Quantifying energetics of topological frustration in carbon nanostructures

Zachary Bullard, Eduardo Costa Girão, Colin Daniels, Bobby G. Sumpter, and Vincent Meunier
Phys. Rev. B 89, 245425 – Published 17 June 2014
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Abstract

We develop a graph theoretical formalism to account for the fact that sp2 carbon can become spin ordered or generate free radicals for purely topological reasons. While this phenomenon has been previously considered a binary operator, we here show a quantification in discrete units of frustrations. The graph theory method is combined with open density functional theory calculations to establish the existence of an energy of frustration that is shown to greatly improve the description of carbon nanostructure energetics using classical force fields. The methodology is illustrated for a number of systems and, owing to the small computational overhead associated with its evaluation, is expected to be easily integrable into any modeling approach based on a structure's adjacency matrix.

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  • Received 10 March 2014
  • Revised 14 May 2014

DOI:https://doi.org/10.1103/PhysRevB.89.245425

©2014 American Physical Society

Authors & Affiliations

Zachary Bullard1, Eduardo Costa Girão2, Colin Daniels3, Bobby G. Sumpter4, and Vincent Meunier1,3

  • 1Department of Materials Science, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
  • 2Departamento de Física, Universidade Federal do Piauí, CEP 64049-550, Teresina, Piauí, Brazil
  • 3Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
  • 4Center for Nanophase Materials Sciences and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA

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Issue

Vol. 89, Iss. 24 — 15 June 2014

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