  Generation of equilibrium configurations is the major obstacle for numerical
investigation of the slow dynamics in supercooled liquid states. The parallel
tempering (PT) technique, originally proposed for the numerical equilibration
of discrete spin-glass model configurations, has recently been applied in the
study of supercooled structural glasses. We present an investigation of the
ability of parallel tempering to properly sample the liquid configuration space
at different temperatures, by mapping the PT dynamics into the dynamics of the
closest local potential energy minima (inherent structures). Comparing the PT
equilibration process with the standard molecular dynamics equilibration
process we find that the PT does not increase the speed of equilibration of the
(slow) configurational degrees of freedom.
