Isomorph Invariance of Higher-Order Structural Measures in Four Lennard-Jones Systems.

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Computational chemistry

Background:

• Lennard-Jones (LJ) systems in the liquid phase approximate hidden scale-invariance symmetry.
• Isomorphs, lines of constant excess entropy, show approximate invariance in structure and dynamics.
• Previous studies primarily focused on the radial distribution function (RDF) for isomorph invariance.

Purpose of the Study:

• To investigate the isomorph invariance of higher-order structural correlations beyond the RDF.
• To analyze the variation of nearest-neighbor geometry along isomorphs in LJ systems.
• To assess the invariance of Voronoi structures, Frank-Kasper bonds, and icosahedral local order.

Main Methods:

• Simulation of single- and multicomponent Lennard-Jones systems.
• Identification and analysis of isomorphs in the thermodynamic phase diagram.
• Quantification of nearest-neighbor geometry using Voronoi tessellation and bond-orientational order parameters.

Main Results:

• Nearest-neighbor geometry, including Voronoi structures and local order, shows significant variation across the phase diagram.
• However, these geometric measures exhibit good invariance along isomorphs.
• This invariance holds for both the standard LJ system and binary LJ mixtures (Kob-Andersen, Wahnström, NiY2).

Conclusions:

• Higher-order structural correlations are approximately as isomorph invariant as the radial distribution function.
• Isomorph invariance extends beyond the RDF to encompass detailed nearest-neighbor geometric arrangements.
• The hidden scale-invariance symmetry provides a robust framework for understanding structural properties in liquid systems.