2020/07/06 by Tkatchenko, Alexandre, Fedorov, Dmitry V.
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2007.02992
We examine the recently derived quantum-mechanical relation between atomic polarizabilities and equilibrium internuclear distances in van der Waals (vdW) bonded diatomic systems [Phys. Rev. Lett. \bf 121, 183401 (2018)]. For homonuclear dimers, this relation is described by the compact formula α\rm m\rm q = ΦR\rm vdW7, where the constant factor in front of the vdW radius was determined empirically. Here, we derive Φ= (4πε0/a04) × α4/3 expressed in terms of the vacuum electric permittivity ε0, the Bohr radius a0, and the fine-structure constant α. The validity of the obtained formula is confirmed by estimating the value of the fine-structure constant from non-relativistic quantum-mechanical calculations of atomic polarizabilities and equilibrium internuclear vdW distances. The presented derivation allows to interpret the fine-structure constant as the ratio between the polarizability densities of vacuum and matter, whereas the vdW radius becomes a geometrical length scale of atoms endowed by the vacuum field.