A Gravitational-like Relationship of Dispersion Interactions is Exhibited by 40 Pairs of Molecules and Noble Gas Atoms.

We present computational results of many-body dispersion (MBD) interactions for 40 pairs of molecular and atomic species: hydrocarbons, silanes, corresponding fluorinated derivatives, pairs which have multiple H---H contacts between the molecules, as well as pairs having π-π interactions, and pairs of noble gases. The calculations reveal that the MBD stabilization energy () obeys a global relationship, which is . It is proportional to the product of the masses of the two molecules () and inversely proportional to the corresponding distances between the molecular centers-of-mass () or the H---H distances of the atoms mediating the interactions of the two molecules (). This relationship reflects the interactions of instantaneous dipoles, which are formed by the ensemble of bonds/atoms in the interacting molecules. Using the D4-corrected dispersion energy (), which accounts for three-body interactions, we find that the and data sets are strongly correlated. Based on valence-bond modeling, the dispersion interactions occur primarily due to the increased contributions of the oscillating-ionic VB structures which maintain favorable electrostatic interactions; the [Sub─C:HH:C─Sub] and [Sub─C:H H:C─Sub] structures; Sub symbolizes general residues. This augmented contribution is complemented by simultaneously diminished-weights of the destabilizing pair of structures, [Sub─C:HH:C─Sub] and [Sub─:C HH:C─Sub]. The local charges are propagated to the entire ensemble of bonds/atoms by partially charging the Sub residues, thus bringing about the "gravitational-like" dependence of dispersion.