To understand the intermolecular interactions between chalcogen centers (O, S, Se, Te), quantum chemical calculations on pairs of model systems were carried out. For the oxygen derivatives, one of the components of the supermolecules consists of dimethyl ether, while the second component is either dimethyl ether (1) or ethynyl methyl ether (2) or methyl cyanate (3). The model calculations were also extended to the sulfur (4-6), selenium (7-9), and tellurium congeners (10-12). The MP2/SDB-cc-pVTZ, 6-311G* level of theory was used to derive the geometrical parameters and the global energies of the model systems. A detailed analysis based on symmetry adapted perturbation theory (SAPT) reveals that induction and dispersion forces contribute to the bonding in each case. For 1-3 the electrostatic energy also contributes to the intermolecular bonding, but not for 4-12. The NBO analysis reveals that the interaction in the dimers 1-3 is mainly due to weak hydrogen bonding between methyl groups and chalcogen centers. Similar hydrogen bonding is also found in the case of 4 and to a lesser extent in 5 and 7. For the aggregates with heavier centers the chalcogen-chalcogen interaction dominates, and hydrogen bonding only plays a minor role. Electron-withdrawing groups on the chalcogen centers increase the interaction energy and reduce the intermolecular distance dramatically. The one-electron picture of an interaction between the lone pair of the donor and the chalcogen carbon sigma* orbital allows a qualitatively correct reproduction of the observed trend.