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The closely related Green-Kubo and Helfand moment approaches are applied toobtain 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. Directapplication of the Green-Kubo formula exhibits slow convergence of theintegrated thermal conductivity values even for long (120 ns) simulation times.To partially mitigate this slow convergence we developed a numerical procedurethat involves filtering of the MD-calculated heat current. The filtering isaccomplished by physically justified removal of the heat-current componentwhich is given by a linear function of atomic velocities. A double-exponentialfunction is fitted to the integrated time-dependent thermal conductivity,calculated using the filtered current, to obtain the asymptotic values for thethermal conductivity. In the Helfand moment approach the thermal conductivityis obtained from the rates of change of the averaged squared Helfand moments.Both methods are applied to periodic $\beta$-HMX supercells of four differentsizes and estimates for the thermal conductivity of the infinitely largecrystal are obtained using Matthiessen's rule. Both approaches yield similaralthough not identical thermal conductivity values. These predictions arecompared to experimental and other theoretically determined values for thethermal conductivity of $\beta$-HMX.

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