Magnetic anisotropy of endohedral lanthanide ions: paramagnetic NMR study of MSc2N@C80- Ih with M running through the whole 4f row

Abstract

Paramagnetic and variable temperature ¹³C and ⁴⁵Sc nuclear magnetic resonance studies are performed for nitride clusterfullerenes MSc₂N@C₈₀ with icosahedral I_h(7) carbon cage, where M runs through all lanthanides forming nitride clusters. The influence of the endohedral lanthanide ions on the NMR spectral pattern is carefully followed, and dramatic differences are found in peak positions and line widths. Thus, ¹³C lines broaden from 0.01-0.02 ppm in diamagnetic MSc₂N@C₈₀ molecules (M = La, Y, Lu) to several ppm in TbSc₂N@C₈₀ and DySc₂N@C₈₀. Direction of the paramagnetic shift depends on the shape of the 4f electron density in corresponding lanthanide ions. In TmSc₂N@C₈₀ and ErSc₂N@C₈₀ with prolate 4f-density of lanthanide ions, ¹³C signals are shifted down-field, whereas ⁴⁵Sc peaks are shifted up-field versus diamagnetic values. In all other MSc₂N@C₈₀ molecules lanthanide ions have oblate-shaped 4f electron density, and the lanthanide-induced shift is negative for ¹³C and positive for ⁴⁵Sc peaks. Analysis of the pseudocontact and contact contributions to chemical shifts revealed that the pseudocontact term dominates both in ¹³C and ⁴⁵Sc NMR spectra, although contact shifts for ¹³C signals are also considerable. Point charge computations of the ligand field splitting are performed to explain experimental results, and showed reasonable agreement with experimental pseudocontact shifts. Nitrogen atom bearing large negative charge and located close to the lanthanide ion results in large magnetic anisotropy of lanthanide ions in nitride clusterfullerenes with quasi-uniaxial ligand field.

Fig. 1. DFT-optimized molecular structure of representative MSc₂N@C₈₀-I _h (1Pr). Praseodymium ion (shown green) is at the distance of 2.225 Å from the central nitrogen atom (blue), whereas two Sc–N distances are 1.939 and 1.936 Å. Carbon atoms are shown in grey (pentagon–hexagon–hexagon junctions, PHHJs) and orange (triple hexagon junctions, THJs). In (b), the plane of the cluster is normal to the paper. Thin cyan lines denote shortest Pr–C distances: 2.508 Å (C1), 2.553 Å (C2), 2.591 Å (C3), and 2.658 Å (C4).

Fig. 2. ¹³C NMR spectra of 1M compounds measured in CS₂ at 288 K. Note the different scale in the left and right panels; for a better comparison, the spectrum of 1Y is shown in both panels.

Fig. 3. ⁴⁵Sc NMR spectra of 1M compounds measured in CS₂ at 288 K. The δ(⁴⁵Sc) value of diamagnetic 1Y is 191 ppm.

Fig. 4. Variable-temperature ¹³C NMR spectra of selected 1M compounds measured in CS₂ in the 268–308 K range. Vertical dash lines denote chemical shifts at 288 K and are shown to guide an eye. At 288 and 308 K two carbon signals in 1Er are not resolved, and therefore the measurements were performed in o-DCB in a broader temperature range (268–328 K). Low solubility of 1Dy and 1Tb at 268 K resulted in poor signal-to-noise ratio (the noise features in the spectrum of 1Dy are marked by asterisks).

Fig. 5. Variable-temperature ⁴⁵Sc NMR spectra of selected 1M compounds measured in CS₂ in the 268–308 K range. To guide an eye, vertical lines in the spectra or 1Nd and 1Tm indicate signal positions at 288 K.

Fig. 6. Correlations between δparaij/S _{z j} and C _j/S _{z j} for ¹³C-PHHJ (left) and ⁴⁵Sc (right) signals used to distinguish contact and pseudocontact contributions in 1M molecules by Reilley's approach. 1Tm values are shown as red dots; they were not included in the linear fit. The quality of linear fit is R ² = 0.97 for ¹³C-PHHJ and R ² = 0.90 for ⁴⁵Sc.

Fig. 7. Three-nuclei 3D plot in δparaij/S _{z j} coordinates for ⁴⁵Sc, ¹³C-THJ and ¹³C-PHHJ chemical shifts in 1M series (T = 288 K). Red spheres are 3D data; blue, green, and black circles are projections on coordinate planes. Red grid shows a fitted plane (1Pr was not included in the fit).

Fig. 8. Spin-density distribution in GdSc₂N@C₈₀ (two orientations of the molecule are shown). To visualize small spin polarization effects, the isosurfaces are plotted at relatively small spin density values of ±0.0006 a.u. (green (+) and red (–)).

Fig. 9. (a) Correlation between DFT-computed M–N and Sc–N bond lengths in 1M molecules and ionic radii of lanthanides; (b) correlation between the metal–nitrogen stretching mode frequencies and ionic radii of lanthanides (green – M–N bonds, purple – Sc–N bonds); (c) FTIR spectra of selected 1M molecules: 1La, 1Pr, 1Tb, and 1Tm; arrows mark the ν _Sc–N modes.

Fig. 10. Ligand-field splitting of the m _J levels in the 1M compounds computed using point-charge model. The inset shows low-energy levels in 1Er and 1Tm in the range of 0–190 cm^–1. Each degenerate ±m _J level of Kramers ions (Ce, Nd, Dy, Er) and quasi-degenerate (within 3 cm^–1) levels of non-Kramers ions are shown as double lines. To guide an eye, Kramers and non-Kramers ions are denoted in dark blue and wine, respectively.

Fig. 11. (a and b) isosurfaces of 4f electron density in 1Dy (a, green) and 1Er (b, red) computed at 2 and 288 K. Only the nitride cluster and four carbon atoms nearest to the lanthanide ion are shown. Whereas the shape of the lobe remains almost the same in 1Dy, in 1Er the increase of the temperature from 2 to 288 K changes the shape of the 4f density distribution to a more spherical one. (c and d) Pseudocontact shift isosurfaces in 1Dy (c) and 1Er (d) at 288 K computed using the point-charge model (cyan – positive, yellow – negative). Solid/transparent surfaces correspond, respectively, to ±6000/±1500 ppm isovalues in 1Dy and ±2000/±500 ppm isovalues in 1Er.

Fig. 12. Correlation between computed and experimental chemical pseudocontact shifts: ¹³C-PHHJ (left) and ⁴⁵Sc (right). Experimental δ ^pc(¹³C) shifts are obtained by Reilley's approach, whereas ⁴⁵Sc values are estimated using 2-nucleus method, see text for further details. Solid lines is a linear fit for a complete set of data (R ² = 0.94 for both PHHJ and Sc), whereas red dashed lines were obtained for fitting without 1Tm and 1Tb values. The intercept was set to zero in linear fits.