Providing a quantitative insight into light-induced electronic structure reorganization of com- plex chromophores remains a challenging task that has attracted a substantial attention from theoretical communities in the past few years. Indeed, a potential knowledge related to the abil- ity of a chromophore to undergo a charge transfer caused by photon absorption or emission is of seminal importance for designing novel dyes with highly competitive optoelectronic properties. These target systems are at the center of the main societal issues of our time such as public health with anti-cancer phototherapy, sustainable energy with high-performance solar cells, or homeland security with explosive probes for example. In this context, we elaborated systematic and tractable strategies for qualitatively and quantitatively assessing the electronic cloud po- larization of complex molecular structures upon a transition to or from electronic excited states and improve our understanding of the electronic transition process[1, 2, 3]. In addition to providing a clear picture of complex charge transfer processes, our topological metrics are able to act as reliable diagnostic instruments for the exchange-correlation functionals used within the time-dependent density functional theory framework, and therefore constitute a precious tool for computational chemists. After introducing the theoretical elaboration of our strategy and applying it to the aforementioned hot topics, this contribution will detail for the first time the generalization of our topological analyses to fully relaxed excited states density matrices including the so-called Z-vector. Finally, the way our developments allowed us to unravel the physical nature of Handy’s Z-vector itself [4] will be reported.