Presentation #218.01 in the session Laboratory Astrophysics (LAD) Division Meeting: Spectroscopy.
After a long period of diffidence, the strength of molecular diagnostics is now well recognized in Astronomy. My talk will briefly summarize the early stages of molecular astrophysics driven by the millimetric observational capabilities and the detection of molecular species that were yet unknown at the time, including radicals, reactive species and molecular ions. The present inventory of interstellar and circumstellar molecules includes more than 260 species without considering isotopic substitutions. Such a collection supplies an extensive number of multidisciplinary themes of interest to the LAD scientific community and provides essential clues to the present physical conditions. Amongst these, molecular hydrogen has a specific position, providing the mass reservoir of interstellar clouds and the main collisional excitation partner despite the fact that its direct observation is laborious and requires challenging techniques such as vacuum ultra violet or near to mid infra-red emission or absorption. Its presence is also a testimony of the presence of dust particles as no gas phase mechanism may account for its formation in the extremely low density conditions of the interstellar environment. Molecular hydrogen is, last but not least, a unique test case for theoretical quantum chemistry as that ‘simple’ two electrons system allows to solve the Schrödinger equation at an unprecedented accuracy. These different facets will be illustrated in the second part of my presentation devoted to the atomic to molecular transition in galaxy star-forming regions and the so-called Photon Dominated Regions (PDRs) . Isotopically substituted molecules, including D, 13C, 15N, bringing an additional viewpoint to the detailed chemical processes at work will be discussed furthermore with reference to the beautiful new detections performed at Yebes Observatory. My expectations for the future will conclude my presentation.  Abgrall et al. 1994, Can.J.Phys.72:856, Le Bourlot et al. 2012, A&A541:A76, Le Petit et al. 2006, ApJS164:506, Roueff et al. 2019, A&A630:A58, Sternberg et al. 2014, ApJ790:10, Ubachs et al. 2019, A&A622:A127  Agundez et al. 2021, A&A649:A71, Cabezas et al. 2021a, A&A646:L1, Cabezas et al. 2021b, A&A650, L15, Cabezas et al. 2022, A&A657:L5.