Interatomic force constants including the DFT-D dispersion contribution

TL;DR

This paper analytically derives and implements Grimme's DFT-D dispersion contribution to interatomic force constants, demonstrating its importance for accurate vibrational property predictions in weakly bonded materials.

Contribution

The authors derived an analytical expression for dispersion contributions to force constants and validated its implementation, enabling efficient phonon calculations in dispersive systems.

Findings

Dispersion corrections are essential for accurate vibrational properties.

Implementation scales cubically with system size, with minimal computational overhead.

Proper dispersion treatment improves agreement with experimental vibrational data.

Abstract

Grimme's DFT-D dispersion contribution to interatomic forces constants, required for the computation of the phonon band structures in density-functional perturbation theory, has been derived analytically. The implementation has then been validated with respect to frozen phonons, and applied on materials where weak cohesive forces play a major role i.e. argon, graphite, benzene. We show that these dispersive contributions have to be considered to properly reproduce the experimental vibrational properties of these materials, although the lattice parameter change, coming from the ground-state relaxation with the proper functional, induces the most important change with respect to a treatment without dispersion corrections. In the current implementation, the contribution of these dispersion corrections to the dynamical matrices (with a number of elements that is proportional to the square of the number of atoms) has only a cubic scaling with the number of atoms. In practice the overload with respect to density-functional calculations is small, making this methodology promising to study vibrational properties of large dispersive systems.