# Towards a simplified description of thermoelectric materials: Accuracy of approximate density functional theory for phonon dispersions

## TL;DR

This study assesses the accuracy of the density-functional based tight-binding approach (DFTB) in predicting phonon dispersions of 2D materials and diamond, comparing results with DFT and experimental data to evaluate its reliability for thermoelectric property calculations.

## Contribution

It introduces a systematic comparison of DFTB with DFT and experiments for phonon dispersions, highlighting the importance of accurate pair-potentials for reliable predictions.

## Key findings

- DFTB accuracy varies with the choice of repulsive pair-potentials.
- For carbon materials, specific pair-potentials yield errors comparable to DFT differences.
- The method's efficiency makes it promising for thermoelectric property estimation.

## Abstract

We calculate the phonon-dispersion relations of several two-dimensional materials and diamond using the density-functional based tight-binding approach (DFTB). Our goal is to verify if this numerically efficient method provides sufficiently accurate phonon frequencies and group velocities to compute reliable thermoelectric properties. To this end, the results are compared to available DFT results and experimental data. To quantify the accuracy for a given band, a descriptor is introduced that summarizes contributions to the lattice conductivity that are available already in the harmonic approximation. We find that the DFTB predictions depend strongly on the employed repulsive pair-potentials, which are an important prerequisite of this method. For carbon-based materials, accurate pair-potentials are identified and lead to errors of the descriptor that are of the same order as differences between different local and semi-local DFT approaches.