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

Abstract: In the condensed liquid phase, both single- and multicomponent Lennard–Jones (LJ) systems
obey the “hidden-scale-invariance” symmetry to a good approximation. Defining an isomorph
as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate
isomorph invariance of structure and dynamics in appropriate units is well documented.
However, although all measures of the structure are predicted to be isomorph invariant, with few
exceptions only the radial distribution function (RDF) has been investigated. This paper studies the
variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi
structures, Frank–Kasper bonds, icosahedral local order, and bond-orientational order. Data are
presented for the standard LJ system and for three binary LJ mixtures (Kob–Andersen,Wahnström,
NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout
the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order
structural correlations are no less isomorph invariant than is the RDF.