  We show that a number of model liquids at fixed volume exhibit strong
correlations between equilibrium fluctuations of the configurational parts of
(instantaneous) pressure and energy. We present detailed results for thirteen
systems, showing in which systems these correlations are significant. These
include Lennard-Jones liquids (both single- and two-component) and several
other simple liquids, but not hydrogen-bonding liquids like methanol and water,
nor the Dzugutov liquid which has significant contributions to pressure at the
second nearest neighbor distance. The pressure-energy correlations, which for
the Lennard-Jones case are shown to also be present in the crystal and glass
phases, reflect an effective inverse power-law potential dominating
fluctuations, even at zero and slightly negative pressure. An exception to the
inverse-power law explanation is a liquid with hard-sphere repulsion and a
square-well attractive part, where a strong correlation is observed, but only
after time-averaging. The companion paper [arXiv:0807.0551] gives a thorough
analysis of the correlations, with a focus on the Lennard-Jones liquid, and a
discussion of some experimental and theoretical consequences.
