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Significant differences exist among literature for thermal conductivity ofvarious systems computed using molecular dynamics simulation. In some cases,unphysical results, for example, negative thermal conductivity, have beenfound. Using GaN as an example case and the direct non-equilibrium method,extensive molecular dynamics simulations and Monte Carlo analysis of theresults have been carried out to quantify the uncertainty level of themolecular dynamics methods and to identify the conditions that can yieldsufficiently accurate calculations of thermal conductivity. We found that theerrors of the calculations are mainly due to the statistical thermalfluctuations. Extrapolating results to the limit of an infinite-size systemtend to magnify the errors and occasionally lead to unphysical results. Theerror in bulk estimates can be reduced by performing longer time averages usingproperly selected systems over a range of sample lengths. If the errors in theconductivity estimates associated with each of the sample lengths are keptbelow a certain threshold, the likelihood of obtaining unphysical bulk valuesbecomes insignificant. Using a Monte-Carlo approach developed here, we havedetermined the probability distributions for the bulk thermal conductivitiesobtained using the direct method. We also have observed a nonlinear effect thatcan become a source of significant errors. For the extremely accurate resultspresented here, we predict a [0001] GaN thermal conductivity of 185 $\rm{W/K\cdot m}$ at 300 K, 102 $\rm{W/K \cdot m}$ at 500 K, and 74 $\rm{W/K \cdot m}$at 800 K. Using the insights obtained in the work, we have achieved acorresponding error level (standard deviation) for the bulk (infinite samplelength) GaN thermal conductivity of less than 10 $\rm{W/K \cdot m}$, 5 $\rm{W/K\cdot m}$, and 15 $\rm{W/K \cdot m}$ at 300 K, 500 K, and 800 K respectively.

Towards More Accurate Molecular Dynamics Calculation of Thermal Conductivity. Case Study: GaN Bulk Crystals