Experimental details. Sample preparation. Ln14MC5 complexes were prepared as described in 1. Magnetic Compton Scattering measurements

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1 Supporting information for Understanding Spin Structure in Metallacrown Single Molecule Magnets Aniruddha Deb, Thaddeus T. Boron, III, M Masayoshi Itou, Yoshiharu Sakurai, Talal Mallah, Vincent L. Pecoraro, James E. Penner Hahn Figure S1. Schematic illustration of the connectivity in the Dy Mn 4 MC, where the MC core alone is shown on the top; and the top and side views of the full molecule (showing the acetate bridges) shown in wire frame on the bottom. The Gd Mn 4 MC is isostructural to Dy Mn 4. 1 The Ln labeled Ln out in the text is Ln1; Ln is Ln in Experimental details Sample preparation Ln14MC5 complexes were prepared as described in 1. Magnetic Compton Scattering measurements S1

2 MCP experiments were performed at the BL08W high energy inelastic scattering beamline of SPring 8. Circularly polarized x rays were monochromatized to 175 kev and the momentum dependence of the x ray scattering was measured using a ten element Ge solid state detector placed at a scattering angle of The beam size was mm horizontal by 1.5 mm vertical. The abscissa of the data has been transformed from energy to momentum in atomic units (a.u.), where an atomic unit of momentum (1.999 x 10 4 kg m s 1 ) is the momentum of an electron in the first Bohr orbit of hydrogen. The energy scale was calibrated by measuring x ray fluorescence lines from the samples. Measurements were performed at temperatures between 4 K and 1 K. During the measurements, an alternating externally applied magnetic field (±.5 T) was used to magnetize the sample. To ensure reasonable averaging of the magnetic signal, a switching time of 6 s was used, and an acquisition time of 60 s as used throughout the measurements. Since the MCP is a difference between the Compton profile with spin up and spindown, systematic errors from background scattering and multiple scattering are cancelled. The signals from all ten elements of the detector were individually checked for any anomalies, and the signals from all good elements were summed for each scans and all scans were then averaged. The MCP s were corrected for sample absorption and scattering cross section, and normalized to the MCP for Fe using Eq. (4). 3 Finally, since the MCP is symmetric about p z =0, scattering from the low energy and the highenergy side of zero momentum (i.e., the Compton peak) were averaged; the data shown in Figures 1,, and S thus only have positive values of p z. Data Analysis The MCP data were fitted with linear combinations of the Compton profiles f, d and p orbitals. For the 4f and the p orbitals, these were taken from tabulated free atom Compton profiles. 4 For Mn 3d, where we expect different scattering profiles from e g and t g electrons, ab initio restricted Hartree Fock MO calculation for a (MnO 6 ) 8 cluster were used to determine the scattering profiles for t g, e x y, and e 3z r spins. 5 The calculations were performed using the GAMESS program, 6 which take the hybridization between 3d Mn and p O orbitals into account. The triple zeta Gaussian basis by Schäfer et al. 7 [Mn (14s, 9p, 5d)/(8s, 5p, 3d), O(10s, 6p)/(6s, 3p)] was employed. The theoretical orientation dependent MCPs in reference 5 were converted to isotropic MCPs by spherical averaging. For each fit, a reduced χ was calculated as 1 1. where N is the number of experimental data points in the MCP spectra from 0 to 10 a.u., n is the number of fitted components, J mag Exp(p z ) and J mag Fit(p z ) are the experimental and fitted MCP and σ is the experimentally estimated uncertainty in each data point, determined from the standard deviation of the measured profiles. was used to compare different fits (see Table S1) S

3 Figure S. Individual orbital wise contributions of Dy 4f, and Mn 3d (t g and e g ) for Dy Mn 4 at 7K and 10K. S3

4 Table S1. MCP fitting details for alternative fits Y Mn 4 Gd Mn 4 Dy Mn 4 Fit Temp μ spin Dy 4f Gd 4f Mn 3d t g Mn 3d 3z r O p d only d+p d only d+p +d +d +d +d +d 4K K K 8K 1K 7K 10K All magnetic moment values are given in Bohr magnetons (µ B ) per formula unit Data Analysis: Fit of the magnetic data of Y Mn 4 The M T = f(t) and M= f(h) data were simultaneously fitted considering two exchange coupling parameters (Figures S3 and S4) as depicted in the scheme below: Y (1)Mn J' Y Mn(4) J' ()Mn J Mn(3) The best fit (least square R = 5x10 4 ) leads to the following parameters: J = cm 1, J = 4. cm 1 and g =.07, based on the following spin Hamiltonian H = J S S 3 J S 1 S J S 3 S 4. A large antiferromagnetic coupling was found between Mn() and Mn(3), while a weak antiferromagnetic one S4

5 was found between on one hand Mn(1) and Mn() and on the other hand Mn(3) and Mn(4), leading to a S = 0 spin ground state. The energy of the first 5 low lying excited spin states were found to be E(S = 1) = 1.3 cm 1, E (S = ) = 4 cm 1, E(S = 3) = 8 cm 1, E(S = 4) = 13.7 cm 1 and E (S = 5) = 35.5 cm 1. Figure S3. Experimental temperature dependent χ M T compared to the fit considering two exchange coupling as discussed above. 6 5 Mexp M fit M (Bohr Magneton) J' = - 4. cm -1 J = cm -1 g =.07 R = 3.4x µ H (T) 0 Figure S4. Experimental temperature dependent M=f(H) compared to the fit considering two exchange coupling as discussed above. S5

6 14 1 M(BM) T = 4 K and g = H(T) Figure S5. Magnetization of two Gd(III) ions with different values of the coupling parameters J (from +0.5 to 0.5). B.M represents Bohr magneton (µ B ) and H(T) represents the magnetic field in Tesla. The black vertical line shows the magnetic field that was used in the Magnetic Compton scattering experiments. S6

7 References (1) Boron, T. T.; Kampf, J. W.; Pecoraro, V. L. Inorg. Chem. 010, 49, () McCarthy, J. E.; Cooper, M. J.; Honkimaki, V.; Tschentscher, T.; Suortti, P.; Gardelis, S.; Hamalainen, K.; Manninen, S. O.; Timms, D. N. Nuclear Instruments & Methods in Physics Research Section a Accelerators Spectrometers Detectors and Associated Equipment 1997, 401, 463. (3) Sakai, N. Journal of the Physical Society of Japan 1987, 56, 477. (4) Biggs, F.; Mendelsohn, L. B.; Mann, J. B. At. Data Nucl. Data Tables 1975, 16, 01. (5) Rumble, C.; Itou, M.; Hiraoka, N.; Sakurai, Y.; Tomioka, Y.; Tokura, Y.; Penner Hahn, J. E.; Deb, A. Phys Rev B 01, 85. (6) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. Journal of Computational Chemistry 1993, 14, (7) Schafer, A.; Huber, C.; Ahlrichs, R. Journal of Chemical Physics 1994, 100, 589. S7