Development of Quantum Chemical Methods for Excited-State and Response properties

Abstract

The interaction of light and matter is central in some of the most fundamental processes in nature. The theoretical description of these processes is essential for numerous applications in all fields of science. To gain an understanding of light-induced reactions at a microscopic scale, it is necessary to study quantum mechanical phenomena, for which quantum chemical methods are required. Quantum chemical methods offer access to excitation energies, potential energy surfaces and excited-state properties, which are key for the description of photo-chemical reactions. A variety of well-established quantum chemical methods is available, but however, many of these methods have limited applicability due to their exceedingly large computational demands. In general a numerically exact description is only possible for molecules with few atoms. Yet, biologically or technically relevant systems comprise hundreds or thousands of atoms. Examples are protein-chromophore complexes, which take part in photosynthesis or the reception of light in the eyes of humans and animals. An important part in the field of quantum chemistry is the development of suitable methods, which offer both, a sufficiently accurate description of the involved physical effects, and feasible computational requirements. Of the available methods, which fulfil the above-stated requirements, many suffer from severe drawbacks. The central information obtained from quantum chemical calculations is the energy of electronic states. However, for many interesting questions, further properties of the electronic states are required. Hence, an important part of the development of quantum chemical methods is the derivation and implementation of methodologies for the description of excited state properties. A key property is the gradient of the energy. It is required to efficiently explore potential energy surfaces and for the theoretical modeling of experimental findings. Other important quantities are absorption cross-sections, which correspond to absorption coefficients in spectroscopical experiments. In this thesis, the so-called algebraic diagrammatic construction (ADC) scheme for the polarization propagator is considered for the description of electronically excited states. It is a quantum chemical method, which has gained more attention over the last decade. It could be shown that ADC offers for many relevant systems a well-balanced mix of both accuracy and computational demand. In particular, in this thesis the derivation and implementation of excited state energy gradients is presented. Furthermore an approach to obtain optical properties using the so-called intermediate state representation (ISR) is discussed. The ISR/ADC approach for the computation of two-photon absorption cross-sections and its implementation are presented. Both implementations are numerically tested and applied to two model systems, all-trans-octatetraene and trans-bithiophene. The results for trans-bithiophene are very promising, however, in the case of all-trans-octatetraene limitations for the description of the excited state geometry by the presented derivative approach are encountered.