Structure of [60]fullerene with a mobile lithium cation inside

The structure of crystalline [60]fullerene with a lithium cation inside (Li+@C60) was determined by synchrotron radiation X-ray diffraction measurements to understand the electrostatic and thermal properties of the encapsulated Li+ cation. Although the C60 cages show severe orientation disorder in [Li+@C60](TFPB−)·C4H10O and [Li+@C60](TFSI−)·CH2Cl2, the Li+ cations are rather ordered at specific positions by electrostatic interactions with coordinated anions outside the C60 cage. The Li+@C60 molecules in [Li+@C60](ClO4−) with a rock-salt-type cubic structure are fully disordered with almost uniform spherical shell charge densities even at 100 K by octahedral coordination of ClO4− tetrahedra and show no orientation ordering, unlike [Li+@C60](PF6−) and pristine C60. Single-bonded (Li+@C60−)2 dimers in [Li+@C60−](NiOEP)⋅CH2Cl2 are thermally stable even at 400 K and form Li+–C bonds which are shorter than Li+–C bonds in [Li+@C60](PF6−) and suppress the rotational motion of the Li+ cations.


Introduction
Hollow spherical carbon molecules called fullerenes or buckyballs with a molecular formula of C 2n (n ≥ 30) can contain various atoms and molecules [1,2]. Endohedral  atoms and molecules with magnetic and electric moments have the potential to be used for molecular devices such as quantum bits [3,4], magnetic resonance imaging agents [5,6] and molecular switches [7,8].
[60]Fullerene C 60 with a soccer-ball shape of 1 nm diameter is the most abundant fullerene in soot obtained by arc discharge of graphite electrodes and is valuable in applications such as solar cells [9,10]. Endohedral C 60 with a lithium cation inside (Li + @C 60 ) is efficiently obtained by lithium plasma bombardment with C 60 vapour onto a target plate and is commercially available from Idea International Co., Ltd. [11][12][13]. It has been reported that Li + @C 60 shows outstanding electron-accepting properties for applications such as photoelectrochemical solar cells [14][15][16] and non-volatile organic transistor-based memories [17].
Li + @C 60 forms crystalline salts with anions such as SbCl 6 − and PF 6 − [11,18]. The PF 6 − salt, [Li + @C 60 ](PF 6 − ), has a rock-salt-type cubic structure and shows a fast response to an alternating electric field by free rotational motion of the Li + cation on a shell with a radius of 1.5 Å inside the C 60 cage [18][19][20]. The free rotational motion of the Li + cation is suppressed so that it is localized at two off-centre equivalent positions on the threefold inversion axis of the cubic crystal below 100 K. The simultaneous occupation of the two positions at low temperature is attributed to a quantum tunnelling of the Li + cation between the two positions with an interval of 2.7 Å. The tunnelling motion is also hindered below T C = 24 K with an abrupt decrease in the dielectric permittivity by antiferroelectric interactions among local electric dipole moments formed between the Li + cations inside and the PF 6 − anions outside the C 60 cages. The tunnelling motion and intermolecular interaction of the Li + cation suggest that Li + @C 60 has the potential to be used as a quantum bit in quantum computers using electric dipole moments. The position and motion of a Li + cation inside C 60 are significantly affected by the coordinated anions and molecules outside the C 60 . For instance, the Li + cation in the SbCl 6 − salt is localized at two adjoining off-centre positions at 370 K by asymmetric coordination of SbCl 6 − anions around an Li + @C 60 molecule [11]. Such anion exchange effects should be investigated in more depth to understand the electrostatic responses of the encapsulated Li + cations. Crystals of [Li + @C 60 ](PF 6 − ), [Li + @C 60 ](SbCl 6 − ) and [Li + @C 60 ](TFPB − ) (TFPB, tetrakis{3,5-bis(trifluoromethyl)phenyl}borate) were previously obtained and structurally characterized [11,18,21]. Further structural study of [Li + @C 60 ](TFPB − ) is required, because the position and motion of the Li + cation have not been revealed in the previous structural analysis [21]. The anions of the previously obtained crystals are all non-polar. Li + @C 60 crystals combined with polar anions such as TFSI − (TFSI, bis(trifluoromethylsulfonyl)imide) should also be obtained and structurally characterized. PF 6 − and SbCl 6 − are small octahedral anions, whereas TFPB − is a large tetrahedral anion. It is worthwhile obtaining and investigating Li + @C 60 crystals combined with small tetrahedral anions such as ClO 4 − . A crystal of dimerized Li + @C 60 − without anions was also obtained by electrochemical reduction [22]. The crystal is different from other dimerized endohedral metallofullerene crystals that consist of negatively charged endohedral metallofullerenes and positively charged donor molecules [23,24]. The Li + cation in the dimerized Li + @C 60 − is localized near the carbon atom that is nearest to the carbon atom forming an inter-fullerene single C-C bond at 100 K. Temperature dependence of the position and motion of the localized Li + cation in the dimerized Li + @C 60 − would provide us with essential information about the thermal stability of the (Li + @C 60 − ) 2 dimer and the Li + -C bond.
To understand the electrostatic and thermal properties of the mobile Li + cation inside C 60 , we investigated the effects of the coordination structure and temperature on the position and motion of the encapsulated Li + cations in Li + @C 60 crystals by synchrotron radiation (SR) X-ray structure analysis in this study.

Material and methods
We performed the X-ray crystal structure analyses of [  at beamline BL02B1 of the SPring-8 large SR facility [25]. The crystal structures were determined by using SIR [26], SHELX [27] and SP [28]. The experimental conditions and crystallographic data are summarized in  c-axis, as shown in figure 1b,c. The distance from the C 60 centres to the nearest central boron atom of TFPB − is 8.7 Å. The distance from the C 60 centre to the nearest two C 60 centres along the c-axis is 10.0 Å. Therefore, Li + @C 60 to TFPB − distances are increased and Li + @C 60 to Li + @C 60 distances are decreased by intercalation of C 4 H 10 O solvent molecules. The differences in coordination structure around Li + @C 60 between the solvent-free and solventcontaining crystals affect the rotational motion of the C 60 cages. Fullerene molecules often show rotational motion and orientation disorder in crystals. For instance, C 60 cages in [Li + @C 60 ](PF 6 − ) and pristine C 60 crystals show free rotational motion at high temperature [18,29]. orientation disorder with two molecular orientations remains in the low-temperature pristine C 60 [30,31]. This suggests that rotational motion of the C 60 cages is hindered by electrostatic interactions between the cationic Li + @C 60 and coordinated anions. C 60 cages in the reported crystal structure of the solvent-free [Li + @C 60 ](TFPB − ) show no orientation disorder [21]. The electrostatic interactions between Li + @C 60 and TFPB − should be weakened by the increase in Li + @C 60 to TFPB − distances by intercalation of C 4 H 10 O solvent molecules. As a result, C 60 cages in the solvent-containing [Li + @C 60 ](TFPB − ) crystal show a severe orientation disorder with five molecular orientations, as shown in figure 1d. The site occupancies for the five C 60 orientations are 0.372(5), 0.253(4), 0.155(4), 0.132(3) and 0.124(4). A weak electron charge-density peak for an Li + cation was observed inside the disordered C 60 cage of the solvent-containing [Li + @C 60 ](TFPB − ) at 260 K. The Li + position at (x, y, z) = (0.235, 0.758, 0.151) is close to the gravity centre at (0.228, 0.741, 0.147) for the central boron atoms of the six TFPB − anions adjacent to the Li + @C 60 with an interval of 0.13 Å, and, hence, the Li + position is electrostatically consistent with the anion arrangement. The Li + position is beneath the centre of a hexagon of the C 60 with the major orientation, as shown in figure 1e. The average Li + -C distance is 2.35(10) Å, which agrees with the value for [Li + @C 60 ](PF 6 − ) at low temperature [18,19]. Assuming that the site occupancy for the Li + position is the same as that of the major C 60 orientation (0.372 (5)), the isotropic atomic displacement parameter of the Li + is refined to 0.24(3) Å 2 , and the remaining fraction of the Li + cation would occupy other positions inside the C 60 by a positional disorder. The Li + position in the solvent-free [Li + @C 60 ](TFPB − ) has not been determined even at 123 K [21]. The Li + cation of cubic [Li@C 60 ](PF 6 − ) is freely rotating on a shell with a radius of 1.5 Å inside the C 60 cage above 100 K [18][19][20]. Therefore, the Li + cation is partially ordered in the solvent-containing [Li + @C 60 ](TFPB − ) by the asymmetric coordination of TFPB − anions and C 4 H 10 O molecules, as shown in figure 1b,c. should electrostatically interact with the Li + cations inside the C 60 cages in crystals. However, the electric dipole moments of TFSI − and CH 2 Cl 2 are cancelled by the antiferroelectric arrangements in the crystal structure with a non-polar space group of Pnma. If an Li + @C 60 crystal containing polar anions with a polar space group was obtained, the crystal could have a macroscopic electric dipole moment and exhibit ferroelectricity due to a switching of the polar anions and motion of the Li + cations. Ferroelectric crystals of C 60 encapsulating a polar molecule have been predicted theoretically [32]. Actually, a cubic crystal of C 60 with a polar water molecule inside (H 2 O@C 60 ) shows an increase in the dielectric permittivity according to the Curie-Weiss law at low temperature, although no ferroelectric phase transition is observed down to 8 K [33].  and pristine C 60 undergo a phase transition from the fcc structure (space group: Fm3m) to the low-temperature simple-cubic structure (space group: Pa3) at 370 K and 260 K, respectively [18,29]. Surprisingly, [Li + @C 60 ](ClO 4 − ) has an fcc structure even at 100 K. The cubic lattice constant of [Li + @C 60 ](ClO 4 − ) is a = 14.13 Å at 100 K, which is smaller than that of [Li + @C 60 ](PF 6 − ) at 100 K (a = 14.28 Å) and larger than that of pristine C 60 at 100 K (a = 14.06 Å) [18,31]. This relationship is consistent with the fact that a ClO 4 − anion is smaller than a PF 6 − anion. Figure 3c shows the crystal structure model used in the powder pattern fitting. The space group is Fm3m. The uniform spherical C 60 shell with a radius of 3.55 Å centred at 0, 0, 0 and the disordered ClO 4 − anion centred at 1/2, 1/2, 1/2 form a rock-salt-type cubic structure. The disordered ClO 4 − anion was modelled by a Cl atom at 1/2, 1/2, 1/2 and partially occupied O atoms at 1/2 ± 0.059, 1/2 ± 0.059, 1/2 ± 0.059 with a site occupancy of 1/2. The disordered structure is given by orthogonal overlap of two ClO 4 − tetrahedra with a Cl-O distance of 1.44 Å. The powder pattern was fitted by using the simple structure model with acceptable reliable factors (R wp = 0.036, R I = 0.124). However, the reliable Li + position could not be determined due to the multi-site occupation or free rotational motion. The remaining deviations between the observed and calculated intensities in figure 3a,b are mainly due to non-uniformity of the electron charge densities on the C 60 shell.

3.4.
[Li + @C 60 − ](NiOEP)·CH 2 Cl 2 Figure 4 shows the temperature dependence of the molecular structure of the single-bonded (Li + @C 60 − ) 2 dimer in [Li + @C 60 − ](NiOEP)·CH 2 Cl 2 . The (Li + @C 60 − ) 2 dimer has a disordered structure by a ratchettype rotation along the inter-fullerene single C-C bond with a rotation angle of about 39°above the phase transition temperature around 250 K [22]. The disordered structures at 250 and 400 K are omitted in the figure. (C 60 − ) 2 dimers in complex crystals of C 60 with donor and solvent molecules dissociate above 160-220 K [35,36]. By contrast, the (Li + @C 60 − ) 2 dimers in [Li + @C 60 − ](NiOEP)·CH 2 Cl 2 are thermally stable even at 400 K, as shown in figure 4c. It is suggested that the inter-fullerene single C-C bond is stabilized by the encapsulation of Li + cations. Low stability of (C 60 − ) 2 dimers is due to the strong repulsion of two negative charges within the dimer. The Li + cation inside the cage which compensates this negative charge contributes essential stabilization of (Li + @C 60 − ) 2 dimers.
The encapsulated Li + cation is localized with a site occupancy of 1.0 near the carbon atom (C2) nearest to the carbon atom (C1) forming the inter-fullerene single C-C bond (figure 4a). The Li + -C2 distance is 2.21(1), 2.31(2) and 2.36(6) Å at 100, 250 and 400 K, respectively. The value at 100 K is obviously shorter than the Li + -C distance of 2.37(1) Å in [Li + @C 60 ](PF 6 − ) at 40 K [19]. It is also noted that the Li + cation in the (Li + @C 60 − ) 2 dimer locates near the centre of a pentagon involving C2, as shown in figure 4d, [18,19]. The formation of the shorter Li + -C bond contributes to stabilization of the (Li + @C 60 − ) 2 dimer. The inter-fullerene C1-C1 distance shows almost no temperature dependence, which are 1.59(1), 1.59(1) and 1.60(1) Å at 100, 250 and 400 K, respectively. The thermal ellipsoid of the Li + cation is unusually large perpendicular to the radial direction from the C 60 centre at 400 K (figure 4c,f ). The equivalent atomic displacement parameters of the Li + cation and C2 atom are 0.8(1) and 0.077(2) Å 2 , respectively. The thermally induced large librational motion of the Li + cation in the (Li + @C 60 − ) 2 dimer is basically consistent with the free rotational motion of the Li + cation in [Li + @C 60 ](PF 6 − ) above 100 K. The Li + cation bonded to the C2 atom cannot rotate freely in the (Li + @C 60 − ) 2 dimer even at 400 K.

Conclusion
We determined structures of cationic Li + @C 60 monomers and neutral (Li + @C 60 − ) 2  dimers in a complex of C 60 dissociate. The formation of Li + -C bonds, which are shorter and thermally more stable than Li + -C bonds in [Li + @C 60 ](PF 6 − ), stabilizes the inter-fullerene single C-C bond and suppresses the free rotational motion of the Li + cation. The variety of structures of Li + @C 60 revealed in this study proves the controllability of the position and motion of the encapsulated Li + cation from outside the C 60 cage, which would be valuable in future applications of Li + @C 60 as molecular devices. This study shows that the spherical Li + @C 60 cation forms various ionic crystals with common inorganic and organic anions, and the neutral Li + @C 60 − consisting of a positive Li + core and a negative C 60 − cage forms thermally stable molecular crystals of covalently bonded (Li + @C 60 − ) 2 dimers. The results are essential and important to support the strong superatomic character of Li + @C 60 .
Data accessibility. The CIFs are available as the electronic supplementary material and from the Cambridge Crystallographic Data Centre (CCDC) (www.ccdc.cam.ac.uk/structures) with deposition numbers 1826722, 1826723 and 1826724.