The compression of all atoms has been modelled by changing the free-at
om boundary condition obeyed by electronic wavefunctions, from r lim/-
-> infinity, PSI(r) = 0 to r lim/--> r(o), PSI(r) = 0, r(o) < infinity
, in numerical Hartree-Fock-Slater calculations of electronic energy l
evels. As r(o) decreases, energy levels increase uniformly and by tran
sferring the excess energy, an electron escapes from the valence shell
when compression reaches a critical value of r(o), characteristic of
each atom. These ionization radii display remarkable periodicity, comm
ensurate with the known chemistry of the elements, and introduce a new
fundamental theoretical parameter that could serve to quantify chemic
al reactivity. Insofar as the compression of atomic wavefunctions occu
rs within crowded environments that lead to chemical interactions, ion
ization radii provide a more realistic index of the chemical propertie
s of atoms in the bulk, than ionization energies, which are more appro
priate in spectroscopic analyses of free atoms.