Polarizability and van der Waals radius: Two sides of the same coin

The atomic polarizability and the van der Waals (vdW) radius are two key quantities to describe
the vdW interaction in molecules and materials. Normally, they are determined separately from each
other. Based on the rigorous definition of the vdW radius [Bondi, J. Phys. Chem. 68, 441 (1964)],
we derive an analytic relation between these two quantities. The obtained expression, corroborated
by our analysis of the experimental data, is surprisingly different from the widely used direct
proportionality between the polarizability and the atomic volume. This leads to a revision of the
effective vdW radii of atoms in molecules, which are utilized in first-principles vdW approaches.
The unified determination of the vdW radius for all chemical elements in terms of their known
polarizabilities allows an easy parameterization of the repulsive exchange energy. This strongly
supports construction of efficient interatomic potentials, for instance, according to the modified
Tang-Toennies method [Tang et al., PRL 74, 1546 (1995)]. The remarkable nature of the derived formula
unveils a fundamental relationship between the geometric and electronic properties of atoms improving
our understanding of the subtle balance between attractive and repulsive forces on the atomistic level.