We investigated intermolecular interactions in weakly bonded Molecular assemblies from first principles, by combining exact exchange energies (EXX) with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the random phase approximation (RPA). We considered three different types of molecular systems: the benzene crystal, the methane crystal, and self-assembled monolayers of phenylenediisocyanide, which involve aromatic rings, sp(3)-hybridized C-H bonds, and isocyanide triple bonds. respectively. We describe in detail how computed equilibrium lattice constants and cohesive energies may be affected by the input ground state wave functions and orbital energies, by the geometries of Molecular monomers in the assemblies, and by the inclusion of zero-point energy contribution to the total energy. We find that the EXX/RPA perturbative approach provides all overall satisfactory, first-principles description of dispersion forces. However, binding energies tend to be underestimated, and possible reasons for this discrepancy are discussed.