  Supercooled liquids are characterized by relaxation times that increase
dramatically by cooling or compression. Many liquids have been shown to obey
power-law density scaling, according to which the relaxation time is a function
of density to some power over temperature. We show that power-law density
scaling breaks down for larger density variations than usually studied. This is
demonstrated by simulations of the Kob-Andersen binary Lennard-Jones mixture
and two molecular models, as well as by experimental results for two van der
Waals liquids. A more general form of density scaling is derived, which is
consistent with results for all the systems studied. An analytical expression
for the scaling function for liquids of particles interacting via generalized
Lennard-Jones potentials is derived and shown to agree very well with
simulations. This effectively reduces the problem of understanding the viscous
slowing down from being a quest for a function of two variables to a search for
a single-variable function.
