A Qualitative Index of Spatial Extent in Charge-Transfer Excitations

With the aim of defining the spatial extent associated to an electronic transition, of particular relevance in the case of charge-transfer (CT) excitations, a new index, evaluated only from the computed density for the ground and excited state, is here derived and tested on a family of molecules that can be considered as prototypes of push-pull chromophores.The index (DCT) allows to define the spatial extent associated to a given transition as well as the associated fraction of electron transferred. By definition of centroids of charges associated to the density increase and depletion zones upon excitation, a qualitative and easy to visualize measure of the spatial extent of the donor and the acceptor moieties within a given molecular system is also given. Finally, an index (t) allowing to define the presence eventually pathologic CT transitions for time-dependent density functional theory treatment in conjunction with standard generalized gradient approximation or hybrid functional, that is through space CT, is disclosed.