Conceptual DFT: chemistry from the linear response function

Within the context of reactivity descriptors known in conceptual DFT, the linear response function (chi(r,r')) remained nearly unexploited. Although well known, in its time dependent form, in the solid state physics and time-dependent DFT communities the study of the chemistry'' present in the kernel was, until recently, relatively unexplored. The evaluation of the linear response function as such and its study in the time independent form are highlighted in the present review. On the fundamental side, the focus is on the approaches of increasing complexity to compute and represent chi(r,r'), its visualisation going from plots of the unintegrated chi(r,r') to an atom condensed matrix. The study on atoms reveals its physical significance, retrieving atomic shell structure, while the results on molecules illustrate that a variety of chemical concepts are retrieved: inductive and mesomeric effects, electron delocalisation, aromaticity and anti-aromaticity, sigma and pi aromaticity,.... The applications show that the chemistry of aliphatic (saturated and unsaturated) chains, saturated and aromatic/antiaromatic rings, organic, inorganic or metallic in nature, can be retrieved via the linear response function, including the variation of the electronic structure of the reagents along a reaction path. The connection of the linear response function with the concept of nearsightedness and the alchemical derivatives is also highlighted.