Single Molecule Magnetism with Strong Magnetic Anisotropy and Enhanced Dy∙∙∙Dy Coupling in Three Isomers of Dy‐Oxide Clusterfullerene Dy2O@C82

Abstract A new class of single‐molecule magnets (SMMs) based on Dy‐oxide clusterfullerenes is synthesized. Three isomers of Dy2O@C82 with C s(6), C 3v(8), and C 2v(9) cage symmetries are characterized by single‐crystal X‐ray diffraction, which shows that the endohedral Dy−(µ2‐O)−Dy cluster has bent shape with very short Dy−O bonds. Dy2O@C82 isomers show SMM behavior with broad magnetic hysteresis, but the temperature and magnetization relaxation depend strongly on the fullerene cage. The short Dy−O distances and the large negative charge of the oxide ion in Dy2O@C82 result in the very strong magnetic anisotropy of Dy ions. Their magnetic moments are aligned along the Dy−O bonds and are antiferromagnetically (AFM) coupled. At low temperatures, relaxation of magnetization in Dy2O@C82 proceeds via the ferromagnetically (FM)‐coupled excited state, giving Arrhenius behavior with the effective barriers equal to the AFM‐FM energy difference. The AFM‐FM energy differences of 5.4–12.9 cm−1 in Dy2O@C82 are considerably larger than in SMMs with {Dy2O2} bridges, and the Dy∙∙∙Dy exchange coupling in Dy2O@C82 is the strongest among all dinuclear Dy SMMs with diamagnetic bridges. Dy‐oxide clusterfullerenes provide a playground for the further tuning of molecular magnetism via variation of the size and shape of the fullerene cage.


Synthesis and separation
. MALDI-TOF of (a) crude extract, (b) filtered solution, and (c) precipitates on the filter for Dy-metallofullerenes.

X-ray analysis
Crystals were grown by layering the benzene solution of nickel octaethylporphyrin (Ni(OEP)) onto the CS2 solution of the Dy2O@C82 isomers. The as-prepared crystals suitable for X-ray diffraction analysis were measured with a diffractometer. Specifically, Dy2O@Cs(6)-C82•Ni(OEP)•2(C6H6) was measured at 100 K using the wavelength of 0.82653 Å with an CCD detector at beamline BL17U1 of the Shanghai Synchrotron Radiation Facility (SSRF). The structure was found to be a twin. Specifically, on the basis of indexing using the program CELL_NOW, the crystal was determined to be a two-component, nonmerohedral twin with the domains related by a rotation of 179.9 degrees about the direct and reciprocal [1 0 0] axis. Dy2O@C3v(8)-C82•Ni(OEP)•1.5(C6H6)•CS2 and Dy2O@C2v(9)-C82•Ni(OEP)•C6H6 were measured with Bruker APEX II at room temperature and 173 K, respectively. The structures were solved by direct methods and refined using all data (based on F 2 ) by SHELX 2016. 1 Hydrogen atoms were located in a difference map, added geometrically, and refined with a riding model. There is a fourth benzene site at the C19S and C20S with severe disorder present in the Dy2O@Cs(6)-C82•Ni(OEP)•2(C6H6) lattice. Similarly, a second benzene site at the C7S and C8S with severe disorder is present in the Dy2O@C2v(9)-C82•Ni(OEP)•C6H6 lattice. The structure of Dy2O@C3v(8)-C82•Ni(OEP)•1.5(C6H6)•CS2 is a pseudo-merohedral twin with twin law (0 -1 0 1 0 0 0 0 -1) and refined with twin parameter of 0.49271. The crystal data are presented in Table S1. The data can be obtained free of charge from the Cambridge Crystallographic Data Centre with CCDC Nos. 1908347-9. Figure S5 compares the mutual relationship between sites A and B of Dy2O@Cs(6)-C82•Ni(OEP). The fullerene cage of site A is fully ordered, while the fullerene cage of site B is slightly disordered, even though we modeled it with the fully ordered structure. Most of the metal sites locate at similar positions in the fullerene cage except for the strong differences of the site occupancies (Fig. S6).

DFT calculations of cluster conformers
The conformer search algorithm included 3 major steps. In the first one, all possible orientations of M2O cluster inside the C82 cages are generated by the rotation over the Fibonacci nodes (shown at Figure S48, S50, S52; also see main text for details). At the second step, each conformer was optimized at PBE/TZ2P level using M=Y substitution (Priroda code, version 6), which led to a limited number of unique conformers, that further were optimized at the PBE/PAW level of theory using M=Dy substitution (VASP code). The relative energies for the conformers are summarized in Table S4-S6 for cages symmetries Cs, C3v, and C2v, respectively.
As it was argued in the main text, the Y substitution is a very accurate approximation, but in some cases, the potential energy has a very complicated and shallow topology and so the minima location may become sensitive to the optimization procedure. Thus, pre-optimization with M=Y inadvertently might have overlooked some small barrier local minimum accessible for M=Dy. To ensure the comprehensive consideration and most accurate geometric fit between theory and experiment, we optimized set of the Dy2O@C82 conformers for all cage symmetries with starting geometries constructed based on X-ray observed. The main sites for Cs and C3v symmetries were already well-predicted by the search algorithm, thus no new structures were detected this way. However, in the C2v cage, one new conformer (5) was detected. This conformer is less stable by 14.2 kJ/mol then the most stable one in the set. However structurally, this conformer is closely connected to one of the algorithm predicted conformer (Table S6). All this indicates the high complexity of the potential energy surface. Figure S48. Left: the original C82-Cs system. Center: superposed all 120 initial configurations of the Y2O cluster regenerated with Fibonacci algorithm (F). Right: relative energies of Y2O@C82 conformers after DFT optimization at P6/PBE/TZ2P level.

Correspondence between DFT-optimized conformes and X-ray structure of Dy2O@Cs(6)-C82
For the site A of Dy2O@Cs(6)-C82 X-ray diffraction gives three sites for the Dy2O cluster. These sites were used as starting coordinates for DFT optimization. The site Dy1A-O-Dy2A with the occupancy of 0.76 corresponds to the lowest energy conformer 1 found by DFT (Fig. S49). Optimization of the site Dy3A-O-Dy4A also converged to the conformer 1. At the same time, optimization stated from the site Dy5A-O-Dy6A resulted in the conformer 3 (relative energy of 24 kJ/mol). Figure S54. Comparison of the optimized Dy2O positions (intense-colored atoms) with the starting coordinates obtained from X-ray structure (pale atoms). Dy sites and occupancies in the X-ray structures are shown on the right.
For a reliable comparison of diffraction data and the structures of the DFT-optimized conformers, additional calculations were performed, in which coordinates of Dy sites from X-ray structures were used as starting coordinates for optimization. Dy sites in the crystal are divided into two groups, (Dy1, Dy3, Dy5) and (Dy2, Dy4, Dy6, Dy7, Dy8). All pairwise combinations gives 15 different structures used for DFT optimization. DFT optimization did not add new conformes, all optimized structures are among the conformers described in the Table S5. Interestingly, although the site Dy1 has the highest occupancy in the X-ray structures, there are no Dy atoms in the DFT-optimized conformers close to that site. We suggest that the group Dy3-Dy1-Dy5 describes the moving trajectory, rather than the static positions of metal atoms. The same holds for the second group of Dy sites.  Figure S56. Comparison of the optimized Dy2O positions (intense-colored atoms) with the starting coordinates obtained from X-ray structure (pale atoms). Dy sites and occupancies in the X-ray structures are shown on the right.

IR spectra
IR spectra of Dy2O@C82 samples drop-casted on KBr substrates were measured at room temperature with Vertex 80 FTIR spectrometer (Bruker) equipped with Hyperion microscope. The spectra of the three isomers of Dy2O@C82 are found to be strongly sensitive to the isomeric structure of the fullerene cage (Fig. S57). A proper description of the cluster dynamics is also important for the modelling of IR spectra. DFT calculations for different low energy conformers predict a noticeable variation in the spectra depending on the position of the metal-oxide cluster, and hence their possible coexistence should be taken into account. From the BOMD simulations, IR spectra can be obtained by Fourier transformation of the time evolution of the dipole moment. The contribution of different conformers is then included implicitly. Figure S57 shows that a good agreement is obtained between experimental and calculated spectra. Importantly, the simulations predict a considerable variation of the spectral pattern with the isomeric structure of the fullerene cage structure, which agrees well with experimental observations.
Of particular interest is the identification of the vibrations of the Dy2O cluster. In the mid-IR range, DFT calculations reveal only one cluster vibration, the Dy−O antisymmetric stretching mode, which has a relatively high intensity. In the experimental spectra these vibrations can be assigned to medium-intensity absorption bands at 680-700 cm −1 (marked by arrows in Fig. S57). For comparison, analogous vibration in Dy2ScN@C80 98 is found at 740 cm −1 , and the Dy−C antisymmetric stretching mode in Dy2TiC@C80 18 occurs at 660 cm −1 . Figure S57. Experimental infrared spectra of Dy2O@C82 isomers (dark blue lines) compared to the spectra computed from the molecular dynamics simulations (red lines). Black arrows denote antisymmetric Dy-O stretching mode; vibrational displacements of the oxygen atoms in this mode are visualized as blue arrows in the inset: the oxygen atom is moving along the line parallel to the Dy•••Dy axis so that one Dy-O bond is always shortened whereas another one is elongated at the same time.