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This series of papers is devoted to identifying and explaining the propertiesof strongly correlating liquids, i.e., liquids with more than 90% correlationbetween their virial W and potential energy U fluctuations in the NVT ensemble.Paper IV [N. Gnan et al., J. Chem. Phys. v131, 234504 (2009)] showed thatstrongly correlating liquids have "isomorphs", which are curves in the phasediagram along which structure, dynamics, and some thermodynamic properties areinvariant in reduced units. In the present paper, using the fact thatreduced-unit radial distribution functions are isomorph invariant, we derive anexpression for the shapes of isomorphs in the WU phase diagram of generalizedLennard-Jones systems of one or more types of particles. The isomorph shapedepends only on the Lennard-Jones exponents; thus all isomorphs of standardLennard-Jones systems (with exponents 12 and 6) can be scaled onto to a singlecurve. Two applications are given. One is testing the prediction that thesolid-liquid coexistence curve follows an isomorph by comparing to recentsimulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellentagreement is found on the liquid side of the coexistence, whereas the agreementis worse on the solid side. A second application is the derivation of anapproximate equation of state for generalized Lennard-Jones systems bycombining the isomorph theory with the Rosenfeld-Tarazona expression for thetemperature dependence of potential energy on isochores. It is shown that thenew equation of state agrees well with simulations.

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems