Systematic ab initio calculations are combined with a deconvolution of electrostatic contributions to analyze the interplay between potential hydrogen bond acceptors and organic rings with C-sp2-H groups (benzene, pyridine and cyclopentadiene). A distinct anisotropic interaction between the ring systems and the electron lone pairs of cyanide, water and other acceptor species is revealed that favors the in-plane orientation of the proton acceptor group. In the attractive regime this interaction carries a pronounced electrostatic signature. By decomposing the electrostatic contribution into parts attributed to different subunits of the ring systems we demonstrate that a major proportion of the interaction energy gain is originating from the non-adjacent moieties, that are not in close contact with. This behavior holds equally for homocyclic, heterocyclic and non-aromatic rings but contrasts that of the ethyne molecule, taken as reference for a weak hydrogen bond donor clearly exhibiting the expected localized character. The ring interaction requires the presence of pi-electron clouds and typically results in an interaction energy gain of 40 to 80 meV. Our findings suggest the proton acceptor-ring interaction as a new category of intermolecular non-covalent interactions.