**Thermal Conductivity Calculation with the Molecular Dynamics Direct
Method II: Improving the Computational Efficiency**

PC Howell, JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, 8, 2144-2154 (2011).

DOI: 10.1166/jctn.2011.1936

The molecular dynamics non-equilibrium direct method is a well-
established way of predicting thermal conductivity K, but in good
thermal conductors such as crystalline semi-conductors it can yield
unacceptably large statistical uncertainties in the extrapolation to a
bulk system, K infinity.We show how to extract more information from the
simulation data in order to reliably calculate tight confidence
intervals for K infinity. We prove that the measurement error in K for a
single simulation of size L-i and duration D-i is proportional to
(DiLi3)(-1/2), so that using very large simulations reduces the error
more efficiently than using very long durations, as we confirm
explicitly with molecular dynamics data. By considering the error
propagation we derive an algorithm to determine the optimal set of *Li,
Di) which minimizes the probable measurement error in K infinity for
given total computational effort. Overall, these improvements reduce by
an order of magnitude the computational effort required to calculate K
infinity with a given statistical uncertainty.
*

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