High Accuracy Rotation–Vibration Calculations on Small Molecules

High-resolution spectroscopy measures the transitions between energy levels with high accuracy; typically, uncertainties are in the region of 1 part in 108. Although it is possible, under favorable circumstances, to obtain this sort of accuracy by fitting effective Hamiltonians to observed spectra (see Bauder 2011: Fundamentals of Rotational Spectroscopy, this handbook), such ultrahigh accuracy is largely beyond the capabilities of purely ab initio procedures. Given this, it is appropriate to address the question of why it is useful to calculate the spectra of molecules ab initio (Tennyson 1992). The concept of the potential energy surfaces, which in turn is based on the Born–Oppenheimer approximation, underpins nearly all of gas-phase chemical physics. The original motivation for calculating spectra was to provide stringent tests of potential energy surfaces. As discussed in Section 5, this procedure has now been turned round and spectra can be used to construct or more commonly refine potential energy surfaces. The fact that spectra can be recorded with high accuracy does not necessarily mean that they are easy to interpret. The second motivation for first-principles calculation of spectra is to make predictions before any experiment and to aid with the assignment process afterward. A third reason is the analysis of spectra or, indeed, radiation transport models at high temperatures. The rotation–vibration spectra of even rather small molecules become very complicated at elevated temperatures. A