Is the atomic quadrupole moment of a carbon atom in graphene zero?: The case for a rational definition of the properties of atoms in a molecule

Abstract

It is generally assumed that the carbon atoms of graphitic samples and their finite analogs have sizable quadrupole moments, with the out-of-plane component ($Q^{\rm C}_{20}$ in traceless spherical coordinates) being the dominate contribution. However, there is no consensus on what the quantity is for such carbon-based systems and values reported in the literature range from $Q^{\rm C}_{20} \sim -1.14$ to $+0.79$ a.u. In this work we propose a theoretical framework in which well-defined statements can be made about properties of atoms-in-a-molecule (AIMs) even when these properties are not experimentally observable. Using this framework and the distributed multipole method basis-space iterated Stockholder atoms (BS-ISA), we show that the atomic quadrupole moment of a carbon atom in graphene is essentially zero within the limits of precision of the numerical method used. We explain how the experimentally measured atomic quadrupole moment of a graphite sample determined by Whitehouse \& Buckingham likely originated almost entirely from edge dipoles, and we propose a more realistic electrostatic model for finite graphene nanoflakes.