Electronic structure and aromaticity of large-scale hexagonal graphene nanoflakes

Abstract

With the help of the recently developed SIESTA-PEXSI method [J. Phys.: Condens. Matter 26, 305503 (2014)], we perform Kohn-Sham density functional theory (DFT) calculations to study the stability and electronic structure of hexagonal graphene nanoflakes (GNFs) with up to 11,700 atoms. We find the electronic properties of GNFs, including their cohesive energy, HOMO-LUMO energy gap, edge states and aromaticity, depend sensitively on the type of edges (ACGNFs and ZZGNFs), size and the number of electrons. We observe that, due to the edge-induced strain effect in ACGNFs, large-scale ACGNFs' cohesive energy decreases as their size increases. This trend does not hold for ZZGNFs due to the presence of many edge states in ZZGNFs. We find that the energy gaps Eg of GNFs all decay with respect to 1/L, where L is the size of the GNF, in a linear fashion. But as their size increases, ZZGNFs exhibit more localized edge states. We believe the presence of these states makes their gap decrease more rapidly. In particular, when L is larger than 6.40 nm, we find that ZZGNFs exhibit metallic characteristics. Furthermore, we find that the aromatic structures of GNFs appear to depend only on whether the system has 4N or 4N + 2 electrons, where N is an integer.

Optical properties of graphene nanoflakes: Shape matters

“…In general, the calculated DOS are consistent with previous calculations using a simple nearest-neighbor, oneorbital Hückel model 22,29,30,39 and DFT 28,33 . For structures comparable to the ones analyzed here, usually a wide range of energies is considered in the literature, which have very similar DOS profiles among the different structures 53 .…”

“…These edge states have been experimentally observed 45 . Some of these features also hold for GNF: armchair flakes show a band gap,although in zigzag edges gap states occur only in triangular flakes 18,28 . Moreover, the electronic 46,47 , magnetic 48 and optical properties [49][50][51][52] of GNR are well understood from the theoretical point of view.…”

DGDFT: A massively parallel method for large scale density functional theory calculations

“…The PEXSI method can scale to 10, 000 to 100, 000 processors. This has recently been demonstrated in the massively parallel SIESTA-PEXSI method [29,36]. SIESTA-PEXSI uses local atomic orbitals to discretize the KohnSham Hamiltonian.…”

“…Therefore, the PEXSI method is particularly well suited for studying electronic structures of larges scale low-dimensional (1D and 2D) systems. [36,37] The PEXSI method is based on approximating the density matrix by a linear combination of Green's functions, i.e.,…”

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

“…The PEXSI method has a two-level parallelism structure and is by design highly scalable using 10, 000 ∼ 100, 000 processors on high performance machines. The PEXSI software package 2 has been integrated into a number of electronic structure software packages such as BigDFT 26 , CP2K 31 , SIESTA 21,29 , DGDFT 12,23 , FHI-aims 3 , QuantumWise ATK 6 , and has been used for accelerating materials simulation with more than 10000 atoms 13,14 .…”