Evaluation of heat current formulations for equilibrium molecular dynamics calculations of thermal conductivity

Equilibrium molecular dynamics combined with the Green–Kubo formula can be used to calculate the thermal conductivity of materials such as germanium and carbon. The foundation of this calculation is extracting the heat current from the results and implementing it into the Green–Kubo formula. This work considers all formulations from the literature that calculate the heat current for the Tersoff potential, the interatomic potential most applicable to semiconductor materials. The formulations for the heat current are described, and results for germanium and carbon are presented. The formulations are compared with respect to how well they capture the physics of the Tersoff potential and how well the calculated value of the thermal conductivity reflects the experimentally measured value.