A "universal" dependence is predicted of the reduced critical parameters, k
BTc/E0(gamma), Vc/V0(gamma), and P-c/V-c/k(B)T(c). = Z(c)(gamma), on the cr
ystal anharmonicity gamma (closely related to the Gruneisen parameter Gamma
(G)) It is based on a simplified embedded-atom type approach which enables
one to utilize the universal zero-temperature equation of state in a versio
n of fluid perturbation theory. This model's critical temperature and densi
ty agree with the experimental results for both the heavy rare gases (gamma
similar or equal to 2.85) and heavy alkali metals (gamma similar or equal
to 1.35). Predicted critical parameters for many other Liquid metals are co
nsistent with previous estimates, but the model is not applicable when dire
ctional bonding is important.