Abstract
A hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev's table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge 3<or=Z<or=103, using the best single configuration electron density functions available. Different hardness kernels were used and the importance of the different contributions to the kernel was investigated. The atomic self-similarities constructed in this way show a fair correlation with experimental atomic polarizability.
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