The linear response kernel of conceptual DFT as a measure of aromaticity.

We continue a series of papers in which the chemical importance of the linear response kernel χ(r,r') of conceptual DFT is investigated. In previous contributions (J. Chem. Theory Comput. 2010, 6, 3671; J. Phys. Chem. Lett. 2010, 1, 1228; Chem. Phys. Lett. 2010, 498, 192), two computational methodologies were presented and it was observed that the linear response kernel could serve as a measure of electron delocalisation, discerning inductive, resonance and hyperconjugation effects. This study takes the analysis one step further, linking the linear response kernel to the concept of aromaticity. Based on a detailed analysis of a series of organic and inorganic (poly)cyclic molecules, we show that the atom-condensed linear response kernel discriminates between aromatic and non-aromatic systems. Moreover, a new quantitative measure of aromaticity, termed the para linear response (PLR) index, is introduced. Its definition was inspired by the recent work published around the para delocalisation index (PDI). Both indices are shown to correlate very well, which emphasises the linear response kernel's value in the theoretical description of aromaticity.