Beyond histograms: efficiently estimating radial distribution functions via spectral Monte Carlo

Area of Science:

• Condensed-matter physics
• Computational physics
• Materials science

Background:

• Current methods for simulating the radial distribution function (RDF), g(r), rely on histogramming pair-separations.
• These histogram-based approaches suffer from subjectivity, high uncertainty, and slow convergence.
• Existing metrics fail to detect these inherent problems in RDF calculations.

Purpose of the Study:

• To develop novel methods for accurate and efficient simulation of the radial distribution function (RDF).
• To introduce a quantitative metric for assessing the quality of RDF calculations.
• To overcome limitations of traditional histogram-based simulation techniques.

Main Methods:

• Proposed a spectral Monte Carlo (SMC) quadrature method to generate g(r) as an analytical series expansion.
• Introduced a Sobolev norm for quantifying fluctuations and assessing the quality of RDFs.
• Compared SMC performance against conventional histogram-based methods.

Main Results:

• SMC significantly reduces noise in g(r) by orders of magnitude compared to histogram methods.
• SMC requires substantially fewer pair separations for acceptable convergence.
• The Sobolev norm effectively quantifies RDF fluctuations, revealing issues missed by other metrics.

Conclusions:

• SMC provides a more objective, accurate, and efficient approach for simulating the radial distribution function.
• SMC yields differentiable RDF formulas, beneficial for applications like force-field calibration.
• The proposed methods address critical limitations in current condensed-matter physics simulations.