Exact heat flux formula and its spectral decomposition in molecular dynamics for arbitrary many-body potentials

Abstract: In this study we have derived an exact framework for the calculation of the heat flux and its spec- tral decomposition in Molecular Dynamics (MD) for arbitrary many-body potentials. This work addresses several lacks and limitations of previous approaches and allows for the accurate computa- tional study of thermal properties in a wide variety of many-body systems with MD. We have tested our modifications with Green-Kubo (GK) and Non-Equilibrium MD (NEMD) simulations for vari- ous 2D and 3D material systems using the Tersoff and Stillinger-Weber potentials as examples. The spectral decomposition of the heat current was also calculated for monolayer graphene (1LG) and MoS2 , for different system lengths. Our results show that the heat current calculated by our method is consistently in agreement with the thermostat current in NEMD, while previous implementations can estimate quite poorly the thermal conductivity both under GK and NEMD simulations, and both for 2D and 3D materials. The decomposition of the heat current also sheds light on the con- tribution of different phonon modes to thermal conductivity and its dependence on length. Our methodology is implemented in the widely used LAMMPS code specifically for the Tersoff and SW potentials, and it is readily applicable to the vast majority of many-body MD potentials.