The interaction of benzene with a Ag(111) surface has been determined using reliable ab initio electronic structure calculations. The results are compared to a recent detailed analysis of the interaction of benzene with copper and gold surfaces, thus making it possible to derive a consistent picture for the electronic structure changes encountered when benzene is brought into contact with the densely packed coinage metal surfaces. To avoid the problems encountered when the presently most frequently employed computational approach, density functional theory (DFT), is applied to adsorbate systems where dispersion (or van der Waals) forces contribute substantially, we use a wavefunction-based approach. In this approach, the weak van der Waals interactions, which are dominated by correlation effects, are described using second-order perturbation theory. The surface dipole moment and the work function changes induced upon adsorption are also discussed.