In this study we have derived an exact framework for the calculation of the heat flux and its spectral decomposition in molecular dynamics (MD) for arbitrary many-body potentials. This work addresses several deficiencies and limitations of previous approaches and allows for the accurate computational study of thermal properties in a wide variety of many-body systems with MD. We have tested our modifications with Green-Kubo (GK) and nonequilibrium MD (NEMD) simulations for various two- and three-dimensional (2D and 3D) material systems using the Tersoff and Stillinger-Weber (SW) potentials as examples. The spectral decomposition of the heat current was also calculated for monolayer graphene (1LG) and ${\mathrm{MoS}}_2$, 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 contribution 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.

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• Heat transfer
• Thermal conductivity
• Thermal properties
• Molecular dynamics