## Nonadiabatic dynamics in systems with strong vibronic couplings

Nonadiabatic, dynamical processes are directly connected to the treatment of excited states. Particularly, the excited states of radicals are often found in close energetic proximity. This can give rise to strong vibronic interactions in which case the Born-Oppenheimer approximation is not applicable anymore. Such effects even turn out to be important in biomolecules (e. g. DNA), because only the ultrafast dynamics through conical intersections seems to render these molecules photo stable.

A central problem in the treatment of the molecular dynamics is posed by the required potential energy surfaces. Of course, these could be calculated point by point on a multi-dimensional grid. However, for reasons of efficiency they are usually needed in analytical form as multi-dimensional functions. For larger than three-atomic systems this is already a tremendous problem in itself. It is getting even more complicated, if a manifold of vibronically coupled surfaces has to be described. In this case, the potential in the Hamilton operator needs to be represented by a potential matrix which contains the state energies as well as the couplings. An analytical function is required for each matrix element which may have to fulfill further boundary conditions (e. g. symmetry).

Traditionally, such matrix elements have been approximated by linear or quadratic functions which has been quite successful in simple cases. However, we recently could show that higher order couplings can have a significant influence on the nonadiabatic dynamics for systems which are strongly anharmonic. For this reason, one of my research interests focuses on the improvement of the treatment of vibronic coupling and the development of new models. Such models need to include higher order couplings which is not too difficult for highly symmetric systems but problematic in cases with low symmetry. An extension of our methods to unsymmetric systems will be a very important task. Another aspect of our development work is dedicated to the description of reactive processes which cannot be treated yet in the framework of our currently available models.

## Diabatic potential energy surfaces including relativistic couplings

Life, as we know it, could not exist without spin-orbit coupling, which is a relativistic effect. This effect allows for the change of the "spin state" in the course of a chemical reaction or photophysical process. We are interested to investigate the fundamental mechanisms of processes induced by strong spin-orbit couplings. This requires the development of coupled potential energy surfaces that account for the relativistic couplings besides the vibronic couplings. Two major problems are that, first, relativistic electronic structure calculations are very demanding and intrinsically troublesome, and, second, that there is no established theory for the mathematical representation of the resulting potential energy surfaces. Therefore, we decided to develop such a theory and develop a method, which circumvents the electronic structure problems and allows for an elegant representation of the coupled surfaces.

The approach is based on a specific diabatization of the uncoupled spin-space states. Relativistic effects are strongly atom based and often one has just one or two very heavy atoms mainly responsible for the relativistic couplings. In this case the molecule can be decomposed into the heavy atom, carrying all the spin-orbit coupling, and a remaining fragement, which defines an asymptote of the potential surfaces. The electronic states at this asymptote form a diabatic reference basis composed of direct products of atom and fragment states. This special asymptotic basis is used to represent the diabatic electronic Hamiltonian throughout the nuclear configuration space. The advantage is that now the relativistic coupling can be treated effectively as in the isolated atom, which can be solved more or less analytically. Therefore, this new method is called Effective Relativistic Coupling by Asymptotic Representation (ERCAR). If the couplings are known for the atom states, e.g. from experiment, this approach does not require any further electronic structure calculations of the relativistic couplings, accounting for scalar relativistic effects is fully sufficient. Nevertheless, the energies of the fine structure states obtained from ERCAR are amazingly accurate compared to high quality reference calculations. This opens the route to the development of accurate potential energy surfaces including relativistic couplings for polyatomic systems. A major part of this research is developing novel techniques for the diabatization of the spin-space states and is closely related to our research in nonadiabatic dynamics.

## Highly accurate calculation of electronically excited states of radicals and molecules

The advance of new methods and algorithms in theoretical chemistry, along with the progress in computer technology, makes it possible to treat larger and larger systems up to biomolecules and nano particles. This is also true for the treatment of excited states of radicals and molecules. However, the accurate calculation of excited states is still limited to fairly small systems containing only few atoms. One of my central fields of interest deals with radicals and molecules which are just at this borderline of manageability. Many important topics in the chemistry of atmospheres, of combustion, and in interstellar space involve species of such a size. Therefore, their spectroscopic and theoretical investigation is of great interest. Furthermore, a close interplay between theory and experiment is inevitable because otherwise for systems with more than three or four atoms the complexity of the experimental results could hardly be interpreted with reasonable certainty.

For these reasons, one of my main research fields is the highly accurate calculation of electronically excited states. In this case it is not sufficient to just calculate vertical excitation energies, which is only a first step towards more elaborate studies. One rather has to account for the vibrational dynamics in the excited states as well. The results of such calculations can then be compared to vibrationally resolved experimental spectra. Eventually, the interpretation of the measurements can be based on a sound theoretical basis. In order to do this for system sizes beyond three or four atoms, we also need to develop efficient methods which is also one of my interests.

Closely connected to the calculation of electronic spectra is the treatment of photo reactions. On the one hand, such reactions have a strong influence on the band shape of spectra. On the other hand, photochemical processes are of great importance in atmospheric chemistry. A particularly fruitful field is the theoretical investigation of the photochemistry of radicals because many of these processes are hard or impossible to study experimentally. Again, theory and measurement should go hand in hand in order to avoid misinterpretations of experimental results. The theoretical methods can be tested on reliable experimental results and can then be applied to processes which are not experimentally accessible.

## Photostability of greenhouse gases

The identification and investigation of greenhouse gases is another topic in atmospheric chemistry and its relevance reaches far beyond the borders of pure science. It is the goal of this work to identify new potenital greenhouse gases and to study their properties. The sources of such compounds can be found in the currently discussed replacements for the by now banned CFC's (chloro fluoro carbons) which were recognized as the reason for ozon depletion. For technical reasons, a high thermal stability and chemical inertness is required for such substitutes. However, once these compounds escape to the free atmosphere these initially desired properties can turn into a major drawback. If these replacements are greenhouse active and photo stable as well, their large-scale technical application could turn into a real threat for global climate. For this reason, it is of great importance to study the photo stability of such compounds. Again, an accurate treatment of the excited states and their dynamics is required. On the other hand, it is also necessary to investigate decomposition pathways. For example, we were able to show that the super-greenhouse gas SF_{5}CF_{3} can dissociate photolytically into SF_{4} and CF_{4}. While SF_{5}CF_{3} has an estimated atmospheric life-time of about 1000 years, the strong greenhouse gas CF_{4} is almost infinitely stable under atmospheric conditions.