Weak Exchange Interactions in Multispin Systems: EPR Studies of Metalloporphyrins Decorated with {Cr7Ni} Rings

Both metalloporphyrins and heterometallic {Cr7Ni} rings are of significant research interest due to their proposed roles in quantum information processing devices. In this study, we present a series of complexes in which [Cr7NiF3(Etglu)(O2CtBu)15] (N-EtgluH5 = N-ethyl-d-glucamine) heterometallic rings are coordinated to metalloporphyrin linkers: the symmetric [M(TPyP)] for M = Cu2+, VO2+, and H2TPyP = 5,10,15,20-tetra(4-pyridyl)porphyrin; and the asymmetric [{VO}(TrPPyP)] for H2(TrPPyP) = 5,10,15-(triphenyl)-20-(4-pyridyl)porphyrin. The magnetic interactions present in these complexes are unraveled using the continuous wave (CW) electron paramagnetic resonance (EPR) technique. The nature of the coupling between the {Cr7Ni} rings and the central metalloporphyrin is assessed by numerical simulations of CW EPR spectra and determined to be on the order of 0.01 cm–1, larger than the dipolar ones and suitable for individual spin addressability in multiqubit architectures.


S.1 Synthetic procedures
All chemicals were of reagent grade and used without further purification.Ligands H2TPyP and H2TrPPyP were purchased from Sigma-Aldrich and Porphychem Sas, respectively.VO 2+ and Cu 2+ complexes -[VO(TrPPyP)], [VO(TPyP)], and [Cu(TPyP)] -were synthesized by modification of the reported procedures. 1,2,3The syntheses of 1VO and 4M (M = VO, Cu) were performed by adopting the general procedure reported before. 4All operations involving inert atmospheres were conducted under N2 using standard Schlenk techniques.Reactions were followed by TLC.

General synthesis procedure for [M(TPyP)(Cr7NiF3(Etglu)(O2C t Bu)15)4] (4M)
The syntheses of these compounds followed the general strategy reported in ref. 2 [M(TPyP)] and [Cr7NiF3(Piv)15(Etglu)(H2O)] were added to CH2Cl2 and stirred for 72 h at room temperature.The solvent was then removed under reduced pressure, and the crude product was dispersed in acetone and left to stir overnight.The mixture was filtered, and the obtained powder was washed several times with acetone.The crude product was extracted with pentane and filtered again.Acetone was added to the solution in 1:1 ratio.A crystalline powder precipitated from the solution upon slow evaporation of solvents.

S.2 Structural characterization
Data collection X-ray diffraction data for compounds 4VO and 4Cu were collected using a dual-wavelength Rigaku FR-X rotating anode diffractometer using CuKα (λ = 1.54146Å) radiation, equipped with an AFC-11 4-circle goniometer, VariMAX TM microfocus optics, a Hypix-6000HE detector and an Oxford Cryosystems 800 plus nitrogen flow gas system, at a temperature of 150K and 100K, respectively.Data were collected and reduced using CrysAlisPro v42. 5 Absorption correction was performed using empirical methods (SCALE3 ABSPACK) based upon symmetry-equivalent reflections combined with measurements at different azimuthal angles.

Crystal structure determination and refinements.
7][8] Coordinates for all nonhydrogen atoms were freely refined, and atomic displacement parameters were refined anisotropically.Hydrogen atom coordinates and isotropic atomic displacement parameters were constrained to ride on the coordinates and atomic displacement parameters of the parent atom.Global similar neighbor atomic displacement parameter and enhanced rigid bond restraints were applied globally, and strong similar neighbor atomic displacement parameter restraints were applied to all carbon atoms.These were applied to improve and refine realistic atomic displacement parameters, given the low resolution and limited number of data points for the dataset and the statistical disorder of the methyl groups of the pivalate moieties, which could not be modeled due to the limited number of data points and a requirement to not over-parameterize the model.Similar pivalate moieties were refined to have similar 1,2-and 1,3-bond distances, and where necessary when modeling solvent molecules, fixed distance restraints were applied.
Please note: For 4VO, the oxygen of the vanadyl has been modeled over two positions but 100% oxygen; this is because 50% of the time, this is a water hydrogen bonding to the opposite face of the porphyrin to the slightly out-of-plane vanadyl.This is the only explanation that could be rationalized for the electron density present at that position.Table S1.Experimental and refinement parameters extracted from the resolution of crystallographic structures of compounds 4VO and 4Cu.

S.3 CW-EPR spectroscopy
. Plot of all experimental Q-band CW-EPR spectra collected on 1VO 0.5 mM solution in 1:1 CH2Cl2/toluene at different temperatures and their simulations obtained using parameters in Table S2.Table S3.Best-simulation SH parameters for 4VO. a 10 -4 cm -1 .b g-strain (FWHM) components.  .CH2Cl2/toluene at 5 K. On top, simulation was performed by considering FM exchange coupling interaction between Cu and {Cr7Ni} centers.The same strain values reported in Table S4 were used either when exchange coupling interaction is considered or in those with J set to zero.

Figure S1 .
Figure S1.Molecular structure of a) 4VO and b) 4Cu.Solvent molecules and hydrogen atoms have been omitted for clarity.Color scheme: V = pink, Cu = orange, Cr = purple, Ni = green, O = red, N = blue, C = grey; a = red, b = green, c = blue.

Figure S2 .
Figure S2.Crystallographic structure of 4VO.From the left to the right, view of the unit cell along the a, b, and c crystallographic axes.Color scheme: V = pink, Cr = purple, Ni = green, O = red, N = blue, C = grey; a = red, b = green, c = blue.H atoms have been omitted for clarity.

Figure S3 .
Figure S3.Crystallographic structure of 4Cu.From the left to the right, view of the unit cell along the a, b, and c crystallographic axes.Color scheme: Cu = orange, Cr = purple, Ni = green, O = red, N = blue, C = grey; a = red, b = green, c = blue.H atoms have been omitted for clarity.

Figure S4 .
Figure S4.On the left, hypothetic simplified molecular structure of 1VO.Color scheme: V = pink, Cr = purple, Ni = green, O = red, N = blue, C = grey.On the right, table reporting D components computed for VO-Ni placed at a mean distance d, and Jiso from best simulations.

Figure S6 .Figure S7 .
Figure S6.On the left, plot of g-strain components (gx = gy = g┴; gz = g||) variation as a function of T for VO spin in 1VO.On the right, plot of g-strain components variation as a function of T for the {Cr7Ni} ring in 1VO.

TFigure S8 .
Figure S8.Plot of experimental and simulated Q-band EPR spectra of 4Cu 0.5mM solutions in 1:1 CH2Cl2/toluene at 5 K. Simulations were performed for two different sets of g-strain components by varying J (FM).

Figure S9 .
Figure S9.Plot of experimental and simulated Q-band EPR spectra of 4Cu 0.5mM solutions in 1:1 CH2Cl2/toluene at 5 K. Simulations were performed for two different sets of g-strain components by varying J (AF).

Figure S10 .
Figure S10.Comparison between simulated spectra obtained by considering FM and AF exchange coupling interaction in 4Cu.In this case, g-strain components were considered as [0.03 0.03 0.03].Experimental Q-band EPR spectrum of 4Cu 0.5mM solutions in 1:1 CH2Cl2/toluene at 5 K is reported in the same plots.

Figure S11 .
Figure S11.Plot of simulated and experimental spectra for 4Cu 0.5mM solutions in 1:1

Table S4 .
SH parameters for 4Cu (Figures S11).The same values of g and A components were used for all the other simulations reported in FiguresS8 -S10.a 10 -4 cm -1 .b g-strain (FWHM) components.