New insight into the topology of excited states through detachment/attachment density matrices-based centroids of charge

In parallel with the derivation of a novel descriptor (ø_S) related to chromophores' electronic excited states topology, the present article emphasizes some congruence of significance between our ø_Sindex and formerly developed centroid-related indices. We especially point out the possibility to formally adapt a barycenter (centroid) approach to the use of detachment/attachment densities. While the reciprocity of the two approaches can be mathematically evidenced, we will show that some difficulties brought by the use of ground and excited states electron densities in direct space can be overcome by undertaking some operations on the Hilbert space-related detachment/attachment matrices. We further wish to point out the crucial case of some chromophores holding two electron-withdrawing groups symmetrically disposed in a rod-like structure. Finally, we will qualitatively highlight the quadratic-like relationship between the amount of displaced charge induced by light absorption and the ø_Sindex.