Slow Spin Relaxation in a Low-Spin S=1/2 FeIII Carborane Complex

In this communication, we report the first evidence of slow-spin relaxation of a low-spin FeIII carborane complex. Iron S = 1/2 complexes showing such behaviour are particularly appealing as qubit candidates because they fulfil some of the main requirements to reach long decoherence times, such as moderate magnetic anisotropy, small spin, metal element mainly with zero-nuclear spin and furthermore, large versatility to introduce chemical modifications.


II.-Computational details
Table S3.Calculated relative energies (in kcal/mol) between the three isomers for the isolated molecules or in a CPCM model using THF as solvent.
Table S4.Calculated NEVPT2 state energies (in cm -1 ) including spin-orbit effects using the three active spaces using the experimental X-ray structure.
Table S5.Calculated energy splitting of the 5 d orbitals using the NEVPT2 (5,5)   method using the experimental X-ray structure.
Table S6.Calculated g components using NEVPT2 method including spin-orbit effects using the three active spaces using the experimental X-ray structure.
Table S7.Calculated g components and excited states (D doublet or Q quartet states, in cm -1 ) for the three DFT optimized isomers using B3LYP calculations and CPCM model to simulate the THF solvent.
Table S9.Spin relaxation values (t) extracted from the Cole-Cole diagram for different temperatures using the CC-fit code for a saturated THF solution of the [NMe4] [3,3'-Fe(1,2-C2B9H11)2] compound with an external field of 0.05 T.

References
Experimental section:

Instrumentation.
Elemental analyses were performed using a Carlo Erba EA1108 microanalyzer.IR spectra (ν, cm -1 ; ATR) were recorded on a JASCO FT/IR 4700 spectrophotometer.NMR spectroscopy: The 1 H-NMR, 1 H{ 11 B}-NMR (400 MHz), 11 B-NMR and 11 B{ 1 H}-NMR (128.38 MHz), and 13 C{ 1 H}-NMR (100 MHz) spectra were recorded with a Bruker Advance III (400MHz) instrument equipped with the appropriate decoupling accessories.Chemical shift values for 11 B-NMR and 11 B{ 1 H}-NMR spectra were referenced to external BF3•OEt2, and those for 1 H-, 1 H{ 11 B}-and 13 C{ 1 H}-NMR spectra were referenced to Si(CH3)4.Chemical shifts are reported in units of parts per million downfield from reference, and all coupling constants are reported in Hertz.EPR.Bruker ELEXYS E500 X band EPR spectrometer equipped with a variable temperature unit, a field frequency (F/F) lock accessory and built in NMR Gauss meter.Mass spectra were recorded in the negative ion mode using a Bruker Biflex MALDI-TOF-MS [N2 laser; λexc 337 nm (0.5 ns pulses); voltage ion source 20.00 kV (Uis1) and 17.50 kV (Uis2)].
Cyclic Voltammetry was obtained with an Autolab PGSTAT302N at a scan rate of 100 mV/s.A three-electrode set up was used, being a glassy carbon the working electrode; an Ag as pseudoreference electrode and Pt wire as counter electrode.All measurements were done in dry and pure acetonitrile with TBA[PF6] 0.1 M as the inert electrolyte and referenced to internal Fc + /Fc.The concentrations of all the measured samples were always 1 mM.All solvents and electrolytes used for the electrochemical measurements were purchased from Sigma-Aldrich.
Reagent grade acetonitrile was pre-dried over CaCO3, and then distilled over P2O5.Prior to use, acetonitrile was degassed by the standard freeze-pump-thaw technique in order to remove the dissolved oxygen, and stored over 0.4 nm molecular sieves.TBA[PF6] was dried overnight at 50º under vacuum to remove possible traces of water.UV-Vis spectrum was recorded on Shimadzu UV-1700 Pharmaspec spectrophotometer, using 1 cm cuvette.Different concentrations of the compounds were used to calculate the molar extinction coefficient: 15.86 mmol•L -1 .

Crystallography Experimental X-ray diffraction
Measured crystal was prepared under inert conditions immersed in perfluoropolyether as protecting oil for manipulation.A suitable crystal was mounted on MiTeGen Micromounts TM , and this sample was used for data collection.Crystallographic data was collected at 100K at XALOC beamline at ALBA synchrotron (l = 0.82654 Å).Data were indexed, integrated and scaled using with APEX3 program 3 and corrected for absorption using SADABS.4a The structure was solved by direct methods and subsequently refined by correction of F 2 against all reflections.4b All non-hydrogen atoms were refined with anisotropic thermal parameters by fullmatrix least-squares calculations on F 2 .All hydrogen atoms were located in difference Fourier maps and included as fixed contributions riding on attached atoms with isotropic thermal displacement parameter 1.2 (C-H, B-H) or 1.5 (-CH3) times those of the respective atom.A summary of crystal data is reported in Table S1.The crystal structure of the monoanionic meta-ferrabis(dicarbollide) complex was recently reported by Bennour et al. 5 A structural comparison with the new monoanionic orthoferrabis(dicarbollide) reported in this paper was carried out in order to evaluate the effect of the position of the carbon atoms.Both monoanionic ferrabis(dicarbollide) isomers crystallize in the monoclinic crystal system, but unlike the meta isomer, the ortho-ferrabis(dicarbollide) complex belong to a lower symmetry space group (Cc) and exhibits an ordered tetramethylammonium cation and two dicarbollide units sandwiched around an iron ion adopting a cisoid conformation with the C2B3 faces of the two ligands which are nearly parallel (Fig. S1).The distance between the iron atom and the two pentagonal planes is the same in the meta isomer (1.519 Å) meanwhile in the ortho isomer that distance is slightly different (1.525 and 1.527 Å) but higher than in the case of meta isomer, showing an increased volume of this space as observed from the Fe─C and Fe─B bond distances (Table S2).In the crystal of the meta-isomer, each monoanionic ferrabis(dicarbollide) is connected with four additional adjacent anions through dihydrogen bonds involving (C7─H7•••H3─B3, 2.317 Å and C1─H1•••H8─B8, 2.233 Å) generating a 2D layer structure running parallel to the bc plane (Fig. S2).Tetramethylammonium cations connect these structures to finally build up the supramolecular 3D architecture (Fig. S3).zig-zag chain (Fig. S4).Additional dihydrogen interactions involving tetramethylammonium cations connect these structures to build up the supramolecular 3D architecture (Fig. S5).The ac susceptibility data were analyzed within the extended Debye model using the CC-fit code 6a in which a maximum in the out-of-phase component χM″ of the complex susceptibility is observed when the relaxation time τ equals (2πν) −1 .6b-c The Cole-Cole expression is introduced to describe distorted Argand plots,

Comparison between [
where ω = 2πν, χT and χS are the isothermal and adiabatic susceptibilities i.e., the susceptibilities observed in the two limiting cases ν → 0 and ∞, respectively.The a parameter (between 0 and 1) describes the distribution of relaxation times, wider distribution larger a.If a is equal to 0 only one single t value.The frequency dependence 6d of χM' and χM″ can be split into:   results of energies and g components in the main text are those corresponding to the (5,5) active space to have all the information (AILFT only can be obtained with such active space) despite that lowest energy at CASSCF level was calculated with the (5,10) active space.Differentiation of the QDPT Hamiltonian with respect to the magnetic field allowed the calculation of magnetization and magnetic susceptibility curves.
Table S4.Calculated NEVPT2 state energies (in cm -1 ) including spin-orbit effects using the three active spaces using the experimental X-ray structure.

Figure S2 .
Figure S2.View of the 2D layer structure in the crystal of

Figure S4 .
Figure S4.Zig-zag chain view though a axis in

Figure S6 .
Figure S6.Static susceptibility and magnetization measured

Figure S7 .
Figure S7.Real and Imaginary susceptibility measured at different

Figure S9 .
Figure S9.Static susceptibility and magnetization measured

Figure S6 .
Figure S6.Static susceptibility and magnetization (at 2 K) measured for a powder sample of

Figure S7 .
Figure S7.Real and Imaginary susceptibility measured at different frequencies (above) dependence with temperature with an external field of 0.05 T and (below) dependence with the external field for a saturated THF solution of the [NMe4][3,3'-Fe(1,2-C2B9H11)2] at 4 K.The last representation is for comparison the dependence of the powder sample.

Figure S9 .
Figure S9.Static susceptibility and magnetization (at 2 K) measured for a powder sample of

Table S6 .
Calculated g components using NEVPT2 method including spin-orbit effects using the three active spaces using the experimental X-ray structure.

Table S7 .
Calculated NEVPT2 g components and excited states (D doublet or Q quartet states, in cm -1 ) for the three DFT optimized isomers using B3LYP calculations and CPCM model to simulate the THF solvent.