetic fields, where the temperature reached as low as 1.6 K. [3] The maximum field reached was 35 T. Polycrystalline samples with a typical mass of 15 mg were mounted in a capillary tube made of polyimide. The sample, which was not fixed within the sample tube, was aligned along the magnetic field direction. Magnetisation curves were found to be identical after we applied the magnetic field several times due to the saturation of the orientation effect.

Heat Capacity
Heat capacity data were collected in the temperature range 0.3-20 K using a Quantum Design PPMS equipped with a 3 He cryostat. The powdered, polycrystalline sample of 1 was pressed into a thin pellet with mass of about 0.5 mg. Apiezon-N grease was used to facilitate the sample thermalization at low temperatures, and its contribution to the heat capacity was subtracted using a phenomenological expression.

High Field, High Frequency EPR (HFEPR)
HFEPR spectra for polycrystalline samples were obtained on the Terahertz ESR Apparatus (TESRA-IMR) installed in the magnetism division of Institute of Material Research, Tohoku University. [4a] A case made of polyethylene was used for packing the sample. The radiation was produced by Gunn oscillators and backward traveling wave oscillators (BWO).       In agreement with the susceptibility data ( Fig. 4), both sets of data become field-dependent on lowering the temperature below ~10 K, weakly at first and then stronger for T < 2 K. In further agreement with the magnetic data, the heat capacity and entropy are very small at the lowest temperatures. For instance, the zero-field magnetic entropy content reaches ca. S = 1.6 R at T = 2 K, which is significantly smaller than that expected for 34 uncoupled Fe III spins, i.e., S = 34 ln(6) = 60.9 R. Figure S7: (left) HFEPR spectra of a polycrystalline sample of 1 recorded at 4.2 K and frequencies between 135-405 GHz (left). A linear fit of field-frequency plot affords a g-value of 2.04 ± 0.01, and extrapolation of the field-frequency plot gives a zero field resonance frequency of 8.10 GHz (0.26 cm -1 ). (right) HFEPR spectra at 405 GHz and tempearatures between 4.2 -50 K, revealing a narrowing and shift of the resonance field position to higher field with increasing temperature. The asymmetry / line broadening observed is likely due to one of, or a combination of (a) multiple transitions within multiple S states, (b) anisotropy, and (c) correlation effects.
[4b] The Fe34 cluster demonstartes very strong exchange coupling between the Fe centres, and given the relative symmetry, one would expect the local anisotropies of different Fe sites to cancel out and the effective local anisotropy of the whole cluster to be small.

Computational Details
We have used the diamagnetic substitution method to calculate the exchange coupling constants in 1 employing the Gaussian 09 suite. [5] Since the calculation on the full structure of 1 is prohibitively expensive and time-consuming, we have divided the Fe34 cluster into five model complexes in order to calculate the five exchange coupling constants (J1-J5). See Figures S8-S12 below. In these models, the surrounding Fe(III) ions not involved in the pairwise exchange interaction under investigation were substituted by diamagnetic Ga(III) ions in order to maintain the same coordination environment. The exchange coupling constants were estimated using the broken symmetry approach developed by Noodleman. [6] Ahlrichs' triple-ξ plus polarisation basis set was used for the Fe, O, Br and N atoms, while the split valance plus polarisation basis set was used for Ga, C, and H atoms. [7] All theoretical calculations have been performed using the B3LYP functional since it has been proven to produce excellent estimates of J values. [8], [9], [10] Exchange coupling constants have been derived from the difference between the broken symmetry (BS) and high spin (HS) state, and the quardatic conversion method.      Scheme S1. Schematic of the five different exchange interactions present in 1, together with the exchange part of the corresponding spin-Hamiltonian (1), and the expanded total exchange spin Hamiltonian (2). ̂ is the spin operator of the inner tetrahedral ions, ̂ the octahedral ions, and ̂ the outer tetrahedral ions.     Figure S8).  Table S3. The Mulliken spin density of the atoms surrounding the Fe(III) centre in the J2 exchange pathway (see the atom numbering in Figure S9).   Figure S10).  Figure S11).  Figure S12).