How to characterize the electron defect states of single and double carbon vacancies in graphene by molecular density functional theory?
Preface: This paper describes in detail the electronic manifold with single- and double-vacancy defects in graphene molecular models based on polycyclic aromatic hydrocarbons, using various density functionals, including long-range corrected density functionals, for DFT calculations of pyrene, cyclopyrene, and 7a,7z-weekneoene.
For the pyrene defect model, the DFT results well reproduce a set of closely spaced singlet and triplet states predicted by CCSD and previous MRCI+Q calculations, indicating that the applicability of DFT to access excited manifolds is also applicable to larger graphene models.
For single-carbon vacancy defects, all structures have a triple ground state.
As expected, in the largest system, 7a,7z-neoene-1C, the lowest energy levels are very close in energy. For all double-vacancy defect structures, significant rearrangement of electronic states is observed as the sheet size increases. The state in the closed enclosure 1Ag minimal system is the ground state of the unstable 3B2u state in the extended 7a,7z-perimeter.
As observed for single-vacancy defects, for larger systems, the lowest energy levels are closer energetically because there are more π orbitals that are closer energetically. For all states, the formation of bridges with double vacancies results in shorter distances than single-vacancy defects, indicating greater rigidity of the former structure, which does not allow for stronger distortion.
As one of the most promising materials, graphene has excellent electrical, thermal and mechanical properties, and has broad application prospects in the fields of electronics, optoelectronics and photonics, because graphene is a semimetal, it is necessary to modify its band gap to create appropriate semiconductor properties.
This bandgap engineering is often achieved by introducing defects, and among the various methods of generating defects, vacancy defects constitute an interesting possibility by which strong changes in the electronic properties of graphene sheets can be obtained. These defects appear in graphene or graphite nanostructures during defective growth and can also arise after ion radiation.
Experimentally, structural details of these defects have been observed using transmission electron microscopy and scanning tunneling microscopy, where suspended bonds appear due to the removal of carbon atoms from regular honeycomb networks, inducing magnetic behavior in graphene. For the same reason, free radical signatures are expected in this defective graphene material, leading to high chemical reactivity.
The characterization of the electronic structure of defective states, their structure, and energetics is very important and constitutes fascinating and challenging field that is important for regulating the electronic properties of graphene.
The current work focuses on the use of pyrene, cyclopyrene, and 7a,7z-tetracarbon ene as prototypes of graphene molecular fragments with single and double carbon vacancies in model structures. The number 1a shows the increased size of the color-coded original unperturbed structure, where one and two carbon atoms have been removed to form single and double vacancy defects without further structural relaxation, thus maintaining a regular graphene network.
In the first case, three hanging keys are generated in the σ system, and a hole is generated π the system. In the second case, four suspension keys are generated in the σ orbital system and two holes in the π system.
For single- and double-vacancy structures consisting of PAH sheets of increased size, detailed images of electron manifolds have been obtained. For pyrene defect models, it is shown that density functional calculations performed at different computational levels can reproduce well the set of closely spaced singlet and triplet states predicted by CCSD and previous MRCI+Q calculations, which provides the reason for also characterizing manifolds of excited states using computationally efficient DFT methods, and also for significantly larger graphene models.
In the case of single-vacancy defects, all systems are characterized by triple ground states, 3A2 for unreleased and 3B1 for relaxed geometry. This result is consistent with the magnetic response due to the formation of single-vacancy defects in graphene. In a relaxed structure, these two triplet states and the corresponding singlet state always have a single electron occupying 1 suspension key orbital in a.
Another electron either occupies a local defect orbit or is in an off-domain π orbit. The strong decrease in bridge bond C 7-propylene 8 observed distances from the initial 2.46–2.47 in the unrelaxed structure increased to 1.45, 1.64, and 1.74 of pyran-1C, cyclopyrene-1C, and 7a,7z-tetracarbon-1C, respectively.
For unrelaxed and relaxed double-vacancy defects, significant rearrangement of electronic states is observed as the sheet size increases. The closed shell 1Ag was in a significantly unstable state when it went from the ring Pyrenees defect to the 7a,7z-Periolene defect. In the latter case, the lowest state is that the triplet and the singlet state are also nearby, indicating high chemical reactivity due to the shell-opening characteristics of these states.
For smaller structures, the first two states are more than one electron volt higher than the ground state. On the other hand, the first excited state in pyrene-2C is based on a single occupation of the π* orbital at the defect, corresponding to the higher-order excited state in the extended system, due to the appearance of more π* delocalized orbitals.
conclusion
For all presented states, the optimized structure has a distance between the bridge bonds C7-C89-C 101.45 and 1.67, which corresponds to a substantial reduction compared to the unrelaxed structure. These values are smaller than the values for single-vacancy defects, indicating greater rigidity of double-vacancy structures.
Compared to the B3LYP results, the results using HSE06 and CAM-B3LYP functionals present a partially different image, mainly for the largest system with a 1C vacancy case, due to its open-shell feature. Since long-range correction should play a major role in extended systems, the CAM-B3LYP results are expected to give a more reliable description, especially in DFT-based methods for charge transfer states.
