Theoretical insights into the topology of molecular excitons from single-reference excited states calculation methods

This chapter gives an introduction to qualitative and quantitative topological analyses of molecular electronic transitions. Among the possibilities for qualitatively describing how the electronic structure of a molecule is reorganized upon light-absorption, we chose to detail two of them, namely the detachment/attachment density matrix analysis and the natural transition orbitals strategy. While these tools are often introduced separately, we decided to formally detail the connection existing between the two paradigms in the case of excited states calculation methods expressing any excited state as a linear combination of singly excited Slater determinants, written based on a single-reference ground state wave function. In this context, we show how the molecular exciton wave function plays a central role in the topological analysis of the electronic transition process.