Is there a one-to-one correspondence between interparticle interactions and physical properties of liquid?

TL;DR

This paper introduces a machine learning-based method to reconstruct interparticle potentials from structural data, revealing that multiple potentials can produce identical structures and dynamics in liquids, challenging the one-to-one structure-property assumption.

Contribution

The study presents a novel differential evolution algorithm approach to reconstruct interparticle potentials, demonstrating the non-uniqueness of structure-potential relationships in liquids.

Findings

Multiple potentials can reproduce the same liquid structure.

The family of potentials accurately predicts transport and dynamic properties.

No one-to-one correspondence exists between structure and interaction potential.

Abstract

In this study, we present the original method for reconstructing the potential of interparticle interaction from statistically averaged structural data, namely, the radial distribution function of particles in many-particle system. This method belongs to a family of machine learning methods and is implemented through the differential evolution algorithm. As demonstrated for the case of the Lennard-Jones liquid taken as an example, there is no one-to-one correspondence between structure and potential of interparticle interaction of a many-particle disordered system at a certain thermodynamic state. Namely, a whole family of the Mie potentials determined by two parameters $p_{ 1 }$ and $p_{ 2 }$ related to each other according to a certain rule can reproduce properly a unique structure of the Lennard-Jones liquid at a given thermodynamic state. It is noteworthy that this family of the potentials quite correctly reproduces for the Lennard-Jones liquid the transport properties (in particular, the self-diffusion coefficient) over a temperature range as well as the dynamic structure factor, which is one of the key characteristics of the collective dynamics of particles.