A quadratic Euler-Lagrange equation has been solved self-consistently
for defining two types of radii for atoms which match closely with exp
erimental covalent radii. The calculated radii values are either bette
r than or comparable to any hitherto known calculated radii values. Ex
cellent correlations have been observed between these radii values and
other physical properties like softness, ionisation potential, electr
onegativity etc. in the vertical groups of the periodic table and the
trends are found to match with that predicted by experimental covalent
radii.