Various properties of two polymorphs
of carbon, highly oriented
pyrolytic graphite (HOPG) and diamond, were investigated at the ab
initio level using different Hamiltonians with all-electron Gaussian-type
functions (GTF) and projector augmented wave (PAW) basis sets. Their
equilibrium lattice parameters, cohesive and interlayer interaction
energies, band structures, vibrational frequencies, and elastic constants
were evaluated. The calculations were performed at the Hartree–Fock,
density functional theory (DFT), and hybrid (B3LYP and PBE0) levels.
As regards DFT, the local density and generalized gradient (PBE and
PBEsol) approximations were used. For GTF, the influence of the basis
set superposition error (BSSE) was assessed. Since these approaches
do not take dispersion interactions correctly into account, two different
versions of Grimme’s dispersion correction, D2 and D3, were
evaluated. The D2 and D3 corrections were reparameterized in order
to reproduce the experimental structure of HOPG. For the properties
depending on the description of the covalent bonds, such as the cohesive
energy, C
11 and C
12, the dispersion corrections have a negligible influence.
The best agreement is found for B3LYP-GTF-D3, PBE providing close
results. For the properties depending on the description of the interaction
between different layers, such as the interlayer interaction energies, C
33, and C
44, using
the dispersion corrections improves the results. In general, D3 performs
better than D2. PBE overall provides better results than the other
functionals. As regards the basis sets, PAW describes the vibrational
frequencies better than GTF due to the BSSE, whereas GTF provides
a better description of the bandwidths and interband separations,
elastic constants, and thermodynamical data. On the basis of the overall
results, PBE-GTF-D3 appears to be a good compromise for an accurate
description of the properties of graphite.
