Density functional calculation of a characteristic atomic radius

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