Abstract
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.
Highlights
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
Owing to the similarity of pressure and heat flux formulation, the same atomic stress approximation has been applied to computing heat flux and thermal conductivity without any rigid validation for either molecular dynamics systems containing simple many-body interactions such as angle, torsion
It will be demonstrated via several test simulations that the new atomic stress approximation produces excellent agreement with results obtained via rigorous computation, while the conventional atomic stress approximation substantially underestimates heat flux and overestimates thermal conductivity
Summary
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. A new atomic stress definition will be derived in accordance to precise formulation of heat flux for manybody interactions It will be demonstrated via several test simulations that the new atomic stress approximation produces excellent agreement with results obtained via rigorous computation, while the conventional atomic stress approximation substantially underestimates heat flux and overestimates thermal conductivity. The component W is the virial contribution to the pressure and for a system consisting of only pairwise interactions
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