# 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

## TL;DR

This paper challenges the assumption that carbon atoms in graphene have significant quadrupole moments and proposes a new theoretical framework to define atomic properties in molecules.

## Contribution

A theoretical framework is introduced to define atomic properties in molecules, showing that carbon atoms in graphene have nearly zero quadrupole moments.

## Key findings

- The atomic quadrupole moment of a carbon atom in graphene is essentially zero within numerical precision.
- The experimentally deduced quadrupole moment of graphite likely comes from edge dipoles, not the carbon atoms themselves.
- A more realistic electrostatic model for finite graphene nanoflakes is proposed.

## 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 (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.