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

Abstract

The molecular dynamics non-equilibrium direct method is a well-established way of predicting thermal conductivity , but in good thermal conductors such as crystalline semi-conductors it can yield unacceptably large statistical uncertainties in the extrapolation to a bulk system, . We show how to extract more information from the simulation data in order to reliably calculate tight confidence intervals for . We prove that the measurement error in for a single simulation of size L i and duration D i is proportional to D i L 3 i −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 L i D i which minimizes the probable measurement error in for given total computational effort. Overall, these improvements reduce by an order of magnitude the computational effort required to calculate with a given statistical uncertainty.

Comparison and Evaluation of Spectral Energy Methods for Predicting Phonon Properties

“…With the Green-Kubo or non-equilibrium direct methods, molecular dynamics (MD) simulations can be used to predict thermal conductivity, but only in a classical (i.e., high-temperature) framework [8,17,[24][25][26][27][28][29][30]. Because the analysis in these two MD-based methods is performed at the system level, no information about the phonons is obtained.…”

Predicting Phonon Properties From Equilibrium Molecular Dynamics Simulations

“…The Green-Kubo and direct methods can be applied to crystals, alloys, amorphous solids, and fluids. Recent work has focused on computational aspects, notably accounting for size effects, quantifying and reducing uncertainty, and reducing computational time [56,[61][62][63][64][65][66][67][68].…”

“…detailed suggestions on what system sizes to use and how long to run the simulations to optimize use of the direct method [65,66].…”