Perspective: Accurate ro-vibrational calculations on small molecules

Abstract: In what has been described as the fourth age of Quantum Chemistry, variational nuclear motion programs are now routinely being used to obtain the vibration-rotation levels and corresponding wavefunctions of small molecules to the sort of high accuracy demanded by comparison with spectroscopy. In this perspective I will discuss the current state-of-the-art which, for example, shows that these calculations are increasingly competitive with measurements or, indeed, replacing them and thus becoming the primary source of data on key processes. To achieve this accuracy {\it ab initio} requires consideration small effects, routinely ignored in standard calculations, such those due to quantum electrodynamics (QED). Variational calculations are being used to generate huge list of transitions which provide the input for models of radiative transport through hot atmospheres and to fill in or even replace measured transition intensities. Future prospects such as study of molecular states near dissociation, which can provide a link with low-energy chemical reactions, are discussed.