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

Mahajabin Rahman, Benjamin Carter, Shibu Saw, Ian Michael Douglass, Lorenzo Costigliola, Trond Ingebrigtsen, Thomas Schrøder, Ulf Rørbæk Pedersen, Jeppe Dyre*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
Article number1746
Issue number6
Pages (from-to)1-18
Number of pages18
Publication statusPublished - 20 Mar 2021


  • Frank-Kasper bonds
  • Lennard-Jones system
  • Voronoi structures
  • bond-orientational order
  • density scaling
  • excess entropy
  • hidden scale invariance
  • icosahedral local order
  • isomorph invariance
  • Excess entropy
  • Bond-orientational order
  • Icosahedral local or-der
  • Hidden scale invariance
  • Density scaling
  • Isomorph invariance

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