Dye-sensitized solar cells (DSSCs) represent a great challenge in the world of photovoltaics, both in experimental and theoretical domain. The most important thing is to find an overall efficiency of the solar cell as a combination of several facors which work together, like light harvesting, transport of electrons and holes, hybridization of the molecule-metal oxide interface, charge transfer behaviour from the dye to the conduction band (CB) of the semiconductor and lastly, the way in which the cell regenerates itself. Density functional theory (DFT) and linear-response time-dependent density functional theory (LR-TDDFT) are the main methods to capture essential properties while studying systems separately (dye and semiconductor alone) and combined. Our focus goes beyond the standard and already known ruthenium complexes and it is directed towards organic dyes which are combined with titanium-dioxide (TiO2) as a semiconductor. We also used laser-induced electron injection with the hybrid LR-TDDFT and configuration interaction methodology (CI) to obtain information on photon-to-current conversion mechanism. The second part of the thesis covers research on hydroxyapatites (OHAp), a calcium phosphate mineral which is the main component of human hard tissues, like bone and enamel. The problem occurs when these minerals change their struc- ture with different substitutions, leading to changes in the chemical properties and mineralization, and at the end evolving some diseases, such as osteoporosis. Our main focus was on the pristine hydroxyapatite and three different substi- tutions for the carbonated apatites, A-type, B-type and AB-type. In order to understand changes within the structure, we used two main methods used in the vibrational spectroscopy: Infrared (IR) and Raman. Using these methods we can understand the chemical properties and percentage of carbonate inside the specific types, as well as the importance of the orientation of the sample.