Heterospin frustration in a metal-fullerene-bonded semiconductive antiferromagnet

Lithium-ion-encapsulated fullerenes (Li+@C60) are 3D superatoms with rich oxidative states. Here we show a conductive and magnetically frustrated metal–fullerene-bonded framework {[Cu4(Li@C60)(L)(py)4](NTf2)(hexane)}n (1) (L = 1,2,4,5-tetrakis(methanesulfonamido)benzene, py = pyridine, NTf2− = bis(trifluoromethane)sulfonamide anion) prepared from redox-active dinuclear metal complex Cu2(L)(py)4 and lithium-ion-encapsulated fullerene salt (Li+@C60)(NTf2−). Electron donor Cu2(L)(py)2 bonds to acceptor Li+@C60 via eight Cu‒C bonds. Cu–C bond formation stems from spontaneous charge transfer (CT) between Cu2(L)(py)4 and (Li+@C60)(NTf2−) by removing the two-terminal py molecules, yielding triplet ground state [Cu2(L)(py)2]+(Li+@C60•−), evidenced by absorption and electron paramagnetic resonance (EPR) spectra, magnetic properties and quantum chemical calculations. Moreover, Li+@C60•− radicals (S = ½) and Cu2+ ions (S = ½) interact antiferromagnetically in triangular spin lattices in the absence of long-range magnetic ordering to 1.8 K. The low-temperature heat capacity indicated that compound 1 is a potential candidate for an S = ½ quantum spin liquid (QSL). Conductive and magnetically frustrated solids may enable the development of high-performance molecule-based spintronic devices. Here the authors report a conductive and magnetically frustrated metal–fullerene-bonded framework prepared from a redox-active dinuclear copper complex and lithium ion-encapsulated fullerenes.

S ince the pure form of the lithium-ion-encapsulated fullerene salt [Li@C 60 ](SbCl 6 ) was isolated and structurally determined by X-ray diffraction analysis in 2010 1 , studies on this smallest endohedral metallofullerene (EMF) have taken precedence over photoinduced electron transfer (ET) in noncovalent donor-acceptor (D-A) complexes [2][3][4][5][6] , covalent metal complexes 7 , organic photovoltaics 8 , and molecular electronics 9 over the past decade because of the salt's unique structure and electronic properties relative to pristine C 60 [10][11][12][13][14] . Although the optical bandgap (E g ) is very close to that of pristine C 60 , the lowest unoccupied molecular orbital (LUMO) of Li + @C 60 has been observed to decline significantly to −3.90 eV with an initial reduction potential at −0.39 V versus Fc/Fc + in odichlorobenzene (o-DCB) 1 . Furthermore, the oxidisation state of Li + @C 60 can be easily tuned from 1+ to 3− by external chemical stimuli to realise various electronic states 1 . Therefore, this compound has been widely used as a π-electron acceptor owing to the small reorganisation energy required, which leads to highly delocalised π-electrons over a 3D sphere 2,3 . It is possible that Li + @C 60 can be doped by alkali metals to produce A 3 (Li@C 60 ) species (A = K + , Rb + , and Cs + ) in imitation of A 3 C 60 superconductors with three electrons accommodated in the triply degenerated LUMO [15][16][17][18] . In particular, the emergence of Li + @C 60 •− requires a milder chemical oxidant than for C 60 •− . Such a low reduction potential provides many opportunities for coordination chemistry. According to the Mulliken theory [19][20][21][22] , the formation of the CT complex requires efficient orbital overlap between the highest occupied molecular orbital (HOMO) of D and the LUMO of A. The CT interactions in the ground state increase with a decrease in the energy difference between the HOMO of D and LUMO of A. In this regard, Martin and co-workers reported several CT complexes between comparatively strong electron donors such as π-extended tetrathiafulvalene derivatives and fullerenes 23,24 . Additionally, Yamada et al. observed a triplet charge-separated state by laserexciting a curved π-surface donor and Li + @C 60 in solution 3 .
Although C 60 is an ideal ligand to realise topological architectures owing to its isotropic coordination environment 25 , to date, reports on the preparation of electrically conductive and magnetically frustrated solids based on Li + @C60 remain elusive. On the other hand, the S = ½ electronic system holds promise for exploring interesting quantum phenomena such as unconventional superconductivity [26][27][28][29] and QSLs, which are commonly observed in triangular or kagomé lattices [30][31][32][33][34][35][36] . Herein, we selected an electronically active donor, Cu 2 (L)(py) 4 , and a 3D chargetuneable metallofullerene, Li + @C 60 , as both the ligand and electron acceptor to construct a conductive and spin-frustrated framework based on the Mulliken theory.
In this work, an S = ½ electronic framework {[Cu 4 (Li + @C 60 ) (L)(py) 4 ](NTf 2 )(hexane)} n (1) is isolated by constructing the donor and acceptor. The donor is bonded to the acceptor via Cu-C bonds. It is noteworthy that the HOMO of Cu 2 (L)(py) 4 has the equivalent energy level of the LUMO of Li + @C 60 , thereby facilitating CT interactions in the ground state. From our calculations, we find that the d xz orbitals of the Cu ions in Cu 2 (L)(py) 4 are delocalised and strongly coupled with the N(p z ) orbitals (πelectrons) of the ligand, thereby yielding delocalised electrons in the HOMO. In 1, the four-terminal d xz orbitals of Cu ions coordinate with one Li + @C 60 cage and the remaining four Cu ions coordinate with the next Li + @C 60 cage to form an infinitely scaled 1D chain structure. The four Cu(L)(py) sites transfer a single electron into the Li + @C 60 cage, and the resulting four Cu 2+ (S = ½) ions and Li + @C 60 •− (S = ½) interact with each other and exhibit magnetic frustration in a triangular-like lattice. Our study demonstrates long-range electrical conductivity (σ) and spin frustration using Li + @C 60 superatoms in such a bonded D-A-type framework.

Results and discussion
Metal-fullerene bonded donor-acceptor-type framework. Compound 1 was synthesised by reaction of Cu 2 (L)(py) 4 and (Li + @C 60 )(NTf 2 − ) with a molar ratio of 2:1 in o-DCB solution. It crystallises in the triclinic P À 1 space group with the unit-cell dimensionality of a = 9.9963(3) Å, b = 13.3087(3) Å, c = 19.7031(5) Å, α = 77.323(2)°, β = 76.572(2)°, and γ = 69.500(2)°at 120 K. One Li + @C 60 cage coordinates with four Cu ions from four Cu 2 (L)(py) 2 molecules (Fig. 1a), and the remaining four Cu ions coordinate with the next Li + @C 60 cage to afford infinite 1D ladder-like structures along the b-axis (Fig. 2a). Each Cu ion exhibits an equivalent of five coordination numbers (two Cu-C and three Cu-N bonds) in a distorted trigonal bipyramid geometry (Supporting Information Fig. 1). The rectangular plane formed by the four Cu ions perfectly divides the C 60 cage into two (Fig. 1b), and the shell-like Li + ion is off-centred and localised above or below the Cu plane with thermal ellipsoids at 50% probability. Similar Li + -ion arrangements are also observed in the other forms of Li + @C 60 salts 37,38 . The inner Li + ion coordinates with the six-carbon ring with Li-C bond lengths in the range of 2.337-2.527 Å, which are consistent with the reported results 7,39 . The encapsulated Li + ions should strengthen the π backbonding from the transition-metal centre to the fullerene cage 7 ; however, the Cu ions do not coordinate with the rings of the sixcarbon (pink atoms in Fig. 2) owing to the highly symmetrical array of the four Cu ions.
The benzene ring of the ligand is slightly distorted (Supporting Information Fig. 2), and the bond patterns indicate the loss of aromaticity (Fig. 1c). On the other hand, the hexane molecules are trapped inside the squared structure of [Cu 2 (L)(py) 3 (Li + @C 60 )] 2 and strongly disordered along two lines (Supporting Information Fig. 3). Close to the square structure, the NTf 2 − molecules interact  3 ] 4 (Li + @C 60 ) and the arrangement of Li-ion. One Li + @C 60 coordinates with four Cu ions. The four Cu ions form a rectangular-like plane with a length and width of 9.5 and 5.5 Å, respectively. b The Li-ion coordinates with six carbon-ring and locates above or below the Cu-plane with thermal ellipsoids at the 50% probability. The Cu-plane perfectly splits the Li + @C 60 cage in half. c The structure of the donor, Cu 2 (L) and its bond length. Colour code: C (black), Cu (blue), N (cyan), S (yellow), O (red) and Li (pastel blue). electrostatically with ligands through hydrogen bonds. Inside the ladder chain, the π···π distance (r π ) between the two Li + @C 60 cages is 6.5 Å (Fig. 2a), indicating well-separated π electrons along the baxis. The 1D ladder structures self-stack along the a-axis to form 2D interacting nanosheets with r π of 3.2 Å (Fig. 2b). To determine the structure phase purity, the temperature dependence of crystal structures were determined at various temperature points (25,50,100,200, and 300 K) by using synchrotron radiation. The structure analysis indicated that there are no structural changes or distortions in 25-300 K (PXRD patterns in Supporting Information Fig. 4). Above 100 K, we did not detect the Li + position because of the fast motion of the Li + ion inside the cage. Below 100 K, the Li + ion was disordered and localised at two equivalent positions due to the symmetry. As the localised Li + ions strongly attract the negative radicals (via Li-C bonds), the C 60 •− radicals localised on the sixcarbon ring (pink atoms in Fig. 2).
Spontaneous charge transfer between Cu 2 (L)(py) 4 and (Li + @C 60 ) (NTf 2 − ) by precise control of the redox activities. Figure 3a shows the CV plot to Fc/Fc + . Four reversible redox processes with the first and second oxidisation potentials are observed at −0.36 and −0.04 V, respectively. Meanwhile, the first and second reduction potentials are observed at −0.92 and −1.08 V, respectively. The potential at −0.36 V corresponds to the first oxidisation process of Cu 2 (L)(py) 4 to [Cu 2 (L)(py) 4 ] + . In this regard, Aoyagi et al. reported that the first reduction process from Li + @C 60 to Li + @C 60 •− occurs at −0.39 eV in o-DCB versus Fc/Fc +1 . Consequently, the HOMO energy level of Cu 2 (L)(py) 4 can be simply treated as equivalent to the LUMO energy level of Li + @C 60 if the dissolution-free energy effect is ignored (Fig. 3b). According to the Mulliken theory, ET from Cu 2 (L)(py) 4 (donor) to Li + @C 60 (acceptor) can spontaneously occur without external energy to generate a triplet ground state [Cu 2 (L)(py) 4 ] + [Li + @C 60 •− ]. The solution-state absorption spectra in Fig. 3c evidence this mechanism. (Li + @C 60 )(NTf 2 − ) does not show any absorption band from 750 to 1500 nm whereas Cu 2 (L)(py) 4 shows a strong and broadband at 920 nm. Once the two pristine molecules are mixed in o-DCB, two new bands at 886 and 1032 nm are observed, strongly indicating that Li + @C 60 •− is generated 40 . Moreover, the strong band at 920 nm in Cu 2 (L)(py) 4 vanishes from the mixed solution, strongly indicating ET occurrence. The solid-state absorption spectrum of 1 shows several broad absorption bands at 1.30, 1.91, 2.42, and 3.48 eV (Supporting Information Fig. 5), where the band at 1.30 eV extends to the IR region (inset of Supporting Information Fig. 5), which indicates that 1 has a small optical bandgap (E g ). Figure 3d shows the Tauc plot of the Kubelka-Munk-transformed spectrum, with E g = 0.57 eV, as obtained from a linear fit to the low-energy onset of absorption. However, it is difficult to assign the Li + @C 60 •− band owing to absorption-band superpositions. Nevertheless, the generated Li + @C 60 •− can be detected by the EPR spectra. Figure 3e shows the temperature dependence of the EPR spectra of 1 for 3.5-300 K with all spectra showing two EPR active bands. At the lower magnetic field, parallel g II values of 2.45(3), 2.32(1), and perpendicular g ⊥ value of 2.09(1) are observed at 300 K. The g values and peak-to-peak linewidth, ΔH pp = 217.5(4) G, are entirely consistent with the Cu 2+ ion (S = ½) 41,42 . Another weak signal observed near the Cu 2+ signal with g = 2.0008(3) and ΔH pp = Fig. 2 The structure arrangements of the ladder-like chains. a 1D ladder-like structure along the b-axis in the bc plane (anion NTf 2 − and hexane molecules are omitted). One Li + @C 60 cage coordinates with four Cu ions and the remaining four-terminal Cu ions coordinate with the adjacent Li + @C 60 cage to form a 1D ladder-like structure. Distance r π between adjacent Li + @C 60 cages is 6.5 Å. The Li atoms are off-centred and polarised above/below the Cu plane. b Top view of the 1D ladder-like structure in the ac plane. Each structure stacks along the a-axis to form a 2D interacting sheet with intermolecular distance = 3.2 Å between two Li + @C 60 cages. Colour code: Cu (blue), sulphur (yellow), oxygen (red), nitrogen (pastel cyan), carbon (black/pink). Hydrogen atoms are omitted for clarity. NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-28134-w ARTICLE 8.1(2) G, signifies the presence of electronically active Li + @C 60 •− radical 3,40,43 . However, it is difficult to assign significant interactions between Cu 2+ ions and Li + @C 60 •− radical from the EPR spectra, probably owing to the superposition of the two characterised bands, but the spectra demonstrate that spontaneous ET occurs from Cu 2 L(py) 4 to Li + @C 60 and 1 remains in a triplet ground state up to 3.5 K. S = ½ heterospin frustration between Cu 2+ and Li + @C 60 •− in the ladder-like chains. The intensity of main peaks in the EPR spectra mimics the thermal dependence of the magnetic susceptibility (χ). The χ−T plot of 1 does not show any magnetic phase transition from 1.8 to 300 K under 1 T (Fig. 4a) and 4 T fields (Supporting Information Fig. 6), thereby indicating no long-range magnetic ordering. In addition, no sign of a spin-glass state is observed in the rectangular Cu lattices, as there is no deviation between the zero-field-cooled (ZFC) and field-cooled (FC) measurements. This suggests that Li + @C 60 •− radicals are involved in the magnetic reactions. Fitting the (χ − χ 0 ) −1 to the Curie-Weiss law at high temperatures (T > 175 K) yields a large negative Curie-Weiss temperature, θ cw = −190 K, suggesting strong antiferromagnetic (AF) interactions between the spins (χ 0 is defined as core diamagnetic or Van-Vleck paramagnetic susceptibility 44 and determined to be 8.8 × 10 −4 cm 3 mol −1 in Supporting Information Fig. 7). Even the fitted low-temperature χ −1 (T = 1.8-10 K) results in a θ cw = −1.6 K, indicating significant AF interactions. The (χ − χ 0 )T value at 300 K is 1.71 cm 3 K mol −1 (Supporting Information Fig. 8), which follows the theoretical prediction of four Cu 2+ ions and one Li + @C 60 •− radical per unit (χT calc = 0.375 × 5 = 1.875 cm 3 K mol −1 ). The rapid decrease in (χ − χ 0 )T with temperature reduction indicates that AF exchange interactions are dominant. In addition, the magnetic-field dependence of magnetisation from 1.8 to 300 K does not show any visible hysteresis loops (Fig. 4b).
To elucidate such strong exchange coupling in 1, we consider Fig. 4c, which shows the spin arrangements in a ladder-like structure with four Cu 2+ ions positioned at the corner of the rectangular plane and one Li + @C 60 •− at the centre. In this magnetic pattern, owing to symmetry, one Cu 2+ ion magnetically interacts with three adjacent Cu 2+ ions (J 12 and J 13 ), which are magnetically linked by the Li + @C 60 •− radicals. Moreover, the Cu 2+ ions interact with Li þ @C ÁÀ 60 ðJ CuÀC ÁÀ 60 Þ via Cu-C bonds. Such complicated and competitive interactions lead to a magnetically frustrated ground state. To obtain the J values, we used the following spin HamiltonianĤ using Eq. 1 by considering two kinds of exchange coupling J Cu-Cu and J Cu À C ÁÀ 60 .
To avoid overparameterization, we assumed the interactions of J 14 and J 23 are ignored compared to J 12 , J 34 and J CuÀC ÁÀ 60 due to their long metal-metal distances and the interactions between C 60 •− and Cu1, Cu2 are equivalent. The effective exchange coupling parameters of J Cu-Cu = −170(5) K and J 1ÀC ÁÀ 60 ¼ J 2ÀC ÁÀ 60 ¼ À185ð3Þ K with g Cu = 2.09(0) were obtained after the best fit (g C60 •− was fixed to 2.0). The negative J Cu-Cu and J CuÀC ÁÀ 60 values confirm that any two neighbouring spins are AF coupled. Therefore, in this rectangular spin-lattice, composed of several triangular lattices (such as ΔCu 1 Cu 2 C 60 •− ), we can observe the three spins exhibiting competing interactions. Frustration parameter 45 f = |θ cw | /T N is >105 (T N < 1.8 K), indicating that 1 has a highly frustrated ground state. In addition, the real-part alternating current magnetic susceptibility (χʼ) measurements indicated the absence of magnetic ordering to 1.8 K (Supporting Information Fig. 9). Such a frustrated lattice leads to inner Li + ions locating far away from the four coordinated Cu 2+ ions. Moreover, because of the pull forces from the eight external Cu-C bonds and six internal Li-C bonds, the Li + @C 60 cage is geometrically distorted with the diagonal lengths of 6.4 and 7.1 Å, respectively (Supporting Information Fig. 10).
Heat capacity and electrical conductivity. To further demonstrate the absence of magnetic phase transitions, the temperature dependence of heat capacity (C) was measured. The C versus T and C/T versus T plots (Fig. 5a, b) clearly showed that there is no sharp thermal anomaly in 2-20 K, indicative of no magnetic ordering in this temperature range. Usually, heat capacity is mathematically expressed as C = γT + βT 3 , where the γT and βT 3 terms are relevant to the density of state and crystal lattice, respectively. The data at low temperatures below 7 K, shown in Fig. 5c, clearly manifests the existence of a linearly temperaturedependent term (the γ term) despite the semiconducting ground state. The magnitude of γ in 2-7 K is estimated at 12 ± 2 mJ K −2 mol −1 from the linear extrapolation of the C/T versus T 2 plot down to zero K. This finite γ value was reported in organic 2D triangular κ-(BEDT-TTF) 2 Cu 2 (CN) 3 and inorganic honeycomb H 3 LiIr 2 O 6 QSLs 32,46 , suggesting possible QSL state of 1. In addition, the black colour of the single-crystals with metallic surfaces indicates that 1 could be electrically conductive. Figure 5d shows the temperature dependence of σ in the range of 250-300 K, obtained with a two-probe dc method. The σ value at 300 K is (4.4-8.2) × 10 −5 S cm −1 based on measuring several single-crystals. Parameter σ decreases with temperature reduction, indicating that 1 behaves as a semiconductor. The activation energy (E a ) is determined to be 0.44 eV by using the Arrhenius function.
Using generalised charge decomposition analysis (GCDA) method to understand donor-acceptor bonded interactions. To further elucidate the electronic ground states, we first calculated the orbital energy for Cu 2 (L)(py) 4 using the TD-DFT method. The calculated absorption spectrum coincides with the experimental data in the range of 300-1500 nm (Supporting Information Fig. 11 and Supporting Information Table 1). The strong absorption band at 920 nm (1.35 eV) is 100% attributed to ET from the HOMO (Fig. 6a) to LUMO (Fig. 6b). The electrons are predominantly located at both terminal Cu ions and the central ligand in the HOMO. Our calculations showed strong hybridisation with 58% d xz (Cu) electron density and 25% p z (N) electron densities, thus indicating that the electrons are delocalised in HOMO. Thus, the electron-intensive d xz (Cu) orbitals are highly capable of donating electrons to the Li + @C 60 cage through Cu-C bonds. The higher energy absorption band at 443 nm (2.80 eV) calculated at 402 nm (3.08 eV) is 78% assigned to ET from HOMO −1 to LUMO +1 (Supporting Information Fig. 12). To better understand the D-A bonding interactions, we used GCDA to investigate the electron-transfer amounts from Cu 2 L(py) 3 (by adding a pyridine molecule to the Cu 2 L(py) 2 molecule) to the Li + @C 60 cage and the generation of complex orbitals by the fragments molecular orbitals in such an open-shell system. Figure 6c, d shows the calculated α and β forms of the orbital interaction diagrams for the triplet Cu 2 L(py) 3 Li + @C 60 complex, respectively. The [Cu 2 L(py) 3 ] + fragment was assumed to be a doublet with a positive charge, and the other fragment (Li + @C 60 •− ) contained an anionic radical in the C 60 cage (doublet). We calculated the net CT value as 0.275e -(Supporting Information Table 2) by estimating the difference between electron donation and back-donation between the fragments. The partial CT interactions can be understood as follows: each Cu 2 (L)(py) 3 can only transfer 0.25e − to the Li + @C 60 cage as the Li + @C 60 cage is coordinated with four Cu 2 (L)(py) 2 . Thus, the GCDA calculation shows good agreement with the CV and magnetic results. From Fig. 6c, we note that the HOMO and LUMO of the complex are quite similar with an energy gap of 0.40 eV in the α form. The small bandgap is due to the significant contributions from HOMO of Li + @C 60 and LUMO of Cu 2 (L)(py) 3 . The electron densities are mainly observed on the central ligand and the Li + @C 60 cage. The HOMO of the complex originates from the mixture of 45% LUMO of Cu 2 L(py) 3 and 32% HOMO and 21% LUMO of Li + @C 60 ; similarly, the LUMO is mixed with 52% Cu 2 L(py) 3 LUMO, 33% Li + @C 60 HOMO, and 12% Li + @C 60 LUMO. This result indicates that the electrons in the complex's HOMO are solely derived from the HOMO of Li + @C 60 ; there is no electron contribution from the occupied Cu 2 L(py) 3 orbitals. Therefore, the complex's orbitals are not strongly mixed by fragments in the α form. In contrast, β electrons exhibit a deeper frontier orbital toward α electrons, indicating that β electrons are more electronically stable. Figure 6d shows that the frontier occupied orbitals of the complex in β form are doubly degenerated, indicating the significant contributions of fullerene orbitals. The electrons in the complex's HOMO are mainly delocalised on the Li + @C 60 cage and a small fraction in the d XZ orbital of Cu ions, and these electrons originate from 11% HOMO, 4% HOMO−1 (Supporting Information Fig. 13), 2% HOMO−2 (Supporting Information Fig. 14) of Cu 2 L(py) 3 , 29% HOMO, 5% HOMO−1 (Supporting Information Fig. 15), and 42% HOMO−3 of Li + @C 60 . It is worth noting that a large number of delocalised d XZ electrons of Cu ions were observed in the HOMO of Cu 2 L(py) 3 ; however, the number diminished in the complex's HOMO. This result strongly suggests that electrons transferred from Cu 2 L(py) 3 to the Li + @C 60 cage once Cu-C bonds were established. Thus, the bandgap is expected to be small because the orbital interactions between the fragments are strong. However, the calculated bandgap (ΔE = 1.17 eV) is only slightly smaller than that of undoped Li + @C 60 (ΔE~1.5 eV), which is probably caused by the strong onsite Coulomb interactions.
In summary, we succeeded in observing a conductive metalfullerene-bonded framework with strong spin frustration, constructed by using redox-active Cu 2 (L)(py) 4 and Li + @C60 molecules. Via the precise control of the redox activities in each species, the chemical bonds between the dinuclear electronic donor and the 3D spherical Li + @C 60 acceptor allow for an interesting S = ½ spin-lattice in a 1D ladder-like magnetic chain. The metal-fullerene bond accompanied by CT leads to a strong spin frustration ground state. Such a heterospin system is promising for the development of high-performance moleculebased spintronic devices and can aid in exploring new QSL candidates. Further studies in this direction aim to control the spin dynamics in a triangular or kagomé network using Li + @C 60 superatoms.
Physical characterisation. Single-crystal crystallographic data (exp_860) were collected at 120 K using a Rigaku Saturn 70 CCD diffractometer (Rigaku, Tokyo, Japan) with graphite monochromated Mo Kα radiation (λ = 0.71073 Å) generated by a VariMax microfocus X-ray rotating anode source. The single-crystal X-ray diffractions were measured at additional temperature points at 25, 50, 100, 200, and 300 K by using synchrotron radiation at Spring-8, Japan. The structures were solved by using Olex2 software 47 . Cyclic voltammetry (CV) was performed using an ALS/HCH Model 620D electrochemical analyser. A glassy carbon (3 mm diameter) electrode was used as the working electrode, a Pt wire was used as the counter electrode, and an Ag/Ag + was used as the reference electrode. The supporting electrolyte was 0.1 M tetrabutylammonium hexafluorophosphate (TBA·PF 6 ) in dry o-DCB. The solid-state absorption spectra were acquired by compound 1 was embedded in KBr pellets with the use of a Shimadzu UV-3100PC instrument, and subsequently, the pellets were inserted into a transparent sealed cell and protected by argon gas. The solution-state absorption spectra were measured in a sealed plate tube filled with argon gas. The temperature dependence of the solid-state EPR spectra was examined by using the JEOL JES-FA100 device. Magnetic susceptibility measurements were conducted on a polycrystalline sample using a Quantum Design SQUID magnetometer (MPMS-7L). The magnetic susceptibility data were fitted by PHI software 48 . The temperature dependence of heat capacity was measured by using the Quantum Design PPMS. The temperature dependence of σ was measured on single-crystals via a two-probe method by using the Quantum Design PPMS 6000 instrument.
Quantum chemical calculation. Geometry optimisation was performed by using density-functional theory (DFT) at the B3LYP/6-31G(d, p) level for pristine Cu 2 (L) (py) 4 . The absorption spectrum was calculated for the optimised geometry by using the TD-DFT method at the CAM-B3LYP/def2TZVP level. The Cu 2 (L)(py) 3 (Li + @C 60 ) complex was cut from the X-ray structure by adding one pyridine molecule as the terminal ligand, and the resulting structure was optimised by applying DFT at the UB3LYP/6-31G(d, p) level. The optimised structure was decomposed into two fragments, [Cu 2 (L)(py) 3 ] + and Li + @C 60 •− , for single-point calculation. The GCDA 49 was used for the open-shell form of this complex and the two fragments by applying DFT at the UB3LYP/def2tzvp level. All calculations were performed using Gaussian 16 software 50 , and the output results were analysed using the Multiwfn programme 49,51 .

Data availability
The crystallographic data generated in this study have been deposited in the CCDC database under accession codes 2039740 (compound 1 at 120 K), 2039286 (Cu 2 (L)(py) 4 at 120 K), and 2121505-2121509 (compound 1 at 25, 50, 100, 200, and 300 K). The data generated in this manuscript are available within the manuscript, its supplementary information, or from the authors upon request.