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

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 (Q₂₀^C in traceless spherical coordinates) being the dominant contribution. However, there is no consensus on what the value is for such carbon-based systems, and values reported in the literature range from Q₂₀^C ∼ -1.14 to +0.79 au. In this work we propose a theoretical framework in which well-defined statements can be made about properties of atoms-in-a-molecule even when these properties are not experimentally observable. Using this framework and the distributed multipole method basis-space iterated Stockholder atoms, 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 deduced 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.