## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

7-15-1993

#### Publication Source

Physical Review B

#### Volume

48

#### Issue

3

#### Start Page

1888

#### Last Page

1898

#### DOI

10.1103/PhysRevB.48.1888

#### Abstract

We calculate electrostatic multipole moments of C_{60} up to *l*=18 using the quantum-mechanical charge distribution with icosahedral symmetry obtained from *ab initio* calculations. It is found that the second nonzero moment (*l*=10) is comparable to the first nonzero moment (*l*=6). The values of several low-order multipole moments are almost 10 times smaller than those found from the charge distribution of recently proposed potential models and thus the actual Coulomb interaction between C_{60} molecules is much smaller than previously predicted. Much better agreement with calculated multipoles is obtained from a model which introduces point charges at the center of hexagonal and pentagonal plaquettes, following the physical arguments of David *et al*. [Nature *353*, 147 (1991)]. We show that a multipole expansion including only *l*=6 and 10 moments can predict the potential due to a C_{60} molecule at distances *R*≥2R_{0} within an error of about 5%, where R_{0} is the radius of the C_{60} molecule. At distances less than *R*<3/2R_{0} the multipole expansion is qualitatively incorrect even if one includes the terms up to *l*=18, indicating the importance of short-range quantum effects at these distances. The Coulomb interaction we obtain predicts two nearly degenerate, locally stable configurations for solid C_{60}: (1) a metastable structure with Pa3 symmetry and setting angle φ=23.3°, close to experimentally observed value, and (2) a global minimum with the Pa3 structure but a setting angle φ=93.6°. We give physical arguments for expecting two such configurations and give a qualitative explanation for their near degeneracy. We conclude that a satisfactory intermolecular potential requires a first-principles calculation of the quantum-mechanical short-range repulsive interactions.

#### Recommended Citation

Yildirim, T.,
Harris, A.,
Erwin, S. C.,
&
Pederson, M. R.
(1993).
Multipole Approach to Orientational Interactions in Solid C_{60}.
*Physical Review B,*
*48*
(3),
1888-1898.
http://dx.doi.org/10.1103/PhysRevB.48.1888

**Date Posted:** 12 August 2015

This document has been peer reviewed.