Biochemie und Chemie
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Photo-initiated processes, like photo-excitation and -deexcitation, internal conversion, excitation energy transfer and electron transfer, are of importance in many areas of physics, chemistry and biology. For the understanding of such processes, detailed knowledge of excitation energies, potential energy surfaces and excited state properties of the involved molecules is an essential prerequisite. To obtain these informations, quantum chemical calculations are required. Several quantum chemical methods exist which allow for the calculation of excited states. Most of these methods are computationally costly what makes them only applicable to small molecules. However, many biological systems where photo-processes are of interest like light-harvesting complexes in photosynthesis or the reception of light in the human eye by rhodopsin are quite large. For large systems, however, only few theoretical methods remain applicable. The currently most widely used method is time-dependent density functional theory (TD-DFT), which can treat systems of up to 200–300 atoms with the excitation energies of some excited states exhibiting errors of less than 0.5 eV. Yet, TD-DFT has several drawbacks. The most severe failure of TD-DFT is the false description of charge transfer states which is particularly problematic in case of larger systems where it yields a multitude of artificially low-lying charge transfer states. But also Rydberg states and states with large double excitation character are not described correctly. Still, if these deficiencies are kept in mind during the interpretation of results, TD-DFT is a useful tool for the calculation of excited states. In my thesis, TD-DFT is applied in investigations of excitation energy and electron transfer processes in light-harvesting complexes. Since light-harvesting complexes, which consist of thousands of atoms, are by far too large to be calculated, model complexes for the processes of interest are constructed from available crystal structures. The model complexes are used to calculate potential energy curves along meaningful reaction coordinates. Artificial charge transfer states are corrected with the help of the so-called ∆DFT method. The resulting potential energy curves are then interpreted by comparison with experimental results. For the light-harvesting complex LH2 from purple bacteria the experimentally observed formation of carotenoid radical cations is studied. It is shown that the carotenoid radical cation is formed most likely via the optically forbidden S1 state of the carotenoid. In light-harvesting complex LHC-II of green plants the fast component of the so-called non-photochemical quenching (NPQ) is investigated. Two of several different hypotheses on the mechanism of NPQ, which have been proposed recently, are studied in detail. The first one suggests that NPQ proceeds via simple replacement of violaxanthin by zeaxanthin in the binding pocket in LHC-II. However, the calculated potential energy curves exhibit no difference between violaxanthin and zeaxanthin in the binding pocket. In combination with experimental results it is thus shown that simple replacement alone does not mediate NPQ in LHC-II. The second hypothesis proposes conformational changes of LHC-II that lead to quenching at the central lutein and chlorophyll molecules during NPQ. My TD-DFT calculations demonstrate that if this mechanism is operative, only the lutein 1 which is one of two central luteins present in LHC-II can take part in the quenching process. This is corroborated by recent experiments. Though several conclusions can be drawn from the investigations using TD-DFT, the interpretability of the results is limited due to the deficiencies of the method and of the models. To overcome the methodological deficiencies, more accurate methods have to be employed. Therefore, the so-called algebraic diagrammatic construction scheme (ADC) is implemented. ADC is a widely overlooked ab initio method for the calculation of excited states, which is based on propagator theory. Its theoretical derivation proceeds via perturbation expansion of the polarization propagator, which describes electronic excitations. This yields separate schemes for every order of perturbation theory. The second order scheme ADC(2), which is employed here, is the equivalent to the Møller-Plesset ground state method MP(2), but for excited states. It represents the computationally cheapest excited state method which can correctly describe doubly excited states, as well as Rydberg and charge transfer states. The quality of ADC(2) results is demonstrated in calculations on linear polyenes which serve as model systems for the larger carotenoid molecules. The calculations show that ADC(2) describes the three lowest excited states of polyenes sufficiently well, particularly the optically forbidden S1 state which is known to possess large double excitation character. Yet, the applicability of the method is limited compared to TD-DFT due to the much larger computational requirements. To facilitate the calculation of larger systems with ADC(2) a new variant of the method is developed and implemented. The variant employs the short-range behavior of electron correlation to reduce the computational effort. As a first step, the working equations of ADC(2) are transformed into a basis of local orbitals. In this basis negligible contributions of the equations which are due to electron correlation can be identified based on the distances of local orbitals. A so-called “bumping” scheme is implemented which removes the negligible parts during a calculation. This way, the computation times as well as the disk space requirements can be reduced. With the “bumping” scheme several new parameters are introduced that regulate the amount of “bumping” and thereby the speed and the accuracy of computations. To determine useful values for the parameters an evaluation is performed using the linear polyene octatetraene as test molecule. From the evaluation an optimal set of parameter values is obtained, so that the computation times become minimal, while the errors in the excitation energies due to the “bumping” do not exceed 0.15 eV. With further calculations on various molecules of different sizes it is tested if these parameter values are universal, i.e. if they can be used for all molecules. The test calculations show that the errors in the excitation energies are below 0.15 eV for all test systems. Additionally, no trend is visible for the errors that their magnitude might depend on the system. In contrast, the amount of disregarded contributions in the calculations increases drastically with growing system size. Thus, the local variant of ADC(2) can be used in future to reliably calculate excited states of systems which are not accessible with conventional ADC(2).