The characterization of electronic defect states of single and double carbon vacancies in graphene sheets using molecular density functional theory

Max Pinheiro,Daniely V V Cardoso,Adélia J A Aquino,Francisco B C Machado,Hans Lischka

doi:10.1080/00268976.2019.1567848

Abstract

ABSTRACTA detailed picture of the electronic states manifolds of single- and double-vacancy defects in molecular models of graphene based on polycyclic aromatic hydrocarbons (PAHs) is presented. DFT calculations using various density functionals including long-range corrected ones have been performed for pyrene, circumpyrene and 7a,7z-periacene. It has been found for pyrene defect models that DFT results reproduced well the set of closely-spaced singlet and triplet states predicted by the CCSD(T) and previous MRCI + Q calculations, indicating the applicability of DFT for accessing the excited states manifolds also for larger graphene models. For the single-carbon vacancy defect, all structures have a triplet ground state. As expected, in the largest system, 7a,7z-periacene-1C, the lowest lying states are much closer in energy. For all double-vacancy defect structures, a significant rearrangement of the electronic states with increasing size of the sheet is observed. The closed-shell 1Ag state in the smallest systems is destabilised in the extended 7a,7z-periacene system, which has the 3B2u state as the ground state. As observed for the single-vacancy defect, the lowest lying states are closer in energy for the larger systems, since there are more π orbitals close in energy available. For all states, the formation of the bridging bonds for the double vacancy leads to distances shorter than for the single vacancy defect indicating a larger rigidity of the former structure which does not allow stronger distortions.

Highlights

Graphene became one of the most promising materials since its discovery in 2004 by Geim and Novoselov [1]
For pyrene-2C, as observed to pyrene-1C structures, we have shown previously [45] a strong reduction of the C7–C8 (C9–C10) distances from originally 2.47 Å in the unrelaxed structure to distances between 1.45 Å and 1.54 Å for all states, with similar results obtained at complete active space self-consistent field (CASSCF) and density functional theory (DFT)/B3LYP levels
The calculations using different density functionals show that they can reproduce quite well the set of closely-spaced singlet and triplet states predicted by the CCSD(T) and previous multireference configuration interaction (MRCI) + Q calculations for the local defects of both the SV and DV pyrene models

Summary

Introduction

Graphene became one of the most promising materials since its discovery in 2004 by Geim and Novoselov [1]. It possesses exceptional electronic, thermal, and mechanical properties with promising applications in electronics, optoelectronics and photonics [2,3,4,5,6,7,8,9]. Since graphene is a semimetal, it is necessary to modify its band gap in order to create appropriate semiconductor properties. This band gap engineering is frequently accomplished by the introduction of defects.

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