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 introduces a theoretical framework for defining atomic properties in molecules, demonstrating that the quadrupole moment of a carbon atom in graphene is effectively zero, challenging previous assumptions and clarifying experimental measurements.

Contribution

It proposes a new theoretical approach to define atomic properties in molecules and applies it to show the quadrupole moment of carbon in graphene is nearly zero.

Findings

Atomic quadrupole moment of carbon in graphene is essentially zero.

Previous measurements likely reflect edge dipoles, not intrinsic atomic properties.

A more realistic electrostatic model for 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 ($Q^{\rm C}_{20}$ 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.