Covalency versus magnetic axiality in Nd molecular magnets: Nd-photoluminescence, strong ligand-field, and unprecedented nephelauxetic effect in fullerenes NdM2N@C80 (M = Sc, Lu, Y)

Nd-based nitride clusterfullerenes NdM2N@C80 with rare-earth metals of different sizes (M = Sc, Y, Lu) were synthesized to elucidate the influence of the cluster composition, shape and internal strain on the structural and magnetic properties. Single crystal X-ray diffraction revealed a very short Nd–N bond length in NdSc2N@C80. For Lu and Y analogs, the further shortening of the Nd–N bond and pyramidalization of the NdM2N cluster are predicted by DFT calculations as a result of the increased cluster size and a strain caused by the limited size of the fullerene cage. The short distance between Nd and nitride ions leads to a very large ligand-field splitting of Nd3+ of 1100–1200 cm−1, while the variation of the NdM2N cluster composition and concomitant internal strain results in the noticeable modulation of the splitting, which could be directly assessed from the well-resolved fine structure in the Nd-based photoluminescence spectra of NdM2N@C80 clusterfullerenes. Photoluminescence measurements also revealed an unprecedentedly strong nephelauxetic effect, pointing to a high degree of covalency. The latter appears detrimental to the magnetic axiality despite the strong ligand field. As a result, the ground magnetic state has considerable transversal components of the pseudospin g-tensor, and the slow magnetic relaxation of NdSc2N@C80 could be observed by AC magnetometry only in the presence of a magnetic field. A combination of the well-resolved magneto-optical states and slow relaxation of magnetization suggests that Nd clusterfullerenes can be useful building blocks for magneto-photonic quantum technologies.

spectra did not show any changes during repeated measurements, indicating high photo-stability of the fullerene samples.
The PL decay measurements were performed with TCSPC technique based on ID900 Time Controller (ID Quantique).The 488 nm Omicron PhoxX diode laser was digitally modulated with the pulse width of 1 ns, and the ID230 NIR single-photon counter (ID Quantique) was used for broad-band time-resolved detection in the NIR range.HPLC chromatogram (Buckyprep column, 1 mL/min) of the highlighted fraction collected in the first step, only small traces of Y3N@C86 could be removed with this column, while the main fraction is a mixture of NdY2N@C80 and Y3N@C80.(c) Recycling HPLC chromatogram with Buckyprep-D column (1 mL/min), the inset shows 8th cycle, the part of peak with pure NdY2N@C80 is highlighted in blue.(d) Positive-ion LDI mass spectrum of isolated NdY2N@C80; the insets show theoretical and experimental isotope distributions.

UV-Vis absorption spectra
Figure S4.UV-Vis absorption spectra (room temperature, toluene solution) of isolated NdM2N@C80 (M = Sc, Lu, Y) compared to the spectra of LaSc2N@Ih-C80 and Y3N@Ih-C80.The inset shows magnification of the low-energy part of the spectra.
When M3N@Ih-C80 contains no Sc, the low-energy part of the absorption spectrum has several well-defined absorption features, with the lowest one near 700 nm.Y3N@Ih-C80 can serve as a typical example, and the spectra of NdLu2N@C80 and NdY2N@C80 are very similar to that.The energy is only slightly affected by the size of the endohedral cluster (observe ≈5 nm shift between NdY2N@C80 and Y3N@C80).When Sc is present in the cluster, the bands usually become broader, and the lowest-energy absorption shows a red shift to 740 nm.Here LaSc2N@C80 is a typical example, to which the spectrum of NdSc2N@C80 appears very similar.None of NdM2N@C80 fullerenes shows additional absorption features which might be ascribed to f-f transitions of Nd 3+ .
Vibrational spectra of NdSc2N@C80 Figure S5.FTIR (dark blue trace) and Raman (red and green traces) spectra of NdSc2N@C80 drop-casted on KBr substrate.Raman spectra were excited at 532 and 660 nm and measured at 78 K. Brown trace is the Raman spectrum of NdSc2N@C80 drop-casted on gold SERS substrate and measured at room temperature with the excitation at 785 nm.

Single-crystal X-ray diffraction
Molecular structure of NdSc2N@Ih-C80 was established by single-crystal X-ray diffraction using a co-crystal with nickel(II) octaethylporphyrin (NiOEP) grown by layering solutions of fullerene in benzene and NiOEP in benzene and allowing slow diffusion thereof for one month.Measurements were performed at 100 K with synchrotron irradiation at the BESSY storage ring (BL14.2,Berlin-Adlershof, Germany). 1 XDSAPP2.0suite was employed for data processing. 2,3 he structure was solved by direct methods and refined by SHELXL-2018.In the spectra measured between 50 K and 250 K, the bandpass filter with a threshold of 890 nm cuts the short-wavelengths part, thus the hot band at 880 nm is not seen.

Figure S17
. VT-PL spectra of polycrystalline NdY2N@C80 in the range of the 4 F3/2→ 4 I9/2 band, excitation with 488 nm laser line.The features disappearing upon cooling are assigned to hot bands and marked with h, the ligand field splitting in the 4 F3/2 excited state is estimated as 440 cm −1 .In the spectra measured between 50 K and 250 K, the bandpass filter with a threshold of 890 nm cuts the short-wavelengths part, thus the hot band at 880 nm is not seen.Assignment of the broad asymmetric peak at 955 nm (ΔE ≈ 400 cm −1 ), which becomes visible only at low temperature, is not very clear.We tentatively assign it to the transition ending at KD2 of the ground state multiplet, but it remains ambiguous because of its very large width different from features of all other pure transitions of this type.Another feature with questionable assignment is at 992 nm (labelled "h?").Its temperature evolution corresponds to that of hot bands, but the energy does not match.
Table S2.LF splitting in 4 IJ and 4 F3/2 multiplets of NdSc2N@C80, NdLu2N@C80, and NdY2N@C80, determined from low-temperature PL measurements.The free-ion energies of Nd 3+ multiplets are from Ref. 14 For the 4 I13/2 multiplet in NdLu2N@C80 and NdY2N@C80, we cannot identify KD1 peaks and thus ΔE values are not available, and the table lists absolute values of observed features.Their assignment to particular KDs is ambiguous.
Additional designations: "v br" -very broad, "vw" -very weak, "sh" -shoulder         S5b.Ligand-field splitting and pseudospin g-tensors of Kramers doublets of Nd 3+ -4 I9/2 multiplet computed at the CASSCF/RASSI level for Nd 3+ ion surrounded by point charges in positions of all other atoms in NdSc2N@C80 (conf Sc-3), the charges are the same as used for calculations in Table S5a.Experimental data are determined by various optical spectroscopic techniques in Ref 16 Our ab initio calculations for Nd(η 5 -C5Me5)3 and Nd(η 5 -C5Me4H)3 gave the ΔLF values of 532 cm −1 and 629 cm −1 , respectively (see Table S6), meaning that either CASSCF/RASSI underestimates the LF splitting by as much as 60%, or some of the experimental lines may require re-assignment.

CASSCF calculations for NdLu2N@C80 and NdY2N@C80
Based on the results of CASSCF calculations for conformers of NdSc2N@C80, we chosen two representative conformers of NdM2N@C80 (M = Lu, Y) for ab initio calculations, Lu(Y)-1 and Lu(Y)-3.These conformers are different in the way how Nd is coordinated to the fullerene: in Lu(Y)-1, coordination is to hexagon nearly of η 6 type, while Lu(Y)-3 features less central position of Nd above pentagon with η 3 hapticity (Fig. S19).
The difference of LF splitting between these conformers appeared to be less pronounced than in NdSc2N@C80 conformers, presumably because even in the case of η 6 coordination, Nd-N axis and gz axis of KD1 are in facto oriented not to the center of the hexagon but closer to one of carbon atoms.
In CASSCF calculations of NdLu2N@C80, the use of full-electron basis for Lu appeared problematic because of the poor convergence.We therefore performed calculations with DFT-optimized structures of NdLu2N@C80 and using Sc or Y instead of Lu in CASSCF calculations.For consistency, analogous calculations were also performed for NdY2N@C80.Comparison of the results shows that the replacement of Lu with Sc or Y has little effect on the wavefunction composition and only slightly affects pseudospin g-tensors, but has more pronounced influence on the LF splitting.For instance, for conformers and Y-3, the energy of KD2 appeared not sensitive to the use of Sc or Y, while the energies of higher KDs tend to be higher for Y than for Sc by 20-30 cm −1 .Considering that ionic radius of Lu is between that of Sc and Y, we used mean values when plotting calculated energies for NdLu2N@C80 in Fig. 3.
It is remarkable that in agreement with experimental spectra, the energy of KD2 in NdY2N@C80 in conformer Y-3 is ca 50 cm −1 smaller than in the analogous conformer NdLu2N@C80, while other KDs have similar energies.Calculated results for conformer Lu(Y)-1 give higher energy of KD2 for Y than for Lu.We therefore preferred to use conformer Lu(Y)-3 for comparison with experimental data in Fig. 3, as this conformer displays closer resemblance to experimental spectra.The best match between the shapes of XMCD and SQUID curves is obtained for T = 5.5 K.We thus assume that the sample temperature during XMCD measurements was T ≈ 5.5±0.5 K.

XMCD measurements and sum rule analysis
In the unpolarized X-ray absorption spectrum at the Nd-M4,5 absorption edges (3d→4f excitations), NdSc2N@C80 shows typical XAS features of Nd(III) (Fig. S20).When a magnetic field is applied, circular polarized XAS develops a dichroism proportional to the sample magnetization in the direction of the beam (which was kept parallel to the field in our measurements) (Fig. S20).The maximum of the XMCD signal at 1001.5 eV was used to follow magnetization of NdSc2N@C80 during magnetic field ramps from +6 T to -6 T and from −6 T to +6 T with the sweep rate of 2 T/min.No magnetic hysteresis was observed.The obtained magnetization curve averaged over four segments ([-6→0], [0→6], [6→0], and [0→-6] T) is shown in Figure S21.The shape of the curve indicates that the sample magnetization was not saturated at 6 T. Precise temperature estimation on the sample was done by comparison of the magnetization curve measured by XMCD to the curves measured with SQUID magnetometry with the step of 0.5 K.The best match of the curves was obtained for 5.5 K. Thus, we assume that during XMCD measurements the sample had a temperature of T ≈ 5.5±0.5 K.
Using Eq.S1a and S1b, we obtained expectation values of angular and spin momentum operators, ⟨' ( % ⟩ = 2.02 µB and ⟨+ , % ⟩ = -0.45µB, and the magnetic moment along the beam direction, $ % = 1.11 µB.The uncertainty in determined $ % is mainly caused by ambiguities in integration limits for Nd-M4 edge and is estimated to be less than ±0.1 µB.The obtained ratio ⟨+ , % ⟩/⟨' ( % ⟩ = -0.22 is close to -0.25, a theoretical expectation for the f 3 system.Coexistence of tunneling and thermal relaxation processes results in rather large values of the α parameter, which tend to decrease with the increase of the external field because of the gradual suppression of the QTM mechanism.

Figure S1 .
Figure S1.(a) HPLC chromatogram of crude CS2 fullerene extract from Nd-Sc nitride clusterfullerene synthesis, NdSc2N@C80 is found in the highlighted fraction (2×Buckyprep columns, 5 mL/min).(b) Recycling HPLC chromatogram of the highlighted fraction collected in the first step, the inset shows the 10th cycle, the peak of NdSc2N@C80 is highlighted in purple (Buckyprep column, 1 mL/min).(c) Positive-ion LDI mass spectrum of isolated NdSc2N@C80; the insets show theoretical and experimental isotope distributions

2194854 a.Figure S6 .
Figure S6.(a) Single-crystal X-ray structures of NdSc2N@C80۰NiOEP۰2C6H6, the solvent molecules are omitted for clarity.(b) View on the same unit along Nd-N bond; to highlight the relative position of the encapsulated NdSc2N to the NiOEP, the fullerene cage C80 and the solvent molecules are omitted.The displacement parameters are shown at the 30% probability.Color code: grey for carbon, blue for nitrogen, white for hydrogen, red for nickel, pink for scandium, and cyan for neodymium.

Figure S8 .
Figure S8.Six lowest-energy conformers of NdLu2N@C80 (conf Lu-1 -conf Lu-6) found in DFT survey with their relative energies and selected structural parameters (hN is the height of the pyramid formed by elevation of nitrogen above the plane of three metals).Color code: Nd -cyan, Lu -green, N -blue, Clight gray.Lu-C distances shorter than 2.5 Å for and Nd-C distances shorter than 2.6 Å are shown as bonds.

Figure S9 .Figure S10 .
Figure S9.Six lowest-energy conformers of NdY2N@C80 (conf Y-1 -conf Y-6) found in DFT survey with their relative energies and selected structural parameters (hN is the height of the pyramid formed by elevation of nitrogen above the plane of three metals).Color code: Nd -cyan, Y -green, N -blue, C -light gray.Y-C distances shorter than 2.5 Å for and Nd-C distances shorter than 2.6 Å are shown as bonds.

Figure S13 .
Figure S13.VT-PL spectra of polycrystalline NdSc2N@C80 in the range of the 4 F3/2→ 4 I9/2 band, excitation with 488 nm laser line.The features disappearing upon cooling are assigned to hot bands and marked with h, the ligand field splitting in the 4 F3/2 excited state is estimated as 385 cm −1 .

Figure S15 .
Figure S15.VT-PL spectra of polycrystalline NdLu2N@C80 in the range of the 4 F3/2→ 4 I9/2 band, excitation with 488 nm laser line.The features disappearing upon cooling are assigned to hot bands and marked with h, the ligand field splitting in the 4 F3/2 excited state is estimated as 440 cm −1 .Assignment of the peak at 960-965 nm is rather ambiguous.The temperature shift of this peak is considerably stronger than for other peaks, and we suggest that the two features occur at close energies: the hot band visible at room temperature, and the broadened KD transition, which becomes distinguishable at lower temperature, when intensity of the hot band gradually decreases.The apparent shift during cooling is the result of the hot band disappearance.

Figure S16 .
Figure S16.Photoluminescence spectra of polycrystalline NdY2N@C80 in the range of 860-1300 nm ( 4 F3/2→ 4 I9/2 and 4 F3/2→ 4 I11/2 bands) measured at different temperatures, excitation with 488 nm laser line.In the spectra measured between 50 K and 250 K, the bandpass filter with a threshold of 890 nm cuts the short-wavelengths part, thus the hot band at 880 nm is not seen.

Figure S18 .
Figure S18.The fine structure of 4 F3/2→ 4 I11/2 (left) and 4 F3/2→ 4 I13/2 (right) photoluminescence bands of NdSc2N@C80 measured at 5 K compared to LF splitting of 4 I11/2 and 4 I13/2 multiplets in six conformers of NdSc2N@C80 from CASSCF calculations (see Fig.S7for molecular structures and Tables S3a-S3f for energies of LF states).While conformers Sc-3 and Sc-6 give reasonable agreement to the experimental spectra of LF states (except for some systematic underestimation of the splitting by ca 10%), the lowest-energy conformer Sc-1 is far off.Surprisingly, it appears that only the conformers, in which Nd is coordinated close to one C atom in η 1 -η 3 manner, contribute to the fine structure of PL spectra.At the same time, the broader features at lower energies can be caused by other conformers.

Figure S19 .
Figure S19.Coordination of Nd atom to the closest carbon atoms in two representative conformers of NdLu2N@C80 and NdLu2N@C80, their geometrical Nd-N axes (thin blue lines) and gz axes of the two lowestenergy Kramers doublets from CASSCF calculations (KD1 -red lines, KD2 -green lines).Color code: Ndcyan, N -blue, C -light cyan (dNd−C ≤ 2.6 Å) or light gray (dNd−C > 2.6 Å).Nd-C distances shorter than 2.6 Å are shown as bonds.Also listed for each conformer are its relative energy from DFT calculations and Δ1,2 and ΔLF splitting from CASSCF calculations.

Figure S20 .Figure S21 .
Figure S20.XAS (upper panel) and XMCD (lower panel) spectra of NdSc2N@C80 at the Nd-M4,5 edges (3d→4f), T ≈ 5.5 K, µ0H = 6 T. Left-hand and right-hand polarized XAS spectra are denoted as σ + and σ -, non-polarized XAS spectrum is their sum, while XMCD (in %) is their difference normalized to the maximum of XAS.Red lines are integrated XAS and XMCD curves, also shown is the definition of integrals ( , ! and , "# ) used in the sum rule analysis, see Eq. S1
terms to LF splitting: 94.7%; angle between gz axis of KD1 and Nd-N bond is 12.8°
terms to LF splitting: 95.9%; angle between gz axis of KD1 and Nd-N bond is 9.0°

Table S10 .
Magnetization relaxation times of NdSc2N@C80 and α parameters determined by AC magnetometry at different fields

Table S11 .
Magnetization relaxation times of NdSc2N@C80 and α parameters determined by AC magnetometry at different temperatures