here α fsc is the fine-structure constant, ϵ 0 is the permittivity of free space, and a 0 is the Bohr radius. The numerical value of the prefactor in the above equation was initially found by fitting the scaling law using reference dipole polarizabilities and the equilibrium vdW radii of Batsanov. Therefore, using the well-known exact polarizability of the hydrogen atom of 9/2 a.u. (see for example Ref. 64) and the inverse of Eq. 4, we obtain a free hydrogen vdW radius of 3. 16 Bohr. Yet another approach to define the vdW radius of free atoms is to employ first principles of quantum electrodynamics (QED) for an atom interacting with the everpresent electromagnetic field. An atom spontaneously emits and absorbs radiation, with the equilibrium state of the atom-field system only achieved for large enough timescales. Hence, at any given instant the atom is surrounded by a cloud of virtual photons. The properties of this photon cloud can be calculated from QED. Such calculations are rather involved, but they have been carried out for hydrogen by Passante and collaborators. In particular, the radius of the photon cloud (in the elec-FIG. . Recommended values for free atomic van der Waals radius (in Bohr) for elements Z = 1 to Z = 118, obtained from the recommended dipole polarizabilities compiled in reference 85 by using Equation . Estimated uncertainties in parentheses. 3.70 tromagnetic field reference frame) for the dominant 1s-2p transition of hydrogen atom is R ph = 2πc E1s-2p ≈ 2297 Bohr, where c is the speed of light and E 1s-2p is the 1s-2p transition energy. To transform this radius to the atomic reference frame, one needs to multiply R ph by α 4/3 fsc , as explained in Ref. . This yields a radius of 3.25 Bohr.