A Gravitational-like\nRelationship of Dispersion Interactions\nis Exhibited by 40 Pairs of Molecules and Noble Gas Atoms

We present computational results of many-body dispersion\n(MBD)\ninteractions for 40 pairs of molecular and atomic species: hydrocarbons,\nsilanes, corresponding fluorinated derivatives, pairs which have multiple\nH---H contacts between the molecules, as well as pairs having π–π\ninteractions, and pairs of noble gases. The calculations reveal that\nthe MBD stabilization energy (<i>E</i><sub>DISP,MBD</sub>) obeys a global relationship, which is <i>gravitational-like</i>. It is proportional to the product of the masses of the two molecules\n(<i>M</i><sub>1</sub><i>M</i><sub>2</sub>) and\ninversely proportional to the corresponding distances between the\nmolecular centers-of-mass (<i>R</i><sub>COM‑COM</sub>) or the H---H distances of the atoms mediating the interactions\nof the two molecules (<i>R</i><sub>H–H</sub>). This\nrelationship reflects the interactions of instantaneous dipoles, which\nare formed by the ensemble of bonds/atoms in the interacting molecules.\nUsing the D4-corrected dispersion energy (<i>E</i><sub>DISP,D4</sub>), which accounts for three-body interactions, we find that the <i>E</i><sub>DISP,MBD</sub> and <i>E</i><sub>DISP,D4</sub> data sets are strongly correlated. Based on valence-bond modeling,\nthe dispersion interactions occur primarily due to the increased contributions\nof the oscillating-ionic VB structures which maintain favorable electrostatic\ninteractions; the [SubC<sup>+</sup>:H<sup>–+</sup>H:C<sup>–</sup>Sub] and [SubC:<sup>–+</sup>H <sup>–</sup>H:C<sup>+</sup>Sub] structures; Sub\nsymbolizes general residues. This augmented contribution is complemented\nby simultaneously diminished-weights of the destabilizing pair of\nstructures, [SubC<sup>+</sup>:H<sup>––</sup>H:C<sup>+</sup>Sub] and [Sub:C<sup>–</sup> H<sup>++</sup>H:C<sup>–</sup>Sub]. The local charges\nare propagated to the entire ensemble of bonds/atoms by partially\ncharging the Sub residues, thus bringing about the “gravitational-like”\ndependence of dispersion.