Heat-current filtering for Green-Kubo and Helfand-moment molecular dynamics predictions of thermal conductivity: Application to the organic crystal $\beta$-HMX

TL;DR

This paper introduces a heat-current filtering method to improve the convergence of Green-Kubo and Helfand-moment calculations of thermal conductivity in molecular dynamics simulations of the organic crystal $eta$-HMX, providing more accurate predictions.

Contribution

The paper develops a physically justified filtering procedure for heat current in MD simulations, enhancing the convergence of thermal conductivity estimates from Green-Kubo and Helfand methods.

Findings

Filtering accelerates convergence of thermal conductivity calculations.

Both methods produce similar estimates consistent with experimental data.

The approach is validated on different supercell sizes for $eta$-HMX.

Abstract

The closely related Green-Kubo and Helfand moment approaches are applied to obtain the thermal conductivity tensor of $\beta$-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane ($\beta$-HMX) at $T=300$ K and $P=1$ atm from equilibrium molecular dynamics (MD) simulations. Direct application of the Green-Kubo formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) simulation times. To partially mitigate this slow convergence we developed a numerical procedure that involves filtering of the MD-calculated heat current. The filtering is accomplished by physically justified removal of the heat-current component which is given by a linear function of atomic velocities. A double-exponential function is fitted to the integrated time-dependent thermal conductivity, calculated using the filtered current, to obtain the asymptotic values for the thermal conductivity. In the Helfand moment approach the thermal conductivity is obtained from the rates of change of the averaged squared Helfand moments. Both methods are applied to periodic $\beta$-HMX supercells of four different sizes and estimates for the thermal conductivity of the infinitely large crystal are obtained using Matthiessen's rule. Both approaches yield similar although not identical thermal conductivity values. These predictions are compared to experimental and other theoretically determined values for the thermal conductivity of $\beta$-HMX.