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Theoretical chemistry has become an important branch of modern chemistry. Theoretical investigations improve our understanding of chemical problems and can predict properties or reaction pathways. Especially in photochemistry, quantum chemical calculations are used along with spectroscopy to analyze the interactions of molecules with light. In recent years, new methods like time-dependent density functional theory (TD-DFT) and the algebraic diagrammatic construction scheme for the polarization propagator (ADC) have been developed allowing calculations of excited states of molecules of chemical relevant size with an accuracy directly comparable with experimental results. These methods allow not only for the calculation of excitation energies, but also of excited state properties, electron densities, absorption strengths and even photoreaction pathways can be calculated. This paves the way for the theoretical investigation of all photochemical processes. Typically, however, chemical reactions and spectroscopic measurements are performed in solution. Unlike in gas phase, molecules in solution are comparatively close together, leading to an interaction between the solvent and solute molecules. In biochemistry, reactions often take place in the active center of a protein and in technical photochemical applications such as organic light emitting diodes (OLEDs) the chromophore is packed in a matrix. Hence, for comparable quantum mechanical calculations, the influence of the environment has to be considered as well. Since a direct treatment of the full environment is generally not feasible due to the computational demand of quantum chemical methods, an approximative treatment of the interaction using specific environment models is made. In my dissertation, I focused on two main topics involving both the application of existing theoretical methods, and the development of new theoretical methods. In the first part, I investigated the photochemical and electrochemical properties of various phosphorus-tetrathia-[7]heterohelicenes. The ground and several excited states of tetrathia-[7]heterohelicene-dialkylphosphane-borane (TTH-DAPB) and tetrathia-[7]heterohelicene-diphenylphosphane-gold(I)-chloride (TTH-DPP-Au(I)) have been analyzed using DFT, TD-DFT and RI-CC2. These molecules belong to the the class of helicenes, which are characterized by multiple annelated aromatic rings forming a helical structure which induces chirality. The optimized ground state equilibrium structures were compared with experimental structures determined by X-ray crystallography and showed generally good agreement. The eight energetically lowest excited singlet states have been calculated. Employing a constant shift accounting for environment effects and intrinsic errors of the applied method, the calculated spectra almost perfectly resemble the experimental absorption and circular dichroism spectra. In both molecules, both the S1 and S2 state contribute to the first absorption band. Therefore, vibrationally resolved absorption spectra have been calculated for these two states for both molecules. It could be shown that only the first excited state determines the absorption band. The second excited state exhibits a very broad band due to many normal modes contributing to the vibronic excitation. In general, the TTH backbone dominates the photochemical properties and the phosphorus and gold atoms exhibit only minor influences. In addition, electrochemical properties of the phosphine-oxide TTH derivatives TTH-(PO(n-Bu)2)2, TTH-(PO(Ph)2)2 and TTH-PO(Ph)2 as well as of the two phosphine-selenide TTH derivatives TTH-(PSe(Ph)2)2 and TTH-PSe(Ph)2 have been calculated. Ionization energies and electron affinities have been computed both in gas phase and solution. In solution, all first electron detachments and attachments are localized on the TTH moiety with only minor influence of the substituents. Each process is qualitatively determined in all molecules by a single frontier orbital, which has been verified by difference density analysis. For the phosphine-oxide TTH derivatives the gas phase results resemble the results in solution. The phosphine-selenides, however, show a different picture. The lone-pairs are shifted higher in energy without stabilization of the environment, leading to an ionization localized at the selenium atom in the gas phase. The second focus of my dissertation was the development, implementation, and testing of a new method for including environment interaction in the excited state of a central molecule. To this end, I combined frozen density embedding thoery (FDET) with the ADC method to develop the new FDE-ADC method. This method is implemented in the quantum chemical program package Q-Chem as the module fdeman, which manages the FDE-ADC calculation. In FDET, the supersystem is divided in two subsystems: the embedded system (A) and the environment (B). The name „embedded system“ comes from the fact that it is embedded in the electron density of the environment. The inuence of the environment is expressed in an embedding potential, which depends on both electron densities of A and B. In fdeman, the whole FDE-ADC calculation is performed in a four step process: a) generation of the electron density of the embedded system _A(~r), b) generation of the electron density of the environment _B(~r), c) calculation of the embedding potential vlin emb(~r) and _nally d) applying vlin emb(~r) in an FDE-ADC calculation by adding it to the Fock matrix during the SCF The second focus of my dissertation was the development, implementation, and testing of a new method for including environment interaction in the excited state of a central molecule. To this end, I combined frozen density embedding theory (FDET) with the ADC method to develop the new FDE-ADC method. This method is implemented in the quantum chemical program package Q-Chem as the module FDEman, which manages the FDE-ADC calculation. In FDET, the supersystem is divided in two subsystems: the embedded system (A) and the environment (B). The name „embedded system“ comes from the fact that it is embedded in the electron density of the environment. The influence of the environment is expressed in an embedding potential, which depends on both electron densities of A and B. In FDEman, the whole FDE-ADC calculation is performed in a four step process: a) generation of the electron density of the embedded system rho_A, b) generation of the electron density of the environment rho_B, c) calculation of the embedding potential v_emb and finally d) applying v_emb in an FDE-ADC calculation by adding it to the Fock matrix during the SCF followed by an ADC calculation using the orbitals influenced by the environment. While the straight-forward implementation of FDE-ADC uses a supermolecular basis to express both density matrices and the embedding potential, an approximate variant named re-assembling of density matrix (RADM) has been introduced in which the density matrix of A is built together from MP(2) and HF based density matrices like a patchwork. The created embedding potential is subsequently cut to the monomer basis which features an FDE-ADC calculation using only the basis functions of the embedded system. This can be done since in the contraction of the density of A with the embedding potential, only the values of the block in the density matrix representing the embedded system contribute. FDE-ADC has been benchmarked up to third order perturbation theory employing three test systems, designed to exhibit an increasing strength of environment interaction. The test systems are 1) benzene with a hydrogen fluoride molecule in plane with the benzene ring, 2) benzaldehyde with a hydrogen-bonded water dimer and 3) uracil surrounded by five hydrogen-bonded water molecules. In the benchmark, the FDE-ADC results have been compared with supermolecular ADC calculations. The deviation from the reference calculation in excitation energies and oscillator strengths determines the accuracy of FDE-ADC. For SE-FDE-ADC(2) and RADM-FDE-ADC(2), mean absolute errors (MAEs) of 0.025 eV and 0.040 eV in excitation energies have been determined, respectively. For RADM-FDE-ADC(3), an MAE of 0.029 eV has been calculated. These errors are well below the intrinsic error of the underlying ADC methods, thus demonstrating the performance of FDE-ADC. This is furthermore demonstrated in three representative applications. First, the excited states of benzoquinone in 42 methanol molecules have been investigated. Next, the vertical photochemical properties of the photoswitch spiropyran in 100 water molecules have been investigated. In the last application, the core-valence excited states of carbon monoxide inside a C60-cage have been calculated. Using a frozen environment neglects the influence of the embedded system on the environment. This is called environment polarization and can be added following two different approaches. In the first variant referred to as pre-polarization, the ground state influence of the embedded system on the environment is treated by an electrostatic potential which is applied during the calculation of the environment density. This way, rho_B is not calculated in the gas phase but instead in the presence of A. In the second variant, referred to as excitation-induced environment polarization, the influence of an electronic excitation of A on the environment is considered. Therefore, the subsystems are interchanged and alternatingly embedded in each other until self-consistency (freeze and thaw). Here, two approximate variants to include excitation-induced environment polarization are introduced. In the first variant, named state-specific iteration (SSI), the alternate embedding is performed once, which prevents changes in the order of the excited states. In the second variant called difference density polarization potential (DDPP), the environment is embedded consecutively in the ground and excited state density of system A. The electron difference density describing the polarization of the environment is used to create a potential which is employed to calculate an energy correction for the excitation energy of the excited state of A. Both SSI and DDPP as well as the pre-polarization are implemented in the module FDEman in Q-Chem. In tests, both the pre-polarization and SSI could increase the accuracy of FDE-ADC. In the case of SSI, up to 35 % increased accuracy is observed. DDPP currently does not improve the results. In total, the FDE-ADC method is a promising approach for considering environmental effects on electronically excited states. The error of this method is lower than the intrinsic error of the employed ADC method. Using the RADM approximation, explicit treatment of extended environments is directly feasible, making FDE-ADC a „black box“ method for the calculation of excited states in complex environments.

The journal of chemical physics 155(8), 084801 (2021). doi:10.1063/5.0055522, Published by American Institute of Physics, Melville, NY