Edinburgh Explorer Magneto-structural correlations in a family of ReIVCuII chains based on the hexachlororhenate(IV) metalloligand

Six novel one-dimensional chloro-bridged Re IV Cu II complexes of formula {[Cu(L) 4 ][ReCl 6 ]} n , where L = imidazole (Imi, 1 ), 1-methylimidazole (Meim, 2 ), 1-vinylimidazole (Vim, 3 ), 1-butylimidazole (Buim, 4 ), 1-vinyl-1,2,4-triazole (Vtri, 5 ) and N , N’ dimethylformamide (DMF, 6 ) are characterised structurally, magnetically and theoretically. The structures exhibit significant differences in Cu–Cl bond lengths and Re–Cl–Cu bridging angles, resulting in large differences in the nature and magnitude of magnetic exchange interactions between the Re IV and Cu II ions. Theoretical calculations reveal the coupling to be primarily ferromagnetic, increasing in magnitude as the bridging angle becomes smaller and the bond lengths shorten.


Introduction
The ability of the synthetic chemist to design and manufacture molecule-based magnetic materials conforming to specific architectures and topologies, whilst controlling symmetry, metal geometries and metal-ligand interactions, is key to the commercial applicability of such species in, for example data storage and spintronics. 1 This effort relies upon the systematic study of large families of closely related compounds such that the relationship between structure and magnetic properties can first be quantitatively understood, and second be exploited and improved through bottom-up, controlled chemical manipulation at the molecular scale. 2 In this context, the most studied transition metal moleculebased magnets are polynuclear complexes based on paramagnetic 3d ions. 2e In comparison, systems containing the heavier 4d and 5d ions have been much less explored, despite these metal ions being characterised by more radially extended magnetic orbitals (5d > 4d >> 3d) which results in larger spin delocalisation onto coordinated atoms/ligands creating stronger magnetic exchange between paramagnetic metal ions. [3][4][5] The extremely large spin-orbit coupling constants (λ) of 4d and 5d ions is a direct cause of their unusually large zerofield splitting (zfs) values manifested in the axial (D) and rhombic (E) components, and highly anisotropic g factors. 4 Zero-field splitting plays an important role in the energy barrier for reversal of the magnetisation in these systems, and for this reason the 5d 3 Re IV ion is of great interest due to its large magnetic anisotropy, 5 which arises from second order spinorbit coupling caused by a spin-orbit coupling constant for the free ion of λ ≈ 1000 cm -1 . 6 Apart from investigations into the magnetic properties of its salts (e.g. the effect of cation size on intermolecular interactions and Tc), the role of the [ReCl6] 2anion has been largely limited to that of synthetic precursor. [6][7][8][9][10][11][12][13][14][15][16][17][18][19] Indeed, a common strategy for the creation of new Re IV complexes is the functionalisation of the [ReCl6] 2anion through halide exchange with ligands such as heterocyclic amines, pseudo halides such as cyanide, or chelates such as the oxalate anion. 6,[10][11][12][13] These species have subsequently been employed as metalloligands for the creation of larger oligomers. 14 , 4), 1-vinyl-1,2,4-triazole (Vtri, 5) and N,N'-dimethylformamide (DMF, 6) (Scheme 1). The structures exhibit significant differences in Cu-Cl bond lengths and Re-Cl-Cu bridging angles, originating from the differences in the Scheme 1. The ligands (L) employed: a) imidazole, b) 1-methylimidazole, c) 1vinylimidazole, d) 1-butylimidazole, e) 1-vinyl-1,2,4-triazole, f) dimethylformamide.

Results and discussion
The structures of complexes 1-6 ( Fig.1 (Tables S3-4). 5,7 The Cu II ion sits in a trans-X4Cl2 coordination sphere (X = N (1-5) or O (6)) with the chloride ions positioned along the Jahn-Teller (JT) axis, with Cu-N bond lengths of 1.979(3)-2.017(2) Å for 1-5 and Cu-O bond lengths of 1.9450(16) and 1.9609(16) Å in 6 (Cu-O(2), Cu-O(1), respectively). Despite these similarities, the Cu-Cl bond lengths and the Re-Cl-Cu bond angles vary enormously, with Cu-Cl distances ranging between 2.78-3.23 Å, and the Re-Cl-Cu bond angles being as small as 128.6° and as large as 152.8° (Table S3- 4). A search of the Cambridge Structural Database (CSD) reveals that Cu-Cl bond distances in previously published Cu-Cl-TM (TM = transition metal) 1D chains range from ~2.6-3.2 Å, putting those observed in 1-6 at the very top end. There is no 'simple' explanation as to the origin of the ~24° difference in the bridging angle at the chloride ion, but the size/steric bulk of the ligand (L) terminally bonded to the Cu II ion, in concert with the associated effects on intermolecular interactions in the extended structure, are likely the most dominant parameters (Tables S3-4). The chains crystallise in the triclinic space group P1 ̅ (1, 2 and 6), monoclinic space groups C2/c (3) and P21/c (5) and the orthorhombic space group Pccn (4) (Tables S1-2). The asymmetric unit (ASU) of 1 contains two non-equivalent half molecules of the [Cu(Imi)4] 2+ cation, one [ReCl6] 2anion and two isopropanol molecules (Fig. S1). In 2, the ASU contains 1.5 molecules of the [Cu(Meim)4][ReCl6] motif, giving rise to two non-equivalent chains whose structural parameters deviate slightly (Fig. S2). The ASUs of 3-6 contain half a cation and half an anion due to inversion centres located on the Re IV and Cu II metal ions (Figs. S3-6). One solvent acetonitrile molecule at 50% occupancy is also part of the ASU of 6.  (Fig. S8b). The chains in 3 are ordered in 2D networks in the crystallographic ab plane, with each 2D network being pseudoperpendicular to adjacent layers at an inter-chain angle of 81.45° (Fig. S9). The chains pack through an extended network of Cl···π and C(H)···π interactions, with the shortest intra-and inter-chain Cl···π / C(H)···π interactions being approximately 3.4 Å and 3.6-3.9 Å, respectively (Fig. S10). In 4, the chains describe a 'grid' like pattern down the crystallographic c axis (Fig. S11). Each chain is well isolated from its nearest neighbours on account of the bulkiness of the butyl-group of the imidazole ligands, which causes the inter-chain metal···metal distances to all be > 9 Å. Please do not adjust margins Please do not adjust margins In the crystal lattice of 5, the chains propagate down the crystallographic a axis and pack through a myriad of intra-and inter-chain C(H)···N and Cl···π interactions. In each molecular chain, two short Cl···π interactions of ~3.4 and ~3.7 Å are present ( Fig. S12a) with the chains packing through short interchain C(H)···N interactions between triazole groups, and Cl···π interactions from the anions to the vinyl-groups (Fig. S12b). These C(H)···N interactions are of the order 3.2 Å, with interchain Cl···π distances of approximately 3.6 Å. The molecular chains of 6 are oriented in a parallel manner down the crystallographic c axis, with the acetonitrile molecules of crystallisation in the voids between the chains (Fig. S13). The [ReCl6] 2unit interacts with the DMF ligands and acetonitrile solvate molecules through C(H)···Cl contacts, with C···Cl distances in the range of 3.5 to 3.8 Å (Fig. S14a). C(H)···N interactions link the DMF ligands with the acetonitrile molecules, with C···N distances of approximately 3.3 and 3.6 Å (Fig. S14b).

Magnetic behaviour
Plots of the χMT product versus T in the temperature range T = 300-2 K for complexes 1-6 are shown in Fig. 2; where χM is the molar magnetic susceptibility for a Re IV Cu II unit. The χMT values at room temperature (1.86-1.95 cm 3 mol -1 K) are close to that expected for one S = 3/2 ion and one S = 1/2 ion, with g-factors equal to 1.8 and 2.1, respectively. In the T = 300-100 K temperature region complexes 1-6 display very similar behaviour, with little change in the magnitude of χMT being observed. At lower temperatures the data deviates, the differences being due to different magnetic exchange (in both magnitude and sign) between the spins on the Re IV and Cu II ions, together with the zfs associated with the Re IV ion. 5 For 1, χMT falls to 1.37 cm 3 K mol -1 at T = 5.5 K, before rising to 6.28 cm 3 K mol -1 at T = 2.0 K. For complexes 2, 4 and 6 the χMT product continually decreases, reaching values of 1.45, 1.28 and 1.74 cm 3 K mol -1 at T = 2 K, respectively. Complexes 3 and 5 display analogous behaviour: χMT increasing slowly between T = 100-12 K before increasing more rapidly between 12-2 K and reaching maximum values of 4.98 and 6.54 cm 3 K mol -1 at T = 2.4 and 2.0 K, respectively. Quantitative analysis of the magnetic behaviour of Re IV compounds is non-trivial, since one must consider both intraand inter-molecular exchange interactions caused by the strong delocalisation of spin density from the Re IV ion to the coordinated ligands (the latter can be as strong as the former), different g-values for the constituent metal ions (gRe and gCu), and zero-field splitting effects (DRe). 5 In addition we note that some of these parameters are correlated: for example, erroneously large antiferromagnetic intra-or inter-molecular exchange can be deduced at the expense of underestimating zfs, whilst large ferromagnetic exchange is linked to an overestimation of zfs. It is therefore important than any employed model be as simple as possible. In this respect, we have carried out DFT calculations to estimate the magnitude of the exchange between by shortest inter-molecular contacts between [ReCl6] 2moieties in all six complexes. These values, together with the shortest Re•••Re, Re•••Cu, and Cl•••Cl distances between adjacent chains are collected in Table 1.  DFT calculations show that the inter-chain magnetic exchange interactions in 1-6 are negligible, even in the cases of complexes 1 and 2 where the Cl•••Cl contacts are relatively short (Table 1). The magnetic behaviour of 1-6 can therefore be regarded as originating from isolated heterometallic 1D chains. Please do not adjust margins

Compound d(Re•••Re)/Å d(Re•••Cu)/Å d(Cl•••Cl)/Å J/cm
Please do not adjust margins The magnetic properties of certain homo-and heterometallic Re IV based complexes have previously been studied using an approach that considers only the lowest-lying Kramers doublet is populated at low temperature, rendering the ion an effective spin doublet (Seff = ½). 5 However, this approach is only useful when DRe >> JReCu (by at least one order of magnitude). In most cases involving pseudohalide [ReX6] 2ions this condition is not met, and the analytical methodology required for implementing this approach becomes rather complex. 23 In order to verify our starting point, we have therefore performed a NEVPT2 The weak magnetic exchange between the metal ions, clearly observed in the susceptibility data, allows us to use a model wheel that incorporates just eight metal centres (Fig. 3). The magnetic coupling between the paramagnetic centres is described as the sum of the Zeeman (̂), zero-field splitting (̂) and Heisenberg magnetic coupling (̂) contributions, where B is the applied magnetic field and β the Bohr magneton: Fig. 3. Spin topology of the model used to simulate the magnetic behaviour of compounds 1-6, and its corresponding spin-Hamiltonian.
The theoretical curves obtained using this spin-Hamiltonian are shown in Fig. 4. 5 Positive and negative values for DRe and J were used to identify the effects on the thermal dependence of the magnetic susceptibility. When there is zero coupling between the metal ions the magnetic behaviour does not depend on the sign of the axial zfs parameter, and the χMT value decreases to a non-zero value at T = 0 K (χMT0). If the exchange coupling is non-zero, the magnetic behaviour is affected by the sign of DRe, but only at very low temperatures. For example, when the neighbouring spins are antiferromagnetically coupled, the |±3/2> Kramers doublet of the Re IV ion is coupled with the |±1/2> doublet of the Cu II ion for DRe < 0. In such a scenario, the spins do not cancel and an increase in χMT is observed at low temperatures, leading to values slightly larger than χMT0. For DRe > 0, the spin of the |±1/2> ground Kramers doublet on the Re IV ion can be 'cancelled out' by coupling to the Cu II ion, though the curve is also dependent on the different g factors. Thus, a continuous decrease of χMT occurs to values lower than the χMT0 limit. When the exchange is ferromagnetic, χMT increases with decreasing temperature, diverging at low temperature towards a non-finite value, as expected for an ideal one-dimensional system. For small J/DRe ratios a small decrease in χMT is observed leading to values at low temperatures that are greater than χMT0.  We can therefore extract some qualitative conclusions from the experimental thermal dependence of χMT in Fig. 2. The continuous decrease of the χMT value to values close to χMT0 for complexes 2, 4 and 6 suggest that the magnetic coupling in these compounds could be ferro-or antiferromagnetic, but very weak in each case. The higher χMT values at T = 2 K in 2 and 6, suggest these systems possess a small but non-negligible ferromagnetic coupling. The greater decrease in χMT in 4 indicates the presence of antiferromagnetic exchange, whilst the sharp increase in χMT at low temperatures in 1, 3 and 5 is evidence of ferromagnetic exchange interactions. The minimum in the χMT value close to the χMT0 limit observed in 1 points at a smaller J/DRe ratio than detected in 3 and 5.
In order to support these qualitative conclusions, and to establish which structural parameters govern the nature and magnitude of the magnetic exchange coupling (Fig. 5), we have theoretically estimated J from DFT calculations on a [Re IV Cu II 2] fragment (Table 2 and Fig. S15). We note the following points: (a) complexes 1 and 2 each contain two distinct coupling constants (derived from two different geometries), assigned X_1 and X_2; (b) two different Re IV Cu II chains coexist in 2, named 2a and 2b; the exchange is weak and mediated via the axial JT axis of the Cu II ion. Thus the results should be regarded as semi-quantitative with some leeway allowed for the estimated J values.  As predicted from the theoretical simulations (Fig. 4), the strongest ferromagnetic exchange interactions are observed in complexes 3 and 5 (Table 2). Ferromagnetic and antiferromagnetic exchange co-exists in 1, the former stronger than the latter, in agreement with the observed experimental data. The weakest interactions in the family are observed in 2 and 4. The average value of J in 2 is consistent with the experimental data, showing a tendency for χMT to increase at temperatures close to T = 2 K. A comparison of the J values with the Re-Cl-Cu bond angle, α, shows the coupling to become more ferromagnetic with a smaller bridging angle (Fig. S16). As expected, the second-neighbouring Cu-Cu magnetic couplings turned to be null in all calculated [Re IV Cu II 2] fragments. In order to establish a magneto-structural correlation for this family of complexes we have examined how the strength of the exchange varies with the Cu-Cl distance (d(Cu-Cl)), the Cu-Cl-Re angle (α), and the twist of the [ReCl6] 2moiety around the JT axis of the Cu II ion (θ), using the model complex shown in Fig. 5. The d(Cu-Cl) bond length and the α and θ angles have been varied between 2.50-3.25 Å, 125 to 155°, and 0-45°, respectively. The results are summarized in the 2D contour maps shown in Fig. 6 and S17-19. The results confirm our previous conclusions: (1) the magnetic exchange is weak in all cases; (2) they are mainly ferromagnetic in nature; (3) the magnitude of the coupling strongly depends on the α angle, but only slightly on the θ angle; (4) the axial Cu-Cl bond length strongly modifies the magnitude of the magnetic coupling; the shorter the bond the stronger the exchange. This last point is clear from Fig. 7 for two pairs of α and θ values. The Cu II ion has a unique magnetic orbital on its basal plane (d x 2 -y 2 ), with the Re IV ion having all three t2g orbitals half-filled. Of these, the dxz and dyz magnetic orbitals delocalize their spin densities to the px and py orbitals of the bridging chloride ion; the dxy magnetic orbital does not. The former are therefore the only magnetic orbitals to interact with the magnetic orbital of the Cu II ion. A schematic evolution of this interaction is shown in Fig. 8. From this picture, it is clear to see that the contribution caused by the interaction between the dxz orbital on the Re IV ion and the d x 2 -y 2 orbital on the Cu II ion should be ferromagnetic, and invariant with α (Fig. 8). 24,25 Because of zero orbital overlap, the contribution promoted by the dyz magnetic orbital should also be ferromagnetic. For smaller angles of θ this contribution should become larger, due to the increased interaction between the spin densities on the magnetic orbitals, despite orbital overlap remaining zero. The Please do not adjust margins Please do not adjust margins strong dependence of the Cu-Cl bond length on the magnetic exchange is clear from Fig. 7, and can be understood by a decrease in the interaction between the spin densities when this distance increases. Thus complexes 3 and 5 exhibit the strongest ferromagnetic coupling. Note that the theoretical exchange couplings are slightly more ferromagnetic than the experimental ones. Fig. 8. The interaction between the dxz (a) and dyz (b) magnetic orbitals of the Re IV ion with the d x 2 -y 2 orbital of the Cu II ion. α is the Re-Cl-Cu angle and ρ the orbital overlap. The largest ferromagnetic exchange is found for α = 135º. Table 3. Values of gRe, DRe, gCu and J parameters that provide the best-fit of the thermal dependence of χMT for 2-6.
With the theoretical study as a guide, we then attempted to use our model to fit the experimental susceptibility data (Fig. 2), and obtained good simulations with the set of parameters given in Table 3. The analysis for compound 1 was excluded due to the presence of multiple coupling pathways. The experimental behaviour is in agreement with the calculated magnetic coupling constants, and the J values in Table 3 agree well with those in Table 2 and Fig. 9.  Table 3. Grey dots correlate to the values presented in Table 2.

Conclusions
A family of highly unusual one-dimensional chloro-bridged Re IV Cu II chains has been built using the [Re IV Cl6] 2anion as a metalloligand. The complexes have been characterised structurally, magnetically and theoretically. Changing the nature (size/sterics) of the monodentate, terminally bonded ligand, L, on the Cu II ions (L = imidazole (Imi, 1), 1methylimidazole (Meim, 2), 1-vinylimidazole (Vim, 3), 1butylimidazole (Buim, 4), 1-vinyl-1,2,4-triazole (Vtri, 5) and N,N'-dimethylformamide (DMF, 6) and the subsequent changes to the packing of the chains in the crystal, results in the structures exhibiting significant intra-molecular differences in Cu-Cl bond lengths and Re-Cl-Cu bridging angles. This results in large differences in the nature and magnitude of magnetic exchange interactions between the Re IV and Cu II ions. Theoretical calculations show the coupling to be primarily ferromagnetic, with the developed magneto-structural correlation revealing that an increase in the magnitude of J occurs as the bridging angle becomes smaller and the bond lengths shorten.

Computational Details
Calculations were performed with the Gaussian09 package using the CAM-B3LYP functional (a long range corrected version of B3LYP) and the quadratic convergence approach. [31][32][33][34][35][36] Doubleζ and Los Alamos effective core potentials, as proposed by Hay and Wadt, were used for the Re IV and Clions. [37][38][39] Ahlrichs double-ζ basis set was used for the remaining atoms. 40 Twoelectron integrals and their derivatives were computed from Douglas-Kroll-Hess (DKH) 2nd order scalar relativistic calculations. 41,42 An approach based on the use of brokensymmetry (BS) functions built from localised orbitals was employed to evaluate the energies of several spin states. 43 The BS functions were obtained from the guess functions generated with the fragment tool implemented in Gaussian09. Intermolecular magnetic couplings were calculated from the experimental structures. Intramolecular interactions were calculated on Re IV Cu II models designed from experimental geometries. Parameters corresponding to the acetonitrile solvent were included to simulate the electronic effects of the surrounding molecules. 44 Calculations of the zero-field splitting, zfs, parameters were performed with version 3.0 of the ORCA program. 45 The TZVP basis set proposed by Ahlrichs, and tight SCF criteria were used in all cases. 40 Relativistic effects for the Re IV ion were introduced from a zero-order regular approximation (ZORA). 46 For complete active space (CAS) calculations, this auxiliary basis set was replaced by TZV/C. 47,48 The zfs parameters were evaluated from N-Electron Valence State Perturbation Theory (NEVPT2) calculations and an approach based on an effective Hamiltonian for the spin-orbit coupling. This zfs calculation included contributions from ten quartet and twenty doublet states generated from electron promotion between d orbitals, which corresponds to the full active space modelled from only the five d orbitals of the Re IV ion. 49