In the present thesis the electronic properties of two organic molecules were studied by means of density functional theory (DFT) in connection to their possible applications in organic photovoltaics and molecular spintronics respectively. The first analysed system is the C60 derivative PCBM extensively used in polymer solar cells for the charge separation process. Since fullerenes have been shown to undergo modifications as a result of light exposure, investigating their electronic structure is the first step in elucidating the photodegradation process. The electronic excitations from core levels to unoccupied molecular orbitals reveal not only the empty level structure of the molecule, but provide additional information related to the chemical bonds involving a specific atom type. In this way, they represent a means of determining the chemical changes that the molecule might withstand. The electronic transitions from carbon 1s core levels to unoccupied states are explained for the unmodified PCBM by a joint theoretical (DFT) and experimental study using the near edge x-ray absorption fine structure (NEXAFS) spectroscopy. The second investigated system is the transition metal phthalocyanine with a manganese atom as the metal center. Manganese phthalocyanine (MnPc) is a single molecular magnet in which the spin switch process can be triggered by various methods. It has been shown, for instance, that the adsorption of hydrogen to the Mn center changes the spin state of the molecule from 3/2 to 1. More interestingly, the process is reversible and can be controlled, opening up the possibility of using MnPc as a quantum bit in magnetic memory devices. Up to this date, the d orbital occupation in MnPc has been under a long debate, both theoretical and experimental studies revealing different configurations. In this thesis the electronic structure of the phthalocyanine is thoroughly analysed by means of DFT and the calculated results are compared to photoelectron spectroscopy measurements. The combination of theoretical and experimental tools reveals that in gas phase at high temepratures the molecule exhibits a mixed electronic configuration. In this light, the possible control of the specific electronic state of the central metal represents an interesting prospect for molecular spintronics.

The study of magnons is an essential part of combining quantum information science and spintronics, allowing for the investigation of quantum properties such as entanglement in solid-state devices. Magnons are commonly described using the theory of T. Holstein and H. Primakoff, associating the spin operators with bosonic creation and annihilation operators. The quantum mechanical properties inherent to this description are the commutation relations. These relations must be conserved under transformation of the basis. This requires the application of pseudo-unitary transformations U (p, q) when studying the magnon eigenspectrum for example. Depending on the system at hand, the groups U (1, 1) and U (2, 2) are of particular interest and will be the focus of this work. We present a general formalism that leads to a representation of pseudo-unitary matrices via their self-adjoint elements. We apply this representation in examples involving magnons in antiferromagnets to find an explicit picture in connection to material properties. Finally, we explore numerical methods for determining magnon energies and compare them to the analytical counterpart.