This work comprises two main and independent purposes:(1) A new four-parameter model is proposed for the description of self-diffusion coefficients of polar, nonspherical and even hydrogen-bonding substances. It gives accurate results over wide ranges of temperature and pressure (AAD = 4.45%; 2471 data points). This equation is devised from an extension of a Lennard-Jones fluid model embodying the van der Waals model approach.(2) Generalized correlations are suggested for the estimation of the Lennard-Jones force constants (energy and diameter) of a two-parameter equation. From these it is possible to predict tracer diffusivities with satisfactory results, by means of simple combining rules.