Progress and challenges in the calculation of electronic excited states.

A detailed understanding of the properties of electronic excited states and the reaction mechanisms that molecules undergo after light irradiation is a fundamental ingredient for following light-driven natural processes and for designing novel photonic materials. The aim of this review is to present an overview of the ab initio quantum chemical and time-dependent density functional theory methods that can be used to model spectroscopy and photochemistry in molecular systems. The applicability and limitations of the different methods as well as the main frontiers are discussed. To illustrate the progress achieved by excited-state chemistry in the recent years as well as the main challenges facing computational chemistry, three main applications that reflect the authors' experience are addressed: the UV/Vis spectroscopy of organic molecules, the assignment of absorption and emission bands of organometallic complexes, and finally, the obtainment of non-adiabatic photoinduced pathways mediated by conical intersections. In the latter case, special emphasis is put on the photochemistry of DNA. These applications show that the description of electronically excited states is a rewarding but challenging area of research.