Interpolation method for pair correlation function from two-dimensional crystals to three-dimensional liquids
Artur D. Nasyrov 1, Nikita P. Kryuchkov 1
Abstract
The pair correlation function g(r) is a key structural characteristic of condensed matter, widely used in the analysis of liquids, crystals, and complex systems. Knowledge of pair correlations is essential for describing metals, colloidal dispersions, complex plasmas, ionic microgels, and for accurate modeling of phase transitions. In systems with pair interactions, g(r) provides direct access to thermodynamic quantities such as energy and pressure through the virial equation.
Theoretical calculation of g(r) is a challenging task because it involves solving the integral Ornstein–Zernike (OZ) equations with, in most cases, an unknown closure relation. To address this, interpolation approaches have been developed, based on the decomposition of g(r) into individual correlation peaks. Such methods allow for accurate reproduction of g(r) for both crystalline and liquid phases, including active and biological systems, while maintaining computational efficiency.
In this work, it is shown that the interpolation method can also be applied to reconstructing the pair correlation function of a bulk liquid system from data obtained in a finite system. By decomposing g(r) in the finite system into correlation peaks, and then normalizing the peaks with respect to their norm and mean distance, it was found that their shape remains universal, as in the bulk phase. This universality enables reconstruction of the bulk pair correlation function from finite-system results.
Speaker
Artur D. Nasyrov
Bauman Moscow State Technical University, 2nd Baumanskaya street 5, 105005 Moscow, Russia
Russia
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