Rigid and Relaxed Diagonal Orbital Hardnesses of the Valence Shell of Transition Metal Ions from Xα Calculations

Valence shell diagonal hardnesses (electron repulsion) parameters are reported for the first- and second-row transition metal ions, determined via finite differences from the Xα eigenvalues for alternative configurations and charges. Both rigid (unrelaxed orbitals) and orbitally relaxed hardnesses have been calculated. The relaxed parameters provide a convenient basis for generating a realistic hardness tensor of catalytic systems involving transition metals at the atoms-in-molecules (AIM) oxidation state and configurations, thus facilitating the charge-sensitivity-analysis of chemisorption systems both at the AIM and orbital resolutions. The observed trends in the orbital relaxation effects are briefly discussed.