Application of atomic stress to compute heat flux via molecular dynamics for systems with many-body interactions

Although the computation of heat flux and thermal conductivity either via Fourier's law or the Green-Kubo relation has become a common task in molecular dynamics simulation, contributions of three-body and larger many-body interactions have always proved problematic to compute. In recent years, due to the success when applying to pressure tensor computation, atomic stress approximation has been widely used to calculate heat flux, where the lammps molecular dynamics package is the most prominent propagator. We demonstrated that the atomic stress approximation, while adequate for obtaining pressure, produces erroneous results in the case of heat flux when applied to systems with many-body interactions, such as angle, torsion, or improper potentials. This also produces incorrect thermal conductivity values. To remedy this deficiency, by starting from a strict formulation of heat flux with many-body interactions, we reworked the atomic stress definition which resulted in only a simple modification. We modified the lammps package accordingly to demonstrate that the new atomic stress approximation produces excellent results close to that of a rigid formulation.

Figure 1

Heat flux in (a) NEMD and thermal conductivity in (b) EMD decomposition into respective interaction contributions, where results obtained via ${\mathbf{\sigma }}_i^{\text{group}}$ in Eq. (5) (lammps) and ${\mathbf{\sigma }}_i^{\text{cntr}}$ in Eq. (11) (Modified) are displayed together with reference values (Reference), which were rigorously obtained via the VA method [52, 55]. A zero axis and reference values are also indicated by a horizontal dashed line where applicable. Horizontally shifting black error bars indicate standard error of mean of each component that was scaled by 2 for clarity, while horizontally centered thicker red error bars at the top indicate that of the total, and were computed via block average method by dividing sampled data into 30 blocks [58].