Orientationa Disorder, the Orientational Density Distribution and the Rotational Potential in C60

Abstract

Bragg intensities from neutron and X-ray diffraction data of C6o single crystals were used to determine the nuclear-and electron-density distributions of C60 at room temperature. The anisotropic density distribution is reconstructed by the maximum-entropy method and evaluated in terms of symmetry-adapted spherical harmonics. From this analysis, the orientational probability density function f(w) has been calculated and the rotational potential V(w) that is experienced by a C60 molecule in the cubic surrounding at 295 K has been obtained, f(w) shows strong deviations from the uniform orientational probability density function that would result from isotropic rotation. Accordingly, V(w) exhibits well developed minima. The absolute potential minimum is found at an Euler-angle set Wl and a second set of minima at slightly higher energy at w2. The potential difference between V(wl) and V(w2) is 313 K, whereas the overall rotational potential barrier height amounts to 522 K. w~ and w2 are comparable with the major and minor orientations that are adopted by the molecules in their low-temperature arrangement. The angles t,o 1 and w2 are fixed by the intrinsic geometry of the Euler-angle space (a,/3, ,y) under the combined action of the cubic site and the icosahedral molecular point group.

First-principles study on electronic responses of a C60 molecule to external electric fields

“…Moreover, the variation in total energy of 14.5 meV is comparable to the potential barrier height for C 60 molecules to rotate in a C 60 fcc crystal, which has been theoretically evaluated to be 45 meV [29]. Since the dipole moment of an isolated molecule does not exhibit orientational dependence as shown in Table 1, we can suppose that intermolecular dipole-dipole interaction existing for a solid phase is almost independent of molecular orientation as well and is almost constant regardless of the orientations.…”

A Recursive Algorithm for the Generation of Symmetry-Adapted Functions: Principles and Applications to the Icosahedral Group

“…Crystallographic applications of the high-order totally symmetric SAF's include the determination of the orientation probability function f(a,/3, 7) and/or the orientational potential V(a, [3,7) in orientationally disordered molecular crystals, in particular C60 (Schiebel et al, 1996). Further applications may be envisaged in the analysis of scattering data by quasicrystals or by icosahedral biological molecules or assemblies like icosahedral viruses.…”

Real-space calculation of powder diffraction patterns on graphics processing units

“…4 was simulated taking into account the orientation distribution function (ODF) for the C 60 molecules in f.c.c. fullerite (Chow et al, 1992;David et al, 1993;Schiebel et al, 1996), using a spherical harmonics representation (Schiebel et al, 1996). It is interesting to compare this pattern with that of an ideally ordered fullerite, where all C 60 molecules take the same orientation.…”