The manner in which the intermolecular potential u(r) governs structural relaxation in liquids is a long standing problem in condensed matter physics. Herein, we show, in agreement with recent experimental results, that diffusion coefficients for simulated Lennard-Jones m-6 liquids (8 <= m <= 36) in normal and moderately supercooled states are a unique function of the variable p(gamma)/T, where p is density and T is temperature. The scaling exponent gamma is a material specific constant whose magnitude is related to the steepness of the repulsive part of u(r), evaluated around the distance of closest approach between particles probed in the supercooled regime. Approximations of u(r) in terms of inverse power laws are also discussed.
