Nuclear quantum effects in thermal conductivity from centroid molecular dynamics

Abstract

We show that the centroid molecular dynamics (CMD) method provides a realistic way to calculate the thermal diffusivity $a=\lambda /\rho c_{\mathrm{V}}$ of a quantum mechanical liquid such as para-hydrogen. Once $a$ has been calculated, the thermal conductivity can be obtained from $\lambda =\rho c_{\mathrm{V}}a$, where $\rho$ is the density of the liquid and $c_{\mathrm{V}}$ is the constant-volume heat capacity. The use of this formula requires an accurate quantum mechanical heat capacity $c_{\mathrm{V}}$, which can be obtained from a path integral molecular dynamics simulation. The thermal diffusivity can be calculated either from the decay of the equilibrium density fluctuations in the liquid or by using the Green-Kubo relation to calculate the CMD approximation to $\lambda$ and then dividing this by the corresponding approximation to $\rho c_{\mathrm{V}}$. We show that both approaches give the same results for liquid para-hydrogen and that these results are in good agreement with experimental measurements of the thermal conductivity over a wide temperature range. In particular, they correctly predict a decrease in the thermal conductivity at low temperatures -- an effect that stems from the decrease in the quantum mechanical heat capacity and has eluded previous para-hydrogen simulations. We also show that the method gives equally good agreement with experimental measurements for the thermal conductivity of normal liquid helium.

13 pages, 9 figures, 3 tables

References in corpus (4)

• Canonical sampling through velocity-rescaling
• Efficient stochastic thermostatting of path integral molecular dynamics
• Use the force! Reduced variance estimators for densities, radial distribution functions and local mobilities in molecular simulations
• Computing the heat conductivity of fluids from density fluctuations

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