van der Waals Radii of Free and Bonded Atoms From Hydrogen (Z=1) to Oganesson (Z=118)

Reliable numerical values of van der Waals (vdW) radii are required for constructing empirical force fields, vdW-inclusive density functional and quantum-chemical methods, as well as for implicit solvent models. However, multiple definitions exist for vdW radii, involving either equilibrium or closest contact distances between free or bonded atoms within molecules or crystals. For the paradigmatic case of hydrogen atom, its reported vdW radius fluctuates between 2.15 and 3.70 Bohr depending on the definition, leading to a high uncertainty in calculations and different conceptual interpretations of non-covalent interactions. In this work, we systematically review different definitions and methodologies to establish the free and bonded vdW radii for hydrogen, based on equilibrium vdW distances in non-covalently bonded molecules, enveloping electron density cutoffs, non-covalent positron bonds in hydrogen anion dimer, vacuum virtual photon cloud caused by the hydrogen atom, and atomic dipole polarizability. By doing so, we show that the vdW radius of free hydrogen atom is 3.16$\pm0.06$ Bohr. By employing the most general and elegant definition of atomic vdW radius as a function of the atomic polarizability, we tabulate consistent values of vdW radii for all atoms in the periodic table up to $Z=118$.