Structural studies of endohedral metallofullerenes by synchrotron radiation powder diffraction

The endohedral natures of the metallofullerenes Y@C₈₂ and Sc₂@C₈4 are described based on synchrotron radiation powder diffraction experiments. For structural analysis, a combination of the maximum-entropy method (MEM) and Rietveld refinement was employed to analyse the complicated powder pattern. The obtained MEM charge densities show a clear distinction of the endohedral natures of the mono- and dimetallofullerenes.

1. Introduction

Endohedral metallofullerenes have attracted extremely wide interest because of their unique structural and electronic properties (Chai et al., 1991; Bethune et al., 1993). In the past decade, various metallofullerenes supposed to encapsulate one, two or three metal atoms within fullerene cages, such as LaC₈₂ (Chai et al., 1991; Johnson et al., 1992), YC₈₂ (Shinohara et al., 1992), ScC₈₂ (Shinohara et al., 1993), La₂C₈₀ (Kikuchi et al., 1993), Y₂C₈₂ (Shinohara et al., 1992), Sc₂C₇₄, Sc₂C₈₂, Sc₂C₈₄ (Shinohara et al., 1993) and Sc₃C₈₂ (Shinohara et al., 1992; Yannoni et al., 1992), have been successfully synthesized and purified. Recently, the endohedral natures of the mono- and dimetallofullerenes, Y@C₈₂ and Sc₂@C₈₄, have been finally confirmed from synchrotron radiation powder data by using the maximum-entropy method (MEM) (Takata et al., 1995, 1997). Until then, no direct X-ray evidence for the endohedral structures had been reported, which, in fact, had restricted any further study on the solid-state properties of the metallofullerenes.

An X-ray structural study of an endohedral metallofullerene can be very difficult, because only very small amounts of powder samples are generally available and the observable X-ray powder data are limited to the low-angle region. Additional difficulties come from the fact that intrinsic orientational disorder is rather common. Hence, it may be extremely difficult to construct an adequate structural model. The MEM can overcome all these difficulties when it is applied to synchrotron powder data. The success of the structural studies of the metallofullerenes Y@C₈₂ and Sc₂@C₈₄ is possible owing partly to the very high angular resolution and good counting statistics of powder data by using synchrotron radiation and partly to the capability of model-free reconstruction by the MEM.

In the present paper, the work is reviewed to demonstrate that the synchrotron radiation powder experiment is a powerful method for the MEM structural analysis of endohedral metallofullerenes.

2. Experimental

The soot containing Y@C₈₂ or Sc₂@C₈₄ and other metallofullerenes was produced in direct-current (500 A) spark mode under He flow at 6.7 × 10³ Pa and collected under totally anaerobic conditions. The Y@C₈₂ or Sc₂@C₈₄ fullerene was separated and isolated from the various hollow fullerenes (C₆₀–C₁₁₀) and other yttrium or scandium metallofullerenes by the two-stage high-performance liquid chromatography (HPLC) method by using two complementary types of HPLC columns (Shinohara et al., 1993). In previous studies (Shinohara et al., 1994; Yamamoto et al., 1996), we have found two and three structural isomers of Y@C₈₂ (I, II) and Sc₂@C₈₄ (I, II, III), respectively. The MEM structural studies were performed on Y@C₈₂ (I) and Sc₂@C₈₄ (III). The purity of both samples relative to other fullerenes was more than 99.9% in each case.

The powder sample grown from toluene solvent was sealed in a silica glass capillary (0.3 mm diamater.). To collect an X-ray powder pattern with good counting statistics, the synchrotron radiation powder experiment with imaging plates (IP) as detectors was carried out at the Photon Factory BL-6A2 (Takata et al., 1992). The experimental arrangement is shown elsewhere (Takata et al., 1992). The exposure time was 1 h. The wavelength of the incident X-rays was 1.0 Å. The X-ray powder pattern of the Sc₂@C₈₄ crystal was obtained with a 0.02° step up to 29° in 2θ, which corresponds to 2.0 Å resolution in d spacing. For Y@C₈₂, the X-ray powder reflection intensities from 20° to a higher angular region were much weaker than those of Sc₂@C₈₄. Eventually, the data up to 20° in 2θ, which corresponds to d = 2.9 Å resolution, were available, which yielded reliable intensities for Y@C₈₂.

3. Data analysis

The experimental data were analysed in an iterative way by a combination of the Rietveld analysis and the maximum-entropy method (Takata et al., 1995, 1997). It is well known that the MEM (Sakata & Sato, 1990; Collins, 1982; Bricogne, 1988) can provide useful information purely from observed structure-factor data, without a presumed crystal structure model (Takata et al., 1995, 1996; Papoular & Cox, 1996). In MEM analysis, any kinds of deformation of electron densities are allowed as long as they satisfy the symmetry requirements.

The details of the analysis are described in previous papers (Takata et al., 1995, 1997). In this paper, data analysis is mentioned briefly. The space group was assigned as P2₁, which is monoclinic, for both Y@C₈₂ [a = 18.401 (2), b = 11.281 (1), c = 11.265 (1) Å, β = 108.07 (1)°] and Sc₂@C₈₄ [a = 18.312 (1), b = 11.2343 (6), c = 11.2455 (5) Å and β = 107.88 (1)°]. In the preliminary Rietveld analysis where fullerene cages are assumed as homogeneous spherical shells, 105 and 326 observed structure factors were evaluated by dividing the observed intensities at a data point according to the calculated contributions of the individual reflections. At this stage, the reliability factors (R factors) based on the Bragg intensities, R_I, were 14.4 and 14.6% for Y@C₈₂ and Sc₂@C₈₄, respectively.

Following Rietveld analysis, MEM analysis was carried out with the computer program MEED (Kumazawa et al., 1993). In the MEM reconstruction, the structure factors were all treated independently as phased values. The MEM map derived in this process allowed a better structural model to be constructed for Y@C₈₂ and Sc₂@C₈₄. For example, in the case of Sc₂@C₈₄, the MEM map shows a strong indication of the D_2d symmetry represented by many local maxima in the C₈₄ cage charge density. After remodelling, the R_I factors for Y@C₈₂ and Sc₂@C₈₄ finally became 5.9 and 7.9% and the weighted powder profile R factors, R_wp, were 3.0 and 5.3%. In Fig. 1, the best fits of the Rietveld analysis for Y@C₈₂ and Sc₂@C₈₄ are shown.

Figure 1 The Rietveld fitting result for (a) Y@C82 and (b) Sc2@C84. A close up of the profile in the higher angular range is inserted in (b).

The MEM enables us to visualize detailed features included in observed data, like the bonding charge between the C atoms, slight distortion of the molecule charge density and so on, which are difficult to express by a crystal model with an assembly of free atoms. Thus, the R_I factor is expected to decrease. To demonstrate this, the calculated intensities from the final MEM map are calculated to fit the powder pattern by an inverse process of the observed intensity estimation in our modified Rietveld analysis, and are shown in Fig. 2. The R_I factors calculated in such a process are 1.4% (Y@C₈₂) and 2.1% (Sc₂@C₈₄), which prove the validity of the above approach.

Figure 2 The profile fitting based on the calculated intensities from the MEM electron density for (a) Y@C82 and (b) Sc2@C84.

4. The MEM charge densities

4.1. Y@C₈₂

To visualize the endohedral nature of Y@C₈₂, the MEM electron density distributions of Y@C₈₂ are shown for (010) in Fig. 3(a). There exists remarkably high density just inside the C₈₂ cage. The number of electrons around the maximum is about 38, which is very close to the atomic number of a Y atom. Evidently, the density maximum in the interior of the C₈₂ cage is the Y atom.

Figure 3 The MEM electron density distribution of (a) Y@C82 and (b) Sc2@C84 for the (010) section. The contour lines are drawn for 4 unit cells with 0.5 e Å^−3 (Y@C82) and 0.3 e Å^−3 (Sc2@C84) intervals.

The cage structure of Y@C₈₂ differs from that of the hollow C₈₂ fullerene. There are many local maxima along the cage in Y@C₈₂, while the electron density of the C₈₂ cage is relatively uniform (Takata et al., 1995). This suggests that in Y@C₈₂ the rotation of the C₈₂ cage is very limited around a certain axis, while that in C₈₂ is almost free. The MEM electron density map further reveals that the Y atom does not reside in the center of the C₈₂ cage but is very close to the carbon cage wall, as suggested theoretically (Laasonen et al., 1992; Nagase & Kobayashi, 1993; Andreoni & Curioni, 1996). Previous electron spin resonance (ESR) (Weaver et al., 1992; Shinohara et al., 1992) and theoretical studies (Laasonen et al., 1992; Nagase & Kobayasi, 1993) suggest the presence of a strong charge-transfer interaction between the Y³⁺ ion and the C₈₂³⁻ cage, which may cause the aspherical electron density distribution of Y atoms. The Y—C distance calculated from the MEM map is 2.47 (3) Å, which is almost within the range of the theoretical prediction of 2.55–2.65 Å (Nagase & Kobayashi, 1993).

4.2. Sc₂@C₈₄

In Fig. 3(b), the section of the MEM charge density including the encaged Sc atoms is shown for the (010) plane. In the MEM charge density of the C₈₄ cage, there are many local density maxima with a density distribution that is very close to D_2d symmetry, although the MEM analysis was based on the P2₁ lattice symmetry. From the configuration of the local maxima, it is concluded that the symmetry of the endohedral Sc₂@C₈₄ molecule has D_2d symmetry, as suggested by the ¹³C NMR study (Yamamoto et al., 1996).

Two density maxima can clearly be seen inside the section of the carbon cage and are located in symmetric positions with respect to the center of the cage. The number of electrons around each maximum inside the cage is 18.8, which is very close to that of a divalent scandium ion Sc²⁺ (19.0). Evidently, each of the two density maxima in the interior of the C₈₄ cage corresponds to an Sc atom, indicating that Sc₂C₈₄ is endohedral. A theoretical study has predicted that the formal electronic structure of Sc₂@C₈₄ is well represented by (Sc²⁺)₂@C₈₄⁴⁻, where two 4s electrons of each Sc atom transfer to the C₈₄ cage (Nagase & Kobayashi, 1994). The positive charge of the Sc atom from the MEM charge density is +2.2, which is in good agreement with the theoretical value (Nagase & Kobayashi, 1994).

The Sc—Sc distance in C₈₄ derived from the MEM charge density is 3.9 (1) Å, which is a bit smaller than that of the theoretical value of 4.029 Å (Nagase et al., 1996). The nearest Sc—C distance is 2.4 (2) Å, while the theoretical value is 2.358 Å (Nagase et al., 1996). One of the most intriguing observations in Fig. 3(b) is that the charge density of the Sc atoms shows a salient tear-drop feature as if the two Sc atoms (ions) are in a stretching vibration within the C₈₄ cage. The C=C distance of the double bond adjacent to the Sc atom is 1.9 (3) Å, which is considerably longer than the theoretical value of 1.434 (9) Å, indicating some significant distortion of the polar regions of the C₈₄ cage. Such an anomalously large C=C distance [1.90 (15) Å] has been reported for the polymeric fullerene RbC₆₀ (Stephens et al., 1994). The pres­ent result suggests a strong indication of the elongation of the C=C distance, although a further study is required to confirm such an unusual distance by using higher-resolution data. The elongation of the C=C distance is recognized even in the Rietveld analysis. This might be closely related to the thermal motion of the Sc atoms in the C₈₄ cage, and to the existence of some localized interaction caused by the charge transfer between the encapsulated Sc atoms and the C₈₄ cage.

5. Conclusions

The variety in endohedral natures of mono- and dimetallofullerenes, i.e. the Sc₂@C₈₄ molecule has a centered nature in terms of molecular symmetry whereas Y@C₈₂ has a strong off-centered nature, was revealed for the first time by the synchrotron radiation powder structure analyses using the maximum-entropy method. For structure analysis, it was not possible to make a structural model as an arrangement of atoms without the MEM map. The very high angular resolution and good counting statistics of synchrotron radiation powder data brought the detailed and firm features of the MEM maps into relief. From the methodological viewpoint, the combined MEM and Rietveld analysis will become a key method, particularly for structural studies of metallofullerenes, higher fullerenes and other fullerene-related compounds, for which the construction of the appropriate structural model is not always easy.