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Efficient estimation of simulated radial distribution functions via spectral Monte Carlo



Thomas W. Rosch, Paul Patrone


Despite more than 40 years of active research in computational condensed-matter physics, state-of-the-art approaches for simulating radial distribution functions (RDFs) g(r) still rely on binning pair-separations into a histogram. Such representations suffer from undesirable properties, including high uncertainty and slow convergence. Moreover, such problems go undetected by the metrics often used to assess RDFs. To address these issues, we propose (I) a spectral Monte Carlo (SMC) method that yields g(r) as an analytical series expansion; and (II) a Sobolev-type norm that better assesses quality of RDFs by quantifying their fluctuations. Using the latter, we show that, as compared to histograms, SMC reduces both the noise in g(r) and the number of pair separations needed by orders of magnitude. Moreover, SMC yields simple, differentiable formulas for the RDF, which are useful for tasks such as force-field calibration via iterative Boltzmann inversion.
Physical Review Letters


Rosch, T. and Patrone, P. (2017), Efficient estimation of simulated radial distribution functions via spectral Monte Carlo, Physical Review Letters, [online], (Accessed June 24, 2024)


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Created March 5, 2017, Updated October 12, 2021