Atomic interaction lines and (3,-1) critical points were located in the intermoleclar regions of a total of 36 configurations of 11 van der Waals dimers and a trimer, none of which contain a-hydrogen bond. The complexes comprised combinations of five moieties : argon atoms and the molecules C2H2, CO2, OCS, and SO2. Atomic interaction Lines in the intermolecular region denote the dominant atom-atom interactions underlying the weak interactions, The set of complexes allows us to draw conclusions about the role of the intermolecular charge density in binding. We find that the values of the charge density and its principal axes of curvature at intermolecular critical points in these systems are an order of magnitude less than those found in hydrogen-bonded systems and that the (3,-1) critical points display the hallmarks of "closed-shell" interactions. The strong correlation between the value of rho at a bond critical point and the binding energy of the complex that has been found previously for hydrogen-bonded systems is harder to expose with the van der Waals molecules presented here. For example, comparison must be restricted to structures in which the same pairs of atoms are interacting. We find that "conflict structures" may be associated with both equilibrium and transition state conformations but that significant nonrigidity is usually a consequence. We are able to make some predictions concerning the likely occurrence of intermolecular critical points in systems larger than those described here.