Ionized sodium clusters fragmentation channels:: A new extended hardness definition approach

We study the Na-N(+) (N <= 12) cationic clusters fragmentation channels, with all electronic calculations performed at the B3LYP/6-311+G(d,p) DFT level of theory. For these cluster sizes, we obtain for all the neutral, cationic, bi-cationic and anionic species the optimized geometries, total energies and electronic properties such as the adiabatic ionization potentials, electron affinities and global hardnesses. We propose the novel concept of global hardness change, Delta eta, within the conceptual DFT formalism, based on the maximum hardness principle of Chattaraj, Lee, and Parr. Thereafter we compute for all possible fragmentation channels the involved energetics, Delta Epsilon, and the global hardness change, Ail, both methods are shown to be in agreement with available experimental findings for all but one case. We show that hardness and the global hardness change are good DFT descriptors to assess the preferred fragmentation channels, where formation of the hardest fragments seems to be the driving force.