Thermomechanical properties of honeycomb lattices from internal-coordinates potentials: the case of graphene and hexagonal boron nitrides

Lattice dynamics in low-dimensional materials and, in particular, the quadratic behaviour of the flexural acoustic modes play a fundamental role in their thermomechanical properties. A first-principles evaluation of these can be very demanding, and can be affected by numerical noise that breaks translational or rotational invariance. In order to overcome these challenges, we study the Gartstein internal-coordinate potential and tune its 13 parameters on the first-principles interatomic force constants for graphene. We show that the resulting potential not only reproduces very well the phonon dispersions of graphene, but also those of carbon nanotubes of any diameter and chirality. The addition of a cubic term allows also to reproduce the dominant anharmonic terms, leading to a very good estimate of the lattice thermal conductivity. Finally, this potential form works very well also for boron nitride, provided it is fitted on the short-range (analytical) part of the interatomic force constants, and augmented thereafter with the long-range dielectric contribution. This consideration underscores how potentials based on short-ranged descriptors should be fit, in polar materials, to the short-range part of the first-principles interactions, and complemented by long-range analytical dielectric models parametrized on the same first-principles calculations. In this entry, we provide a fully open-source implementation of the potential, for graphene, boron nitride, and carbon nanotubes. To guide the reader, we include examples of phonon calculation for all these systems. We also add the second and third derivatives for graphene, both from DFT-PBE and ICP calculations.