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One of the fundamental problems in few-body physics is the formation of diatomic molecules in three-atom collisions. An experimental technique now explores the resulting distribution of molecular quantum states in an ultracold gas.

Achieving full control over all internal and external degrees of freedom of a molecule has been a long-standing goal in molecular physics. Newly developed methods to prepare translationally, vibrationally and rotationally cold molecular ions have brought this target one step closer.

In quantum-logic spectroscopy schemes, the internal state of an atom or molecule without easily accessible closed-cycling transitions is projected onto a co-trapped atom that serves as a probe. Here, the authors investigate the effect of the motion of trapped ions on the state detection of a single nitrogen molecular ion with such a scheme.

Identifying a concerted or stepwise mechanism in Diels–Alder reactions is experimentally challenging. Here the authors demonstrate the coexistence of both mechanisms in the reaction of 2,3-dibromobuta-1,3-diene with propene ions, using a conformationally controlled molecular beam reacting with trapped ions and ab initio computations

The identification of molecular quantum states becomes challenging with increasing complexity of the molecular level structure. Here, the authors non-destructively identified excited molecular states of the \({{\rm{N}}}_{2}^{+}\) by interfering forces applied to both the molecular ion and to a co-trapped atomic ion.

Water molecules exist as two distinct nuclear-spin isomers denoted ortho and para. Here, the authors separate these two isomers in the gas phase to show that they exhibit different reactivities in a prototypical proton-transfer reaction.

Studies on reactions between cold molecular ions and neutral atoms provide insights into intermolecular interactions. Here the authors explore the kinetics and dynamics of charge-transfer collisions between the cold N\({}_{2}^{+}\) and O\({}_{2}^{+}\) ions and neutral Rb atoms and discuss the role of long- and short-range effects.

Molecular geometry can influence chemical reactivity through several opposing effects. By selecting individual conformers of hydroquinone in the chemi-ionization reaction with metastable neon, it is now shown that reaction pathways can be governed by molecular alignment due to geometry-dependent forces that are, however, countered by molecular rotation.

Dipole-forbidden vibrational transitions in molecular ions are very weak and difficult to characterize. The sympathetic cooling provided by a Coulomb crystal is shown to allow interrogation times long enough to observe them.

Molecular ions and hybrid platforms that integrate cold trapped ions and neutral particles offer opportunities for many quantum technologies. This Review surveys recent methodological advances and highlights in the study of cold molecular ions.

Prospects for new applications in quantum simulations, spectroscopic precision measurements and very low temperature physics and chemistry have resulted in significant advances in the study of cold molecules, with their trapping for long times remaining a major challenge. The authors present an experiment in which polar molecular radicals produced by Stark deceleration are magnetically trapped for a time of order 20 s providing an improvement of up to two orders of magnitude over room temperature experiments.