A [Mn18] wheel-of-wheels.

A [Mn18] wheel of wheels is obtained from the reaction of MnBr2·4H2O and LH3 in MeOH. The metallic skeleton reveals two asymmetric [MnIII6MnII2] square wheels connected into a larger wheel via two MnII ions. Magnetic susceptibility and magnetisation data reveal competing exchange interactions, supported by computational studies.

Beyond beautiful structural aesthetics, wheels of paramagnetic metal ions have proven to be vital for revealing quantum effects, 1 constructing very high spin molecules, 2 engineering toroidal magnetic moments, 3 developing magnetic Möbius strips, 4 understanding frustration effects, 5 probing slow magnetisation relaxation, 6 investigating quantum information processing, 7 and developing magneto-structural correlations. 8 In Mn coordination chemistry wheels have presented nuclearities as large as eighty-four, 9 displaying a variety of topologies constructed from chains of single metal ions and polymetallic building blocks. [10][11][12][13] Amongst ligand types, those containing one or more ethanolamine (eaH) moieties ( Fig. 1) have proven enormously successful in building a breadth of structurally and magnetically fascinating species. 14 Herein we extend this body of work to include the ligand 1,3,5-tri(2-hydroxyethyl)-1,3,5-triazacyclohexane (LH 3 ), which contains three linked eaH units. A search of the Cambridge Structural Database reveals just four hits in 3d transition metal chemistry. The first was the monomer [Cr(CO) 3 (LH 3 )], 15 the second an aesthetically pleasing [Mn 16 ] complex in which the ligand was generated serendipitously in situ, 16 (Fig. 3). Pertinent bond lengths and angles are provided in Table S1 (ESI †).
The [Mn III 6 Mn II 2 (m 3 -O) 6 (m-OH) 2 (OMe) 6 ] core of the square wheel is asymmetric ( Fig. 2 and 3). Three of the four corners (Mn1-3, Mn3-5, Mn5-7) are bridged 'internally' via a 'T-shaped' m 3 -O 2À ion (O11-O13) and two externally via a m-OMe À ion (Mn1-O15-Mn2, Mn6-O16-Mn7). The fourth corner (Mn1, Mn7, Mn9) is connected only 'internally' via one m 3 -OMe À ion (O14) and one m-OH À ion (O10). The Mn II ions (Mn4, Mn9) occupy opposite vertices in the square. There are two m 6 -L 3À and one m 5 -LH 2À ligands in the asymmetric unit (Fig. 3). The former both sit above a [Mn III 3 ] triangle which acts as the corner of the square, with each of the three N atoms coordinated to a different Mn III ion. The O-atoms also bond to the same metal ions but further m-bridge to a neighbouring Mn II ion in the square. The dianionic LH 2À ligands sit above  Table S2, ESI †), which are also easily distinguished since they all involve the triazacyclohexane ring N-heteroatoms.
The closest inter-molecular interactions occur between the terminally bonded Br ions and the C-atoms of the triazacyclohexane ring (CÁ Á ÁN Z 3.85 Å) directing the formation of columns of 1 in the extended structure along the a-axis of the cell (Fig. S4   The magnetic properties of a freshly prepared polycrystalline sample of 1 were measured in an applied field, B = 0.5 T, over the T = 2-300 K temperature range. The experimental results are shown in Fig. 4, in the form of the w M T product, where w M = M/B, and M is the magnetisation of the sample. At room temperature the w M T product of 1 (50.43 cm 3 K mol À1 ) is lower than the sum of the Curie constants expected for a [Mn III 12 Mn II 6 ] (62.25 cm 3 K mol À1 ) unit. As temperature decreases, w M T first decreases to a value of 41.20 cm 3 K mol À1 at T = 60 K, before increasing to a maximum of 44.70 cm 3 K mol À1 at 11 K, and then falls to a value of 26.00 cm 3 K mol À1 at T = 2 K. This behaviour is clearly indicative of competing exchange interactions, with the increase between 60-11 K perhaps suggestive of ferromagnetic exchange between the two square [Mn III 6 Mn II 2 ] wheels. The decrease in w M T at the lowest temperatures is attributed to a combination of intra-and intermolecular antiferromagnetic exchange and zero field splitting (zfs) effects.
Low temperature variable-temperature-and-variable-field (VTVB) magnetisation data were measured in the temperature range 2-7 K, in magnetic fields up to 7.0 T (Fig. 4, inset and Fig. S5, ESI †). At the lowest temperature and highest field measured, M reaches a value of B37 m B but does not saturate. There are no out-of-phase signals in ac susceptibility measurements in zero dc field.
Since the nuclearity of 1 precludes a fit of the experimental data via standard techniques, we have calculated the magnetic exchange interactions using computational tools known to accurately reproduce experimental J values (see the Computational Details section in the ESI † for more details). 18 We have performed calculations on a model complex, 1a, which is simply the asymmetric unit, i.e. one [Mn III 6 Mn II 2 ] square wheel plus one linking Mn II ion (Fig. S6, ESI †). Based on symmetry and the different bridging groups/angles present, the number of unique magnetic exchange interactions can be reduced to six (Table S3 and  The first two interactions ( J 1 and J 2 ) are found to be antiferromagnetic, whereas the remaining four interactions ( J 3 -J 6 ) are estimated to be ferromagnetic (Table S3 and Fig. S8, ESI †). For the J 1 interaction, the JT axis of both Mn III ions are found to be collinear and perpendicular to the bridging plane of the dimer (Fig. 5 and Fig. S9a, ESI †). According to the magnetostructural correlation for [Mn III 2 ] dimers discussed in ref. 19 this describes a Type I geometry that should lead to antiferromagnetic exchange. 19 Overlap integral (|S ab |) calculations (Table S4, ESI †) are in agreement, with two strong and four intermediate interactions detected, leading to a relatively strong antiferromagnetic interaction, J 1 = À10 cm À1 (Fig. S10a-f, ESI †). For the J 2 interaction, the Mn III ions are bridged via m 3 -O 2À ions with Mn-m 3 O-Mn angles between 132-1361. Overlap calculations suggest one strong and four intermediate interactions ( Fig. S10g-k, ESI †), leading to a relatively strong antiferromagnetic interaction, J 2 = À9 cm À1 .
For the J 3 -J 6 interactions, overlap integral calculations reveal that only intermediate interactions are observed, resulting in ferromagnetic exchange coupling with J 3 = +8 cm À1 , J 4 = +1 cm À1 , J 5 = +2 cm À1 and J 6 = +2 cm À1 (Fig. S10l-w, ESI †). These values are in-line with those previously reported for similar bridging moieties, and consistent with published magnetostructral studies. 20 The magnitude and sign of the magnetic exchange interactions can also be related to the calculated average total overlap integral ( P |S a(3d)b(3d) |/n, Fig. S11, ESI †). 21 The smaller the average total overlap integral, the larger the ferromagnetic interaction (or the smaller the antiferromagnetic interaction) and vice versa. Note that for the J 3 interaction, the JT axes of the Mn III ions lie perpendicular to each other, with one lying parallel to the bridging plane and the other perpendicular to the bridging plane. This is a Type III geometry ( Fig. 5 and Fig. S9b, ESI †), and would be expected to promote ferromagnetic exchange. 19 The J 1 -J 4 interactions between Mn III/II -Mn III centres are also mediated via  the (R 2 )N-CH 2 -N(R 2 ) group of the triazatriol ligand, however the expected contribution to the total magnetic exchange through this long bridging group would be expected to be minimal. Indeed the calculated spin density on the connecting -CH 2 -group is close to zero (r0.003, Fig. S12, ESI †) breaking any spin delocalisation/ polarisation pathway. A summary of these results is shown in Fig. S8 (ESI †) alongside a cartoon of the ''spin-up''/''spin-down'' orientations of the individual Mn ions in 1a.
In summary, the reaction between MnBr 2 Á4H 2 O with LH 3 in MeOH affords the species [Mn III 12 Mn II 6 (O) 6 (OH) 2 (OMe) 6 (L) 4 (LH) 2 Br 12 ], 1. The metal core of 1 consists of two square [Mn III 6 Mn II 2 ] wheels linked via two Mn II ions. The wheels incorporate four vertex sharing triangles, which leads to competing exchange interactions, while the link between wheels is ferromagnetic. Future work on a larger library of Mn-based triazatriol complexes will look to develop magneto-structural studies incorporating theoretical calculations in tandem with methodologies capable of simulating the magnetic data of such sizeable species. 22 We speculate that full deprotonation and the conversion of the hydroxides to oxides may lead to a more symmetric wheel, or wheel of wheels, while oxidation of the Mn II ions should also result in significant structural rearrangement. It is also interesting to note that in all the Mn complexes we have isolated with LH 3 thus far 17 -[Mn 10 ], [Mn 16 ] and [Mn 18 ] -the direction of the JT axes of the Mn III ions is dictated by the triaza N-atoms (i.e. perpendicular to the triaza macrocycle). This has important consequences for controlling nearest neighbour magnetic exchange interactions and thus needs to be carefully considered in future design strategies.
We thank the EPSRC for financial support under grant reference numbers EP/N01331X/1, and the Marie Skłodowska-

Conflicts of interest
There are no conflicts to declare.