The thermodynamic behavior of planar hexagonal model molecules interacting through a 6- and 7-center Lennard-Jones potential is considered. The influence of molecular size on various thermodynamic properties is elucidated. It is shown that the second virial coefficients obey a microscopic scaling, which causes serious ambiguities for devising effective potential models for real substances. By use of a perturbation theory the vapor-liquid coexistence curves and the critical points are established. Some regularities of distinct properties on the pVT surface are found. The reduced coexisting curves can be used to obtain unambiguous potential parameters for real substances with hexagonal molecular scaffold by using only two experimental points. Thus, all results are rationalized by empirical correlations for easy use. For benzene as an example this procedure results in a model that reproduces vapor pressures and dew densities over two orders of magnitude. Bubble densities are given within a few percent and second virial coefficients are predicted within the experimental scatter throughout the measured temperature range.