Abstract
The fine-structure constant (FSC) measures the coupling strength between photons and charged particles and is more strongly associated with quantum electrodynamics than with atomic and molecular physics. Here we present an elementary derivation that accurately predicts the electronic polarizability of atoms from their geometric van-der-Waals (vdW) radius RvdW and the FSC α through the compact formula = (4πε0/a04) × α4/3RvdW7, where ε0 is the permittivity of free space and a0 is the Bohr radius. The validity of this formula is empirically confirmed by estimating the value of α from nonrelativistic quantum calculations of atomic polarizabilities and atomic vdW radii obtained from both theory and experiment. Our heuristic derivation based on empirical data extends the influence of FSC from quantum electrodynamics and specific materials properties such as the visual transparency of graphene to atomic electronic properties throughout the periodic table of elements.
Highlights
The fine-structure constant (FSC) measures the coupling strength between photons and charged particles and is more strongly associated with quantum electrodynamics than with atomic and molecular physics
Α is used as a small parameter for perturbative corrections in calculations of field−matter interactions, which are typically expressed as a quickly convergent series in terms of powers of α
Expression is not used in practice since in nonrelativistic quantum mechanics c → ∞; α can be assumed to vanish.[5]
Summary
Owing to the statistical nature of vdW radii determined from crystal structures, higher uncertainties are expected for the transition metals possessing various spin states in crystalline compounds. This is the most likely reason for the increased deviations between obtained for. One just needs to determine the atomic polarizability Both quantities can be computed reliably from state-of-the-art quantum-chemical methods for closed-shell atoms.
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