van der Waals Radii\nof Free and Bonded Atoms from\nHydrogen (Z = 1) to Oganesson (Z = 118)

Reliable numerical values of van der Waals (vdW) radii\nare required\nfor constructing empirical force fields, vdW-inclusive density functional,\nand quantum-chemical methods, as well as for implicit solvent models.\nHowever, multiple definitions exist for vdW radii, involving either\nequilibrium or the closest contact distances between free or bonded\natoms within molecules or crystals. For the paradigmatic case of the\nhydrogen atom, its reported vdW radius fluctuates between 2.15 and\n3.70 Bohr depending on the definition, leading to a high uncertainty\nin calculations and different conceptual interpretations of noncovalent\ninteractions. In this work, we systematically review different definitions\nand methodologies to establish the free and bonded vdW radii for hydrogen,\nbased on equilibrium vdW distances in noncovalently bonded molecules,\nenveloping electron density cutoffs, noncovalent positron bonds in\nhydrogen anion dimer, vacuum virtual photon cloud caused by the hydrogen\natom, and atomic dipole polarizability. By doing so, we show that\nthe vdW radius of the free hydrogen atom is 3.16 ± 0.06 Bohr.\nBy employing the most general and elegant definition of atomic vdW\nradius as a function of the atomic polarizability, we tabulate consistent\nvalues of vdW radii for all atoms in the periodic table up to <i>Z</i> = 118.