*3.2. C60 Fullerene*

Next, we show the VED of C60 fullerene [17,18], which has two types of features of the *sp*<sup>2</sup> and *sp*<sup>3</sup> hybridizations. Many structural studies of C60 have been reported so far [19–24]. The C60 cluster consists of 20 hexagons and 12 pentagons. The former involves the *sp*<sup>2</sup> hybridization, and the latter *sp*<sup>3</sup> hybridization. There are two different types of C–C bonds; one is on the regular pentagon (single bond), and the other is shared by two hexagons (double bond). In the high-temperature phase of a C60 crystal, the C60 molecules are completely orientationally disordered and continue to randomly rotate, where the space group is *Fm*3*m*. At 260 K, C60 exhibits a first-order phase transition; below that temperature, there is a discontinuous reorientation principally around the [111] direction, where the space group is *Pa*3. Below 90 K, the discontinuous rotational motion is frozen, although a small amount of static disorder still exists [19,23].

In this study, we focus on the low-temperature phase at 30 K without a dynamical motion of C60 molecules. The lattice parameter in *Pa*3 is *a* = 14.0279(6) Å at 30 K. The detail of the structural analysis results is shown in Appendix A (Table A1). As reported in previous structural studies [22,23], there may be two types of domains in the low-temperature phase. One is the merohedral domain described in [22], in which *I*(*hkl*) and *I*(*khl*) are superimposed, and the other is the rotational domain around the [111] direction described in [23], in which two kinds of C60 configurations exist. Our structural analysis results show that the ratio of the merohedral domain is 0.4995(8):0.5005, and the ratio of the rotational domain is 0.818(3):0.182. When observing the VED distribution, the contributions of the former domain can be separated analytically. In the latter domain, the two components appear independently, where the VED in two directions coexist in a real space. However, in this case, because the ratio of the rotational domain was quite different, the VED was observed as almost one domain.

Figure 4a shows the crystal structure and VED of a C60 molecule, and Figure 4b shows a sectional view of the - 1 1 1 plane. The (i) and (iii) bonds, ∼ 1.45 Å, correspond to the single bonds, and the (ii) bond, ∼ 1.39 Å, corresponds to the double bond. Certainly, the double bond forms a stronger bond than the single bond. The VED distribution is clearly observed along the shape of the C60 molecule, which is very similar to the results of previous density functional theory calculations [25]. Furthermore, the difference in the ED is confirmed between the single (shown as (i) and (iii)) and double (shown as (ii)) bonds (Figure 4b). The ED at the double bond is higher than that at the single bond, which corresponds to the strength of the C–C covalent bond. We succeeded in quantitatively evaluating the covalent bond strength in the C60 molecule from the VED.

**Figure 4.** VED distribution of C60 fullerene: (**a**) Surface plot; (**b**) Sectional view of the -1 1 1 plane. The (i) and (iii) bonds correspond to the single bonds, which are on the regular pentagons. The (ii) bond corresponds to the double bond, which is shared by two hexagons.
