Two- and three-body interatomic dispersion energy contributions to binding in molecules and solids

We present numerical estimates of the leading two- and three-body dispersion energy terms in van der Waals interactions for a broad variety of molecules and solids. The calculations are based on London and Axilrod– Teller–Muto expressions where the required interatomic dispersion energy coefficients, C₆ and C₉, are computed "on the fly" from the electron density. Inter- and intramolecular energy contributions are obtained using the Tang–Toennies (TT) damping function for short interatomic distances. The TT range parameters are equally extracted on the fly from the electron density using their linear relationship to van der Waals radii. This relationship is empiricially determined for all the combinations of He–Xe rare gas dimers, as well as for the He and Ar trimers. The investigated systems include the S22 database of noncovalent interactions, Ar, benzene and ice crystals, bilayer graphene, C₆₀ dimer, a peptide (Ala₁₀), an intercalated drug-DNA model [ellipticine-d(CG)₂], 42 DNA base pairs, a protein (DHFR, 2616 atoms), double stranded DNA (1905 atoms), and 12 molecular crystal polymorphs from crystal structure prediction blind test studies. The two- and three-body interatomic dispersion energies are found to contribute significantly to binding and cohesive energies, for bilayer graphene the latter reaches 50% of experimentally derived binding energy. These results suggest that interatomic three-body dispersion potentials should be accounted for in atomistic simulations when modeling bulky molecules or condensed phase systems