A low spin manganese(iv) nitride single molecule magnet

Structural, spectroscopic and magnetic methods have been used to characterize the tris(carbene)borate compound PhB(MesIm)3Mn 
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Created by potrace 1.16, written by Peter Selinger 2001-2019
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 N as a four-coordinate manganese(iv) complex with a low spin (S = 1/2) configuration.


Introduction
Since the discovery of a four-coordinate iron(II) complex displaying SMM behaviour, 1 multiple examples of mononuclear dblock SMMs have been reported. 2 In most of these systems, the magnet-like behaviour (i.e. their slow dynamics of the magnetization) was described by an Orbach mechanism involving an energy barrier to spin reversal (D) created by an uniaxial Isinglike magnetic anisotropy (D) acting on a high spin ground state (S T ). 3 Specically: D ¼ |D|S T 2 for integer spins and D ¼ |D|(S T 2 À 1/4) for half-integer spins (with H ¼ DS z 2 ). 4 With appropriate ligand design, spin-orbit coupling can be used to create a signicant uniaxial anisotropy, resulting in large SMM barriers despite the relatively small S T associated with mononuclear d-block complexes. 5 In the case of f-block complexes, spin-orbit coupling is strong and magnetic anisotropy results from crystal eld splitting of the total angular momentum (J) ground states. Strong spin-orbit coupling can lead to SMM properties in complexes having f 1 electron congurations. For example, the SMM behaviour of the 5f 1 U(V) complex, (tren TIPS ) U(O) (tren TIPS ¼ {N(CH 2 CH 2 NSi i Pr 3 ) 3 } 3À ) has been attributed to an energy gap between the M J ¼ AE3/2 ground Kramers doublet and the lowest-lying excited Kramers doublet (either M J ¼ AE1/2 or M J ¼ AE5/2). 6 The SMM properties of 4f 1 Ce(III) complexes have been similarly rationalized. 7 In the case of d-block complexes, there is an intriguing report of a d 9 SMM, [Ni(6-Mes) 2 ] + (6-Mes ¼ 1,3-bis(2,4,6-trimethylphenyl)-3,4,5,6-tetrahydropyrimidin-2-ylidene), 8 although the origin of the barrier for relaxation of the magnetization was not investigated in detail. A more comprehensive investigation of trigonal planar S ¼ 1/2 Ni(I) complexes attributed the observed SMM properties to direct and Raman processes. 9 Indeed the origin of the magnetization dynamics in these and other S ¼ 1/2 SMM systems is oen difficult to establish as it can be induced by different mechanisms (Orbach, quantum tunnelling, Raman, direct, phonon-bottlenecklimited direct, etc.), 3,10 which are indeed oen in intimate competition at a given temperature and applied magnetic eld. 9,11 Some of us have been investigating the properties of transition metal complexes with strongly donating tris(carbene) borate ligands. 12,13 In addition to stabilizing metal-ligand multiple bonds, 14 the three-fold symmetric environment induced by these ligands may also be used to create complexes with signicant uniaxial anisotropy. This anisotropy leads to slow relaxation of the magnetization in certain high spin iron(II) tris(carbene)borate complexes. 15 During the course of these studies, we reported the low spin (S T ¼ 1/2) Fe(V) complex, [PhB( t BuIm) 3 Fe^N] + (Fig. 1). 16 Detailed spectroscopic and computational investigations into the electronic structure of this complex reveals that it undergoes a quadratic Jahn-Teller distortion and signicant e-e mixing that lowers the idealized molecular symmetry but does not completely quench spin-orbit coupling. 16b Building from this work, we report in this contribution the synthesis, characterization, spectroscopic and magnetic properties of the isoelectronic Mn(IV) nitride, PhB(MesIm) 3 Mn^N (PhB(MesIm) 3 À ¼ phenyltris (3-mesitylimidazol-2-ylidene)borato) which shows similar structural and spectroscopic properties to the Fe(V) complex. Magnetic measurements reveal that this new manganese complex shows slow relaxation of its magnetization, which is unexpected for a low spin (S T ¼ 1/2) d 3 conguration. A combined approach using a detailed experimental study of the relaxation time (in temperature and dc eld) and electronic structure theory has been used to delineate the origin of the observed magnetization dynamics in this new SMM.

General considerations
All manipulations were performed under a nitrogen atmosphere by standard Schlenk techniques or in an MBraun Labmaster glovebox. Glassware was dried at 150 C overnight. Diethyl ether, n-pentane and tetrahydrofuran were puried by the Glass Contour solvent purication system. Deuterated benzene was rst dried with CaH 2 , then over Na/benzophenone, and then vacuum transferred into a storage container. Before use, an aliquot of each solvent was tested with a drop of sodium benzophenone ketyl in THF solution. The tris(carbene)borate ligand precursor, PhB(MesImH) 3 OTf 2 , was prepared according to a literature procedure. 13

Synthesis of complexes
Preparation of PhB(MesIm) 3 Mn II Cl (1). Lithium diisopropylamide (153 mg, 0.46 mmol) was added to a precooled slurry of PhB(MesImH) 3 (OTf) 2 (437 mg, 1.43 mmol) in Et 2 O (50 mL) at À78 C. The resulting mixture was stirred at À78 C for 15 min and then slowly warmed to room temperature. Aer stirring until the reaction mixture became golden yellow, the solvent was removed in vacuo. Tetrahydrofuran (15 mL) was added to the resulting yellow solid, followed by MnCl 2 (70 mg, 0.56 mmol). The reaction was stirred at room temperature overnight and then dried under vacuum. Aer washing with Et 2 O and drying under vacuum, the product was obtained (241 mg, yield 71% based on PhB(MesImH) 3 (OTf) 2 ) as white solid. Colorless crystals were obtained by diffusion of pentane into a THF solution of the product at À35 C. m eff ¼ 6.1(3) m B [cT ¼ 4.6(1) cm 3 K mol À1 ]. Elemental analysis calcd for C 42 H 44 BMnCl: (%) C 68.79, H 6.04, N 11.45 found (%) C 68.70, H 6.04, N 11.39.
Preparation of PhB(MesIm) 3 Mn IV^N (2). A 250 mL quartz round-bottom-ask was charged with 1 (333 mg, 0.45 mmol), NaN 3 (146 mg, 2.25 mmol) and THF (100 mL). The mixture was stirred overnight under UV irradiation to yield a yellow solution. The solvent was removed in vacuo. Minor impurities were removed by washing with Et 2 O. The remaining solid was extracted into THF and ltered through Celite to yield a yellow solution. The solvent was removed in vacuo to afford a yellow solid (201 mg, 56% based on PhB(MesIm) 3 MnCl). X-Ray quality crystals were obtained by the slow diffusion of n-pentane into a THF solution of the product at À35 C. 1  Single-crystal X-ray diffraction Complex 1 was measured using a Bruker APEX II Kappa Duo diffractometer equipped with an APEX II detector at 150(2) K. Complex 2 was investigated with synchrotron radiation at 100(2) K at the ChemMatCARS 15IDB beamline at the Advanced Photon Source at Argonne National Lab, Chicago. Additional details of the data collection and renement are included in the ESI. †

Magnetic susceptibility measurements
The magnetic measurements were carried out with the use of Quantum Design MPMS-XL SQUID magnetometer and PPMS-9 susceptometer. These instruments work between 1.8 and 400 K with applied dc elds ranging from À7 to 7 T (MPMS).
Measurements were performed on a polycrystalline samples of 2 (17.7, 19, 3.2 and 4.5 mg) sealed in a polyethylene bag (3 Â 0.5 Â 0.02 cm; typical 20 to 40 mg) and covered with mineral oil or directly in their frozen THF mother liquor within a sealed straw to prevent desolvation of the solid. Only experiments done with 2 maintained in frozen mother liquor and prepared under nitrogen atmosphere led to reproducible dc and ac magnetic data. No evaporation of the mother liquor was observed during these measurements. The mass of the sample was determined aer the measurements and subsequent mother liquor evaporation. Prior to the experiments, the eld-dependent magnetization was measured at 100 K in order to conrm the absence of any bulk ferromagnetic impurities. Ac susceptibility measurements were made with an oscillating eld of 1 to 6 Oe with a frequency from 10 to 10 000 Hz (PPMS). The magnetic data were corrected for the sample holder, mineral oil, mother liquor and the intrinsic diamagnetic contributions.

X-ray photoelectron spectroscopy (XPS)
XPS experiments were performed using PHI Versa Probe II instrument equipped with monochromatic Al K(alpha) source. The X-ray power of 50 W at 15 kV was used for 200 micron beam size. The instrument work function was calibrated to give a binding energy (BE) of 84.0 eV for Au 4f 7/2 line for metallic gold and the spectrometer dispersion was adjusted to give BEs of 284.8, 932.7 and 368.3 eV for the C 1s line of adventitious (aliphatic) carbon presented on the non-sputtered samples, Cu 2p 3/2 and Ag 3d 5/2 photoemission lines, respectively. The PHI dual charge compensation system was used on all samples. XPS spectra with the energy step of 0.1 eV were recorded using soware SmartSo-XPS v2.0 and processed using PHI MultiPack v9.0 at the pass energies of 46.95, 23.5, 11.75 eV for Mn 2p and Mn 3s, for N 1s, and for C 1s regions, respectively. Peaks were tted using GL line shapes, i.e., a combination of Gaussians and Lorentzians with 0-50% Lorentzian content. Shirley background was used for curve-tting.

Ab initio calculations
Electronic structure calculations were performed using the ORCA 3.0.3 soware package and MOLCAS 8.0. 18 Energies, wavefunctions and spin-Hamiltonian parameters for full and model complexes were calculated by the CASSCF methodology. The spin-orbit effects were included in both programs using quasi-degenerate perturbation theory (QDPT) in ORCA and restricted active space state interaction (RASSI) approach with MOLCAS program. The def2-TZVP basis set 19a,b and ANO-RCC 19c,d basis were employed with ORCA and MOLCAS, respectively. Such methods comprise two steps: (i) a CASSCF calculation is performed to obtain the non-relativistic states and energies of the system and (ii) state mixing by the Spin-Orbit Coupling (SOC) operator. Dynamical correlation was introduced by the N-electron valence perturbation theory (NEVPT2). 20 Energies for the d orbitals were obtained from the ab initio ligand eld theory (AILFT) approach. 21a In a nutshell, the AILFT approach allows for the extraction of ligand eld and Racah parameters from a one-to-one mapping of the matrix elements of a model ligand eld matrix to a CI matrix obtained from electronic structure methods (in this case, the CI matrix from a CASSCF (3,5) calculation). Numerical values for the parameters are obtained from least-squares t of the CASSCF matrix elements and orbital energies can be calculated by diagonalization of the ligand eld matrix. Further details about the CASSCF + QDPT approach, the AILFT method and its applications to problems in molecular magnetism have been previously described. 21b

Synthesis and characterization
The manganese nitride complex, PhB(MesIm) 3 Mn^N (2) is accessible by the same synthetic pathway used to prepare the related Fe(IV) nitrides (Fig. 2a). 22 Specically, irradiating a solution of the high spin Mn(II) complex PhB(MesIm) 3 MnCl (1) (Fig. 2b) in the presence of NaN 3 provides 2 as a yellow solid following workup. Structural and spectroscopic methods (detailed below) reveal 2 to be a four-coordinate Mn(IV) nitride complex with a low spin (S T ¼ 1/2) d 3 electron conguration that is subject to a Jahn-Teller distortion. The molecular structure of 2 has been determined by single crystal X-ray diffraction (Table S1 †), revealing a four-coordinate manganese nitride complex supported by the tripodal tris(carbene)borate ligand (Fig. 2c), that crystallizes with interstitial THF molecules. The asymmetric unit contains one THF and two independent molecules with similar metrical parameters; only one of these will be discussed (Table S2 † (2) and X-ray crystal structures of (b) PhB(MesIm) 3 Mn II -Cl (1), and (c) PhB(MesIm) 3 Mn IV^N (2) with thermal ellipsoids shown at 50% probability; H atoms are omitted for clarity. Black, blue, lilac, pink and green ellipsoids represent C, N, Mn, B and Cl atoms, respectively.
(1.938(2)-2.006(2)Å) distances are slightly longer than the equivalent distances in the related tris(carbene)borate Fe(IV) nitrides, 22 likely due to the larger ionic radius of the Mn(IV) centre. The manganese ion lies ca. 0.1Å out of the plane dened by the carbon atoms of the tris(carbene)borate ligand, which is similar to the equivalent distance observed in the iron analogues. Similarly to the isoelectronic [PhB( t BuIm) 3 Fe V^N ] + complex, 16 the Jahn-Teller distortion is manifested in the B-Mn-N vector bending away from 180 (B-Mn-N ¼ 174.7 ). While many of the metrical parameters are similar, there are some key structural differences between 2 and the related Mn Table 1). The most notable structural differences relate to how the Jahn-Teller distortion is manifested (Fig. S3 †). In the case of [(TIMEN xyl )Mn^N] + , which has a relatively exible tris-(carbene)amine ligand, signicant elongation of one Mn-C bond (by 0.15Å) occurs to lower the local symmetry at the Mn site. The greater rigidity of the tris(carbene)borate ligand in 2 evidently hinders such a distortion, and all Mn-C distances are similar in length. Instead, the B-Mn-N angle in 1 is bent away from 180 (B-Mn-N ¼ 174.7 ), whereas the equivalent angle in [(TIMEN xyl ) Mn^N] + is almost linear (179.4 ).
Complex 2 has also been spectroscopically characterized. The solution 1 H NMR spectrum reveals eight paramagnetically-shied resonances with relative integration appropriate for a three-fold symmetric complex. The solution magnetic moment, as determined by the Evans' method (m eff ¼ 2.2(3) m B ; cT ¼ 0.6(1) cm 3 K mol À1 ), is consistent with a single unpaired electron and unquenched spin-orbit coupling seen in the solid state (see below).
The redox characteristics of 2 have been investigated by cyclic voltammetry. As with the structural data, interesting differences with [(TIMEN xyl )Mn^N] + are observed (Table 1), likely stemming from the relative exibilities of the two tris(carbene) ligands. Thus, while both 2 and [(TIMEN xyl )Mn^N] + can be reversibly reduced on the CV timescale, only the latter can be oxidized to Mn(V). 23 The stability of the Mn(V) state for the TIMEN xyl ligand is in part due to the ability of apical bridgehead nitrogen atom of this ligand to bind to Mn in this higher oxidation state, forming a ve-coordinate complex. Such additional stabilization is not possible with the tris(carbene)borate ligand.

Electron paramagnetic resonance
More detailed insights into the electronic structure of 2 have been obtained from EPR spectroscopy. The frozen solution EPR spectrum (Fig. 3, top) incorporates resolved hyperne splitting from the Mn(IV), I ¼ 5/2, centre. The |M I i ¼ |À5/2i and |M I ¼ |À3/2i manifolds at the low magnetic eld edge of g k are well resolved, and simulated with an A 1 ( 55 Mn) ¼ 300 MHz coupling. The g t values are slightly split, with anisotropic 55 Mn hyperne couplings, as determined by simulation of the EPR spectrum, yielding g values (g ¼ [g 1 , g 2 , g 3 ] ¼ [2.35, 1.973, 1.965]) and 55 Mn couplings 74,202] MHz). The average g value, g av ¼ [(g 1 + g 2 + g 3 )/3] ¼ 2.096, is in agreement with the g factor, 2.1(1), determined from the magnetic susceptibility measurements detailed below. The electronic structure of 2 and EPR parameters remarkably resemble those of other low-spin trigonal d 3 centres (Mn(IV) and Fe(V)) with tris(carbene) ligands. 16,23 A solid powder sample of 2 was also prepared for EPR characterization by suspending the solid in pentane to form a slurry. The X-band EPR spectrum of this slurry (Fig. 3, middle) is similar to that observed in solution (Fig. 3, top). The same g t $ 1.97 feature is observed, although with anisotropic line widths. The g k (g 1 ) feature is too broad and not observed, however, the A 3 55 Mn hyperne splitting of 204 MHz is distinctly   observed in the EPR spectrum of the slurry (Fig. 3, bottom dashed lines). The line widths of the A 2 hyperne lines are noticeably broader than A 3 . Therefore, the g 2 , g 3 and 55 Mn hyperne (A 2 , A 3 ) parameters of the slurry sample match those observed for the solution. EPR spectra of this slurry collected at various temperatures (3.6 to 20 K) exhibit only the S ¼ 1 2 Mn(IV) complex identiable by the 55 Mn hyperne structure (see ESI †). In short, the electronic characteristics of the d 3 Mn(IV) nitride are the same in both solution and the solid state.

X-ray photoelectron spectroscopy
The combined structural and spectroscopic data described above indicate the presence of a tetravalent manganese ion in complex 2. This oxidation state assignment has been conrmed using X-ray Photoelectron Spectroscopy (XPS). The standard position of the 2p 3/2 peak for the Mn(IV) state is accepted to be in the range from 641.1 to 642.5 eV with the spin-orbit splitting of 11.7 eV between Mn 2p 3/2 and Mn 2p 1/2 levels. The measured binding energies of Mn 2p 3/2 for 2 are well within this range (Fig. 4a, for details see Table S2 †). It should be noted that the shape of the Mn 2p transition may be different for samples with the same Mn oxidation state. Thus, for example, a shake-up-like satellite (normally characteristic of Mn 2+ ions) is observed for MnPO 4 , but not for Mn 2 O 3 , despite the Mn(III) state of both compounds. 24 Similar shake-up-like features are observed for our Mn(IV) complex, which clearly are more resolved for the Mn(II) complex 1 (Fig. 4c) as expected. The feature similar to the shake-up high energy side of the Mn 2p 3/2 shoulder was also reported for nanoparticles containing Mn(IV) ions in a SnO 2 matrix. 25 The Mn 3s spin-orbit split for both samples was also recorded to better distinguish between the 4+ and 2+ oxidation states of Mn. The clear reduction of the value for the spin-orbit split for 2 in comparison to that of 1 (Fig. 4b and d and Table  S4 †) is consistent with reported in literature values. 26 We found a measurable difference in the binding energies of N 1s as well as differences in the ratio of the components (Fig. S3 and S4 †). The N 1s region for 2 is deconvoluted in a 3 : 3 : 1 ratio, while a 1 : 1 ratio is observed for 1, as expected. Thus, the XPS data are fully consistent with manganese being in the +IV oxidation state in complex 2.
In summary, the combined characterization data reveal that 2 is the latest addition to the small but growing family of compounds having a low spin (S T ¼ 1/2) d 3 electron conguration. 16,23,27,28 It is notable that many of these complexes are supported by ligands that create approximately three-fold symmetric environments. 16,23,28 This electronic conguration is susceptible to a Jahn-Teller distortion away from three-fold symmetry. This distortion is most clearly observed in 3d metal complexes, where the nature of the distortion depends on the supporting ligand.

Magnetic properties
The magnetic properties of 2 have been studied by dc and ac techniques. Perfectly reproducible data were obtained when the compound was maintained below 200 K during the measurements and in its THF mother liquor, which prevents loss of solvent from the polycrystalline sample. At 200 K, the cT product has a value of 0.47 cm 3 K mol À1 in good agreement with a magnetically isolated low-spin (S T ¼ 1/2) Mn(IV) centre (Fig. 5). When lowering the temperature, the cT product decreases rst almost linearly down to 30 K and then in a more pronounced manner to reach 0.32 cm 3 K mol À1 at 1.85 K. As shown by the electronic structure calculations discussed in the next section, the observed thermal behaviour above 30 K is directly the consequence of the thermal depopulation of the rst excited doublet state. As expected, the theoretical cT vs. T data calculated using MOLCAS code 18 (blue line in Fig. 5) compare qualitatively very well with the experimental data (it is worth noting that the higher theoretical cT value is due to the larger calculated g av value; see Electronic structure calculations section). At lower temperatures and as already detected by EPR (vide supra), the marked decrease of the cT product reveals the presence of antiferromagnetic interactions between Mn(IV) complexes. These intermolecular interactions were evaluated at À0.6(1) K (zJ/k B ) by simulating the experimental data in the frame of the Fig. 4 High-resolution Mn 2p spectra of (a) PhB(MesIm) 3 Mn^N (2) and (c) PhB(MesIm) 3 MnCl (1). The black line represents the experimental data, the red line shows the fit, and the blue and green lines represent Mn 2p 3/2 and Mn 2p 1/2 components, respectively, while the brown line represents shake-up satellites. See Table S3 † for fitting parameters. High-resolution Mn 3s spectra of (b) PhB(MesIm) 3 Mn^N (2) and (d) PhB(MesIm) 3 MnCl (1). The black line represents the experimental data, the red line shows fit, and the blue and green lines represent Mn 3s split components. See Table S4 † for fitting parameters. mean-eld approximation 29 applied to the scaled (Â0.88) MOLCAS cT vs. T values (red line in Fig. 5). The eld dependences of the magnetization below 8 K (inset Fig. 5) are also in good agreement with an S ¼ 1/2 species (M ¼ 1.05 m B at 7 T & 1.85 K). The t of the experimental data with an S ¼ 1/2 Brillouin function conrms an average g factor around 2.10(2), which is in perfect agreement with that deduced from EPR (g av ¼ 2.096, vide supra).
The magnetization dynamics of this manganese nitride complex were probed by ac susceptibility measurements. In the absence of a dc eld, the ac data, above 1.8 K and for frequencies up to 10 kHz, display a frequency independent in-phase (c 0 ) susceptibility consistent with the dc susceptibility (Fig. 5), and accordingly do not exhibit any out-of-phase component (c 00 ). However, application of a dc eld leads to the detection of a relaxation process in both components of the ac signal (Fig. 6), revealing the slow dynamics of the magnetization in 2. The ac signal becomes detectable around 5000 Hz for a dc eld of about 200 Oe. At all elds, the c 0 vs. n and c 00 vs. n data can be modelled by a generalized Debye model 30 (Fig. 6) with a small a coefficient (<0.4) indicating a weak distribution of the relaxation time (s) and thus a relaxation mode that is dominated by a single relaxation process. The characteristic frequency of this relaxation mode continuously decreases when applying higher elds (to about 1000 Hz at 1 T) while the amplitude of the mode (c 0 À c N ) exhibits a maximum around 0.45 T (Fig. 6). For this particular dc eld, the temperature dependence of the ac susceptibility was studied as shown in Fig. 7. At all temperatures, the c 0 vs. n and c 00 vs. n data can also be modelled by a generalized Debye model 30 (Fig. 7 and S7 †) allowing an estimation of the temperature dependence of the relaxation time at 0.45 T (Fig. S8 †). As conventionally admitted, the exponential increase of the relaxation time (i.e. it follows an Arrhenius law) suggests the presence of a thermally activated (Orbach) process of relaxation with a pre-exponential factor, s 0 , of 5(1) Â 10 À6 s and an energy gap of only 5.1(5) K (3.5 cm À1 ). While the origin of the relaxation process will be discussed in more detail below, it is important at this stage to note the unusually small energy barrier and the large value of s 0 (at least 4 orders of magnitude larger than expected for typical vibrations of the network which govern the Orbach reversal of magnetization). 3

Electronic structure calculations
The magnetic properties of the low-lying states of 2 were further analysed by means of an ab initio multireference methodology. A symmetrized model complex was rst studied to obtain a qualitative description of the ground state nature of 2 and then these conclusions were corroborated by calculations of the full complex.
The model complex was constructed from its original geometry, where the aryl groups were replaced with methyl substituents, symmetrizing the structure to the C 3v group. Initial CASSCF (3,5) calculations for the model system using the ORCA code indicate the following orbital sequence (obtained with the AILFT theory, see ab initio calculations section): d xy and d x 2 Ày 2 at a reference energy (i.e. 0.0 cm À1 ), d z 2 at 31 000 cm À1 and (d xy , d xz ) at 32 500 cm À1 (which is equivalent to the orbital diagram of Fig. 1; see also Fig. 8). Although this orbital diagram appears to be reasonable, the limitations of this reduced active space are evident in the swapping of the ground state wavefunction due to the inclusion of dynamical correlation (NEVPT2) and the prediction of a quartet state as the ground level. The addition of the s and 2p orbitals of the N 3À ligand in a CASSCF (9,8) leads to the correct spin state ordering and  a NEVPT2 correction that preserves the ground state for the model structure. The lower energy orbitals in the CASSCF (9,8) calculations are still (d xy , d x 2 Ày 2 ), with a doubly degenerate ground state that corresponds predominantly (81% weight in both wavefunctions) to the d 2 x 2 Ày 2 d 1 xy and d 1 x 2 Ày 2 d 2 xy congurations. The next excited state is 7300 cm À1 higher in energy (10 100 cm À1 in NEVPT2) and is not relevant for discussing the SMM properties of 2. Thus, magnetic anisotropy in this system emerges from the quantum mixing of the degenerate ground state by the spin-orbit coupling (SOC), given that the d x 2 Ày 2 and d xy orbitals are connected by the z component of the angular momentum operator. 2b,11b,31 In this way, two strongly anisotropic Kramers' doublets are formed from the rst two S ¼ 1/2 states, separated by 470 cm À1 (676 K). The ground doublet of the model system presents a markedly uniaxial g tensor with g z ¼ 5.15, g x ¼ g y ¼ 0.15. This strong anisotropy is signicantly reduced in the full system due to the deviations from trigonal symmetry that breaks the degeneracy between d x 2 Ày 2 and d xy orbitals, partially quenching the SOC mixing. In the full complex, the calculated ground state is split to an energy difference of 2103 cm À1 (CASSCF (9,8) calculation including only doublets). This splitting leads to a marked decrease of the g tensor anisotropy of the ground doublet to values of g x ¼ 1.940, g y ¼ 1.942 and g z ¼ 2.674, yielding a g av of 2.185, in satisfactory agreement with the values obtained for magnetization and EPR measurements. Equivalent CASSCF + RASSI calculations performed with MOLCAS code provide similar values with a rst excited Kramers doublet at 1932 cm À1 (2800 K) and g x ¼ 1.927, g y ¼ 1.933 and g z ¼ 2.790 values (i.e. g av ¼ 2.217; as mentioned above the calculated g av values is systematically slightly larger than the experimental one, around 2.1, which explains the difference between experimental and calculated magnetic susceptibility exemplied in Fig. 5). This CASSCF + RASSI approach was also used to estimate the possible relaxation mechanisms considering the two lowest Kramers doublets (Fig. 9 inset). As expected due to their large energy separation, thermally activated mechanisms of relaxation, e.g. Orbach, cannot be relevant at low temperatures. Thus, the magnetic dynamics in 2 should only involve the ground Kramers' doublet, allowing possible quantum tunnelling (QTM), direct and Raman mechanisms.

Discussion on the origin of the magnetization relaxation
The electronic structure calculations discussed in the previous section lead to unambiguous conclusions on the origin of the slow dynamics of the magnetization in 2, which (i) should be dominated by QTM, direct and/or Raman mechanisms and (ii) cannot involve Orbach processes. With these elements in mind, the experimental relaxation time has been further analysed starting from its eld dependence at 1.8 K (Fig. 9 le). At low elds (m B H ( k B T), most of the processes inducing a magnetization relaxation (Raman, Orbach, phonon-bottleneck, etc.) are weakly eld dependent and thus they have been included as constant, k(T), in eqn (1). 3,11 On the other hand, the quantum tunnelling of the magnetization is strongly affected by applying even a small magnetic eld as illustrated by the rst term in eqn (1). 32,33 As shown in Fig. 9 (le part), the experimental relaxation time is extremely well described by this simple approach (eqn (1); with B 1 ¼ 24 800(50) s À1 , B 2 ¼ 15.6(5) T À2 and k(T) ¼ 5427 s À1 ) conrming the key role of the quantum tunnelling of the ground doublet in the relaxation mechanism, in agreement with the theoretical predictions ( Fig. 9 inset). As direct processes are also strongly eld dependent (even at low elds), 3,9,32 their possible incidence on the magnetization dynamics of this Kramer system was also tested by including an TH 4 term in eqn (1). The t of the experimental data ( Fig. 9, le part) to this more complete model leads systematically to a negligible prefactor of this additional TH 4 term underlying the irrelevance of the direct processes.  Field (left, at 1.8 K) and temperature (right, at 0.45 T) dependences of the average relaxation time for 2 estimated from the Fig. 6 and 7. The red lines are the best fits obtained with the theoretical approach developed in the text. Inset: lowest two Kramers doublets and ab initio computed relaxation mechanism with the MOLCAS code (CASSCF + RASSI level). The thick black lines are Kramers doublets shown as a function of their magnetic moment, M z , along the main anisotropy axis (z). The green arrows correspond to the quantum tunnelling mechanism (QTM) of ground and first excited states while purple arrow shows the hypothetical Orbach relaxation process. The red arrow indicates the transition between the ground and first KDs. The values close to the arrows indicate the matrix elements of the transition magnetic moments (above 0.1, an efficient spin relaxation mechanism is expected). Thus, this figure highlights that the QTM through the Kramers doublet ground state is dominating the relaxation process at low temperatures.
The temperature dependence of the relaxation at 0.45 T was analysed analogously, considering s QTM as a constant (equal to 1.67 Â 10 À4 s from the rst term of eqn (1)) and including thermally active processes, which are either thermally activated (Orbach) or following a power law of the temperature for Raman mechanisms (with exponents ranging from 1 to more than 9). 3,9,11,32 s À1 ¼ s QTM À1 + bT n Remarkably, eqn (2) is able to reproduce the experimental data with a single power law and an exponent (n) of 2.93(5) (with b ¼ 1105 s À1 K À2.93 and s QTM xed at 1.67 Â 10 À4 s). As discussed recently by Sessoli et al. for an S T ¼ 1 2 V IV complex, 11d the exponent value close to 3 suggests the presence of a Raman process involving both acoustic and optical vibrations. 9 It is worth mentioning that the addition of terms in eqn (2) including different power laws or an exponential function does not signicantly improve the modelling of the experimental data shown in Fig. 9. Overall, the combined eld and temperature dependence of the relaxation time below 4 K and 1 T conrms the predominance of the quantum tunnelling pathway to relax the magnetization with a characteristic time of ca. 2 Â 10 À4 s. Nevertheless, this relaxation mechanism is clearly assisted by Raman processes that rationalize the thermal dependence of the relaxation time.

Conclusions
Structural and spectroscopic methods reveal that the Mn(IV) complex PhB(MesIm) 3 Mn^N (2) is a rare example of a low spin (S ¼ 1/2) d 3 complex. Its degenerate electron conguration is subject to a Jahn-Teller distortion, which is manifested in 2 by bending of the B-Mn-N vector, similarly to the isoelectronic Fe(V) complex, [PhB( t BuIm) 3 Fe^N] + . 16 Electronic structure calculations conrm the role of the spin-orbit coupling to stabilize an anisotropic ground doublet even in presence of the Jahn-Teller distortion. As the rst excited doublet lies more than 2000 cm À1 above the ground state, SMM properties observed by ac susceptibility measurements cannot rely on an Orbach mechanism and even if the traditional semi-logarithm s vs. T À1 presentation of the experimental data could suggest the contrary. A detailed analysis of the eld and temperature dependence of the relaxation time supports the theoretical CASSCF + RASSI calculations, and highlights the key role of the quantum tunnelling mechanism in the slow dynamics of the magnetization in this S ¼ 1 2 species. Additionally, the signature of Raman processes could be detected in the thermal variation of the relaxation time. Since theoretically the Jahn-Teller distortion signicantly activates the quantum tunnelling mechanism, we anticipate that complexes where the structural distortion is smaller than in 2 will have much larger relaxation times. Investigations aimed at testing this hypothesis are currently in progress.