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Abstract

Nowadays research in various fields of natural science and engineering requires insight, which can only be provided by computational simulations, due to the complexity of the systems under consideration. Predicting energies and properties of molecular systems is especially hard, due to the many body problem and the fact, that the mean-field only yields insufficient accuracy in most applications. For this purpose many different methods have been developed over the past century, which all offer a tradeoff between accuracy and computational effort.

Contributing to this field of research, in this thesis major breakthroughs in the development of a novel fragmentation scheme, named Excitonic Renormalization, XR, are presented along with the extension of established methods based on perturbation theory, to consistently describe the influence of polariton formation on the electronic structure of molecules as well as the application of electronic structure methods to investigate a novel crystallization-induced ring opening reaction observed in a derivative of a compound used in organic semiconductors.

The first major achievement in the development of the XR method is the reformulation of the overlap matrix into a series of orbital rotations, which is shown to converge quickly, lifting the necessity of numerically orthogonalizing the full sets of orbitals between fragments, which is a big advantage of XR over related fragmentation methods. Moreover, fast convergence is observed for approximate densities with increasing order of perturbation theory, indicating that densities obtained from established post-Hartree-Fock methods yield sufficient accuracy for the XR method. Method independent approximations to higher particle densities are presented as well, with little success though. It is further pointed out, how to increase the performance of the XR method and its approximations.

The perturbation theoretical methods, extended to describe polaritons consistently, are based on two different partitionings of the Hamiltonian, yielding polaritonic ground and excited state methods corresponding to the M\o ller-Plesset Perturbation Theory and the Algebraic Diagrammatic Construction Theory, respectively. The methods were shown to yield similar results for intermediate coupling strengths, up to second order of perturbation theory. Later the necessity of consistently treating the vacuum field contribution in the strong coupling regime is shown for the photodissociation dynamics of Pyrrole, which is only provided by one of the two partitionings of the Hamiltonian. For the excited state method based on this partitioning of the Hamiltonian a "quasi-diabatic" representation is given as well, which can be utilized to simulate wavepacket dynamics between polaritonically coupled surfaces using standard quantum dynamical methods without further adjustments. This method requires negligible additional computational effort for small state spaces compared to the approach widely applied in literature, which also yields a "quasi-diabatic" representation, but is shown to yield qualitatively wrong dissociation dynamics for Pyrrole for very strong coupling strengths.

In the investigation of the crystallization-induced reversible ring opening of Tetraazahexacene derivatives to Pyrazinopyrazine derivatives the experimental spectra are reproduced first. Further, assuming the Carbon-Carbon distance of the reversibly dissociating bond as the active reaction mode, the energy profile along this reaction path is computed with and without the explicit crystal environment, revealing double wells for all compounds and environments. Within reasonable accuracy the experimental findings of open and closed derivatives could then be mapped onto kinetical as well as thermodynamical stability and the reaction is shown to follow a concerted electrocyclic mechanism. Finally the dominant force, leading to ring opening in Tetraazahexacene derivatives, is found to be the force, that asymmetrically twists the aromatic core.