Extensive DFT calculations for free radicals containing atoms of the second and third row show that the PBE0/N07D computational model provides remarkably accurate magnetic properties at reasonable computational costs. The key of this success is the optimization of core-valence s functions for hyper. ne coupling constants, while retaining ( and even improving) the good performances of the parent 6-31+G(d, p) basis set for valence properties through re-optimization of polarization and diffuse p functions. (c) 2008 Elsevier B. V. All rights reserved.