Fields of Research

Research areas of the Köhn Group

Our main research focuses on molecules with non-trivial electronic structure, such as radicals, transition metal compounds, and electronically excited molecules.

With ‘non-trivial’ we distinguish these systems from the theoretically more simple case of closed-shell molecules with paired electrons. These are, to zeroth order, well described by a single set of occupied molecular orbitals from which a Slater determinant can be formed (we speak of single-reference systems).
Non-trivial electronic structure means that unpaired electrons are present and that spin-symmetry and static correlation effects have to be considered properly. The latter particularly means that a single set of occupied orbitals is not any more a good zeroth-order description of the system (multireference systems).

We develop new electronic structure methods for describing such multireference systems, with particular focus on coupled-cluster theory. We apply these methods in a number of thrilling research areas, such as photocatalysis, magnetic interactions, electronic energy transfer, and organic semiconductors.

New Developments in Coupled-Cluster Theory

It is one of our main research targets to develop a highly accurate method for complex multireference systems that has the same accuracy as that of CCSD(T) for single-reference molecules. Such methods are required to benchmark more approximate methods and for the investigation of systems for which no reliable experimental data are available. Recently, we made considerable progress in this direction by the development of the internally contracted multireference coupled-cluster method (see publication list [1], [2], [3], a more general review is given in [4]).

This method has recently been combined with explicit electron correlation, which allows obtaining even more accurate results (see publication [5]). Explicit electron correlation methods aim at enhancing the basis set convergence of correlated methods, which is hampered by the non-analytic behavior of the electronic wavefunction for colliding electrons (keywords: electron coalescence, Kato’s cusp conditions, for a review see [6]).

Symbolic Algebra in Quantum Chemistry

A basic development strategy in our research of new electronic structure methods is automated implemetation. This allows bypassing the otherwise laborious and error-prone “manual” implementation procedure.

The program package GeCCo („General Contraction Code“) encompasses a specialized symbolic algebra part that automates the derivation on the basis of second-quantization, and a numeric part that can evaluate the generated formulae. In particular, this involves the capability of carrying out general tensor contractions.

The program package has in particular been used to implement our multireference coupled-cluster methods. It can be found on GitHub, see github.com/ak-ustutt/GeCCo-public .

Excited Electronic States of Molecules

Even for molecules with a well-behaved closed-shell ground state, the electronic structure in the excited state become more involved as electron pairs are torn apart. Often anti-bonding orbitals become occupied, leading to significant changes of the equilibrium structure in the excited state. Such effects have been investigated by us for a number of cases (e.g. publications [7], [8], [9]). We have recently looked into electronic energy transfer (EET, aka FRET, e.g. publications [10], [11]), charge transfer (e.g. publication [12]) and couplings of both [13]. We also contribute to the development of methods to treat solvent effects [14]. Most computations of excited states in our group are based on second-order approximate correlation methods for excited states, like ADC(2) and CC2, which can be viewed as analogues of MP2 for excited states. More recently we looked at the potential of multireference coupled-cluster methods to provide an accurate treatment and we currently have set out to develop multireference analogues of CC2, which promise more stable results whenever excitations lead to strong weakening of cleavage of bonds.

Visualization

Models that map abstract processes of nature into something that a human brain can understand are of central importance in the natural sciences. In chemistry, three-dimensional models of molecules are central to the understanding of properties and reactivity. Compared to usual screen-based computer graphics, AR/VR setups have a great potential in allowing a much more natural inspection of complex topologies. Our particular vision is immersive parameter space analysis, i.e. the users can modify the structures and inspect molecular properties (like multipole moments, magnetic anisotropies) as a function of molecular structure.

Currently, we have written a first demonstrator, a molecular builder for common VR devices, which allows simple and intuitive construction and manipulation of molecular structures. In particular for ring and cage structures, the full immersive 3D environment greatly helps in accomplishing this task.

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