Molecular spectroscopy techniques are unique tools to probe molecular systems non-invasively and investigate their structure, properties, and dynamics in different environments and physicochemical conditions. Different spectroscopic techniques and their combination can lead to a more comprehensive picture of investigated systems. However, the increasing sophistication of these experimental techniques makes it more and more complex and difficult to interpret the results without the help of computational chemistry. As a consequence, computational molecular spectroscopy has progressively changed from a highly specialized field to a general tool also employed by experimentally-oriented researchers. Computational spectroscopy, born as a branch of quantum chemistry for providing predictions of spectroscopic properties and features, evolved as an independent field. In this Primer, we focus on the characterization of medium-sized molecular systems by means of different spectroscopic techniques. We first provide essential information about the characteristics, accuracy and limitations of the available computational approaches, and select examples with the aim of illustrating general trends, that is outcomes of general validity that can be used for modeling spectroscopic phenomena. We emphasize the need for estimating error bars and limitations, coupling accuracy with interpretability, and discuss the results in terms of widely recognized chemical concepts.

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Cosmic evolution is the tale of progressive transition from simplicity to complexity. The newborn universe starts with the simplest atoms formed after the Big Bang and proceeds toward ‘astronomical complex organic molecules’ (astroCOMs). Understanding the chemical evolution of the universe is one of the main aims of Astrochemistry, with the starting point being the knowledge whether a molecule is present in the astronomical environment under consideration and, if so, its abundance. However, the interpretation of astronomical detections and the identification of molecules are not all straightforward. In particular, molecular species characterized by large amplitude motions represent a major challenge for molecular spectroscopy and, in particular, for computational spectroscopy. More in general, for flexible systems, the conformational equilibrium needs to be taken into account and accurately investigated. It is shown that crucial challenges in the computational spectroscopy of astroCOMs can be successfully overcome by combining state‐of‐the‐art quantum‐mechanical approaches with ad hoc treatments of the nuclear motion, thus demonstrating that the rotational and vibrational features can be predicted with the proper accuracy. The second key step in Astrochemistry is understanding how astroCOMs are formed and how they chemically evolve toward more complex species. The challenges in the computational chemistry of astroCOMs are related to the derivation of feasible formation routes in the typically harsh conditions (extremely low temperature and density) of the interstellar medium, as well as the understanding of the chemical evolution of small species toward macromolecules. Within the transition state theory, for instance, it is possible to obtain new astrochemical information by identifying the intermediate species and transition states connecting them in a plausible formation route. Depending on the sophistication of the model, different quantities may be needed. Nevertheless, accuracy can be critical, thus requiring state‐of‐the‐art computational approaches to derive geometries, energies, spectroscopic properties, and thermochemical data for each relevant structure along the reaction path. This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

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