Abstract
Reliably obtaining thermal properties of complex systems, which often involves computing heat flux to obtain thermal conductivity via either Fourier’s law or the Green–Kubo relation, is an important task in modern molecular dynamics simulations. In our previous work [Surblys et al., Phys. Rev. E 99, 051301(R) (2019)], we have demonstrated that atomic stress could be used to efficiently compute heat flux for molecules with angle, dihedral, or improper many-body interactions, provided a newly derived “centroid” form was used. This was later successfully implemented in the LAMMPS simulation package. On the other hand, small rigid molecules, like water and partial constraints in semi-flexible molecules, are often implemented via constraint force algorithms. There has been a lack of clarification if the constraint forces that maintain geometric constraints and can also be considered as many-body forces contribute to the overall heat flux and how to compute them correctly and efficiently. To address this, we investigate how to apply the centroid atomic stress form to reliably compute heat flux for systems with constraint or rigid body dynamics. We successfully apply the centroid atomic stress form to flexible, semi-flexible, and rigid water models; decompose the computed thermal conductivity into separate components; and demonstrate that the contribution from constraint forces to the overall heat flux and thermal conductivity is small but non-negligible. We also show that while the centroid formulation produces correct heat flux values, the original “group” formulation produces incorrect and sometimes unphysical results. Finally, we provide insight into the meaning of constraint force contribution.
Highlights
Molecular dynamics (MD) has been widely used as a numerical microscope, where the target systems are either too small or too ideal to be investigated via experimental approach
The heat flux values obtained from the Langevin thermostats, and the corresponding thermal conductivity values via Fourier’s law in Eq (7) are provided in Table II, which indicate that molecules with less constraints have higher thermal conductivity, which is reasonable considering the difference in degrees of freedom and has been reported in previous literature.[26]
We showed that constraint forces in constraint dynamics must be considered when obtaining heat flux
Summary
Molecular dynamics (MD) has been widely used as a numerical microscope, where the target systems are either too small or too ideal to be investigated via experimental approach. While the dynamics of the systems are usually correct, the computation of thermal properties is not always correctly implemented It has been reported by our group, among others, that the “group” form atomic stress[4] used by LAMMPS is unfit to compute heat flux in systems with many-body interactions,[5–7] which originates from assumptions that only hold for pairwise interactions. We clarify if constraint forces contribute to the overall heat flux and demonstrate how to compute them reliably and efficiently We do this by applying the centroid atomic stress formulation to these constraint forces and investigate if and how they contribute to the thermal properties, i.e., heat flux and thermal conductivity, of rigid and semi-flexible water molecules and compare them to a fully flexible water molecule. Even for the TIP3P/rig model, bonds must be explicitly defined so that 1–2 and 1–3 interactions can be detected, even though it has no effect on the dynamics
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