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 (<i>E</i>_DISP,MBD) obeys a global relationship, which is <i>gravitational-like</i>. It is proportional to the product of the masses of the two molecules (<i>M</i>₁<i>M</i>₂) and inversely proportional to the corresponding distances between the molecular centers-of-mass (<i>R</i>_COM-COM) or the H---H distances of the atoms mediating the interactions of the two molecules (<i>R</i>_H-H). 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 (<i>E</i>_DISP,D4), which accounts for three-body interactions, we find that the <i>E</i>_DISP,MBD and <i>E</i>_DISP,D4 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⁺:H^-+H: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⁺:H^--H:C⁺─Sub] and [Sub─:C^- H⁺⁺H: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.