Thermomechanical properties of honeycomb lattices from internal-coordinates potentials

Lattice dynamics in low-dimensional materials and, in particular, the quadratic behaviour of the flexural acoustic modes play a fundamental role in their thermomechanical and thermal transport properties. A first-principles evaluation of these can be computationally very demanding, and can be affected by numerical noise which breaks translational and/or rotational invariance. In order to overcome these challenges in honeycomb lattices, we consider the Gartstein internal-coordinate potential where we tune its 13 parameters on first-principles calculations of the interatomic force constants for graphene. We show that the resulting potential not only reproduces very well the phonon dispersions of graphene, but that it can also describe the vibrational properties of carbon nanotubes of any diameter and chirality, without any additional modifications to its analytic expression or parametrization. In addition, one can augment its functional form with a single cubic term that allows also to be able to reproduce the dominant anharmonic terms of the interactions and obtain a close estimate for the lattice thermal conductivity. Finally, this potential form works well also for other 2D honeycomb materials, such as a monolayer of 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. These considerations underscore how in polar materials potentials based on short-ranged descriptors should be fit to the short-range part of the first-principles interactions, and complemented by long-range analytical dielectric models also parametrized by 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.