Theoretical methods for small-molecule ro-vibrational spectroscopy

Abstract

The solution of the first principle equations of quantum mechanics provides an increasingly accurate and predictive approach for solving problems involving atoms and small molecules. A general introduction to the methods used for the ab initio calculation of rotational–vibrational spectra of small molecules is presented, with a strong focus on triatomic systems. The use of multi-reference electronic structure methods to compute molecular potential-energy and dipole-moment surfaces is discussed. Issues related to the construction of such surfaces and the inclusion of corrections due to relativistic and non-Born–Oppenheimer effects are reviewed. The derivation of exact, internal-coordinate nuclear-motion-effective Hamiltonians and their solution using a discrete-variable representation are discussed. Sample results for the water molecules are used throughout the tutorial to illustrate the theoretical and numerical issues in such calculations.

A database of water transitions from experiment and theory (IUPAC Technical Report)

“…Conversely, there has been significant progress in developing methods for computing the one-photon intensity of water molecules using approaches based on the application of first-principles quantum chemistry [28]. These methods rely on constructing high-accuracy dipole moment surfaces (DMSs) [108][109][110], which are then combined with calculated rotation-vibration wavefunctions to obtain transition dipoles and hence intensities.…”

“…The rotation-vibration energy levels of water have also proved to be an important testing ground for theoretical models [22][23][24][25][26][27][28] and semiclassical theories of molecular structure [29][30][31]. For example, studies have shown that the highly rotationally excited states of water appear not to form the expected four-fold clusters, although the reason for this is not entirely understood [30], but that its energy levels do indeed re-arrange about a so-called monodromy point at linearity [32].…”

The dipole moment surface for hydrogen sulfide H2S

“…The aim of the present study is to produce a systematically improved DMS for H 2 S building on the experience gained from our recent studies on the water molecule [15][16][17], see Lodi and Tennyson [18] for a general discussion. These studies have resulted in a DMS surface, LTP2011 [17], which has been shown in a number of studies of being capable of predicting transition intensities with an uncertainty close to 1% for the majority of lines [17,19,20].…”

Perspective: Accurate ro-vibrational calculations on small molecules

“…128,129 Amongst the theoreticians is a certain consensus on how best to perform such calculations. There are reviews available detailing how to compute accurate rotationvibration line lists, 130,131 so here I will just give a few examples which illustrate strategic issues. Figure 3 illustrates the results achievable by comparing the computed spectrum of H 2 O 2 with measured spectra currently available in the HITRAN database: 132 the main source of spectroscopic data for atmospheric models.…”