The radii of atoms and ions can be defined and measured in a
variety of ways for different purposes. An individual
atom in the gas phase can be assigned a radius based on the
occupied orbitals and their wave functions, as has been presented
by Clementi (E. Clementi, D. L. Raimondi, and W. P. Reinhardt J.
Chem. Phys. 47, 1300-1307 (1967) "Atomic Screening Constants from
SCF Functions. II. Atoms with 37 to 86 Electrons").
Experimentally derived radii are defined so that the sum of radii
give the distance between atoms in compounds, typically as
solids. The radius thus depends on the strength of the
interaction between the two atoms as well as the elements or ions
involved. If the interaction involves only van der Waals
(induced dipole) interactions, then van der Waals radii are
obtained ( A. Bondi, J. Phys. Chem., 1964, 68, 441." van der Waals
Volumes and Radii"). These are typically the largest of the
experimental radii. For covalent interactions, the radius
decreases with the bond order between the atoms. Radii for
covalently bonded neutral atoms have been critically compiled from
thousands of experimental structures. (B. Cordero, V.
Gómez, A. E. Platero-Prats, M. Revés, J.
Echeverría, E. Cremades, F. Barragán and S. Alvarez
Dalton Trans., 2008, 2832-2838 "Covalent radii revisited").
Where there is a choice, the radius in this table is for a singly
bonded atom, e. g. sp3 hydbridized carbon. For ionic
interactions, the radius will depend on the charge, increasing
with the number of electrons, thus larger for anions and smaller
for cations. It also varies with the coordination number of
the ion and the spin state for transition metal ions. For
this table, a coordination numbere of 6 is used, and high spin
ions are chosen, using the "effective ionic radius" of Shannon (R.
D. Shannon, Acta Cryst., 1976, A32, 751-67. "Revised effective
ioinic radii and systematic studies of interatomic distances in
halides and chalcogenides").