Various forms of interionic pair potentials such as the Lennard-Jones, the soft core and the gaussian core have been adopted in the literature to characterize monatomic systems and used in computer simulation studies of the liquid-glass transition. Although the final amorphous structures have generally been produced, there is as yet no detailed account of the structural relation between these different pair potentials and the microscopic process of the liquid-glass transition. In this work, in contrast with the potentials mentioned above, we use mmetallic pair potentials constructed from a non-local model pseudopotential derived from first principles. By choosing pair potentials of varying softness, we present the results of Monte Carlo temperature-quench simulations for the pair distribution functions of chromium, yttrium, zirconium and alkali metal monatomic systems. We find that the softness of the interionic pair potentials of these systems exhibits an interesting correlation with the Wendt-Abraham parameter (Phys. Rev. Lett., 41 (1978) 1244) vs. temperature.