Electric quadrupole moment of graphene and its effect on intermolecular interactions

Carbon atoms in aromatic compounds exhibit a permanent electric quadrupole moment due to the aromatic p electron distribution. In the case of small aromatic hydrocarbons, this quadrupole contributes significantly to their intermolecular interactions, but when the honeycomb lattice is expanded to infinity, the quadrupolar field sums to zero and its significance vanishes. Therefore, electrostatic interactions with graphene are often omitted in force field molecular modeling. However, for a finite sheet, the electrostatic field decays only slowly with increasing size and is always non-negligible near edges. In addition, in a corrugated graphene sheet, the electrostatic field near the surface does not vanish completely and remains sizeable. In the present study, we investigated the magnitude of the graphene quadrupolar field as a function of model size and graphene corrugation, and estimated the error resulting from its neglect in molecular dynamics simulations. Exfoliation energies in benzene and hexafluorobenzene were calculated using the potential of mean force method with and without explicit quadrupoles. The effect on exfoliation energies was found to be quite small. However, the quadrupole moment may be important for graphene sheet association (aggregation) as it affects barrier heights, and consequently kinetics of association. Our results indicate that quadrupolar interactions may need to be considered in molecular modeling when graphene is corrugated or bent.