# Comparison of the Green-Kubo and homogeneous non-equilibrium molecular dynamics methods for calculating thermal conductivity

## TL;DR

This paper compares the Green-Kubo and HNEMD molecular dynamics methods for calculating lattice thermal conductivity, highlighting their relative performance and computational efficiency for bulk and defected silicon.

## Contribution

It provides a detailed comparison of GK and HNEMD methods specifically for silicon, emphasizing the advantages of HNEMD in defect scenarios and guiding future applications.

## Key findings

- Both methods perform well for bulk silicon with acceptable uncertainties.
- HNEMD is computationally cheaper than GK for low thermal conductivity cases.
- HNE-MD shows potential for studying lattice defects like nanovoids and dislocations.

## Abstract

Different molecular dynamics methods like the direct method, the Green-Kubo (GK) method and homogeneous non-equilibrium molecular dynamics (HNEMD) method have been widely used to calculate lattice thermal conductivity ($\kappa_\ell$). While the first two methods have been used and compared quite extensively, there is a lack of comparison of these methods with the HNEMD method. Focusing on the underlying computational parameters, we present a detailed comparison of the GK and HNEMD methods for both bulk and vacancy Si using the Stillinger-Weber potential. For the bulk calculations, we find both methods to perform well and yield $\kappa_\ell$ within acceptable uncertainties. In case of the vacancy calculations, HNEMD method has a slight advantage over the GK method as it becomes computationally cheaper for lower $\kappa_\ell$ values. This study could promote the application of HNEMD method in $\kappa_\ell$ calculations involving other lattice defects like nanovoids, dislocations, interfaces.