On the quality of the hardness kernel and the Fukui function to evaluate the global hardness

An approximated hardness kernel, which includes the second derivative with respect to the density of the kinetic energy, the electron-electron coulomb repulsion, and the exchange density functionals, has been tested for the calculation of the global hardness. The results obtained for a series of 40 cations and neutral systems and 16 anions represent in most cases an improvement of the results obtained using the HOMO-LUMO gap approach and indicate the viability of this approach to evaluate global hardness. In addition, the relevance of the Fukui function approximation and the role of the three components of the hardness kernel in the evaluation of the global hardness have been analyzed.