UNIVERSITY OF COLOGNE

Well, there are different answers to this question:

We're just curious in not just measuring, but also understanding molecules. In fact, molecular physics helps a lot to understand the heuristics found by chemistry and also approach problems from a physicist's point of view which are still puzzling chemists. This is why there is a lively interdiciplinary collaboration not only with chemists but also with meteorologists being interested in the chemistry of our atmosphere.
Decent understanding of the existing models of molecular physics and development of new models is not only useful to understand the molecules themselves but also requires deep understanding of basic concepts of physics a lot of people just skate over by "shut up and calculate" (Feynman). To further develop the models of molecules we really have to understand symmetry in physics, rotations in quantum mechanics, spin, quasi-particles etc. good enough to explain them to children.
A lot of the research of our group aims at enabling astronomers to make sense of their observations. Most of the information provided by different lab groups around the world is therefore collected in the CDMS [link] hosted in Cologne. Indeed, to identify molecules in space you just need experimental spectra from lab to be compared with spectra from astronomy (fingerprint principle). But in fact, the observed spectra convey a lot more information than just the existence of a molecule. They also include information about density, temperature, pressure and so on. To extract these information the experimental fingerprint is not enough but you need to set up the partition function of the molecule. To do so, the energy of the molecular states is needed which is not directly accessible by measurements. (The energy of the transition between molecular states can be measured, not the energies of the states themselves. As the transition energies can be easily calculated from the energies of the states, the other direction is not trivial.)
Approaches
Symmetries
If a physical description is to complicated the first thought is often to try an approximation appropriate to your question (i.e. you're only interested in a certain regime or in a specific feature of the system). However, this is just the second best approach. Using symmetry to simplfy your description is preferable as you avoid the errors of an approximation. In fact, it is very common to do both, i.e. choose polar coordinates for a problem with rotation symmetry resulting in an equation of motion for two angles instead of three carthesian coordinates and then do an approximation of the still challenging equation of motion for the angles. Numeric simulations as i.e. done in our carbon cluster subgroup [link] typically also require to simplfy the problem using symmetries first.

In view of this, our goal is to not only use the obvious symmetries like rotations, but also involve representation theory (a subarea of mathematics) to make use of "hidden symmetries".

It is also a playground to approach chemical reactions in future:

Our understanding of chemical reactions is mainly based on conservation laws and selection rules based thereof (The number of electrons of the left hand side of the reaction equation must equal that on the right hand side). As there is a strong link between symmetries and conservation laws (-> Noether's Theorem) better understanding of molecular symmetries also means better understanding of selection rules, not only for molecular transitions, but also for chemical reactions.
For the long-term plan to observe chemical reactions and understand reaction dynamics it's crucial to not only understand molecules but also intermediates obviously having no fixed geometry.
How far can we get without a model?
In the advent of quantum mechanics people measured atomic and molecular spectra and had no clue what they observed. In these day Ritz invented a combinatorial principle to nevertheless reconstruct the states of hydrogen from the measured transitions. In 2015 our group brought out this old approach again to evaluate the measurements of CH5+ for which no model existed at all and none had a clue what we measured. This evaluation was an important foundation of the recent approaches to develop models for this molecule. It was also the foundation to further develop this principle to a computer program allowing for the semi-automatic reconstruction of the states of a molecule from its transition energies without further preknowledge.

Our aim is to make this tool not only helpful for the development of models of molecules for which no approprpriate models exist so far. Altough there already exist a lot of tools like pgopher or the Loomis-Wood Plot software developed by our absorption subgroup we also want to use the combinatorial approach to make life easier with ordinary molecules allowing for an assignment of model and measurement based on states and experimental selection rules instead of transitions as today.

Another approach to get molecular states without preknowledge is to do absorption spectroscopy with very cold molecules. By cooling down you make sure the molecule is in the state of lowest energy and all transition energies you get are in fact state energies. Unfortunately even with the best cooling technology this approach is restricted to molecules with a single groundstate (no vibration, no rotation) being much lower in energy than all the other states.
A very time-consuming approach to find out how certain transitions are linked to a spectroscopic network is to do Double-Resonance Spectroscopy as done in the absorption subgroup.