The thesis presents methods for the variational calculation of fine and hyperfine resolved rovibronic spectra of diatomic molecules, as part of the ExoMol and ExoMolHD projects. The theory of these methods has been fully discussed. The corresponding algorithms have been implemented based on previous works of the ExoMol Group. The line lists of two molecules, NO and VO has been calculated, which validates the proposed methods.

Nitric oxide is one of the principal oxides of nitrogen, which plays a significant role the investigations of our atmosphere and astrophysics. Due to its importance, the radical has been investigated in numerous theoretical and experimental works. However, there is no NO ultraviolet line list in well-known databases. A major issue in generating a UV line list for NO results from the difficulty of modelling the valence-Rydberg interaction between its B2Π and C2Π states. To address the problem, a spectroscopic model has been proposed to resolve the energy structures of B2Π and C2Π coupled states. Based on the model, an accurate line list, called XABC, has been computed, which covers the pure rotational, vibrational and rovibronic
spectra of 14N16O.

Vanadium monoxide is also an open shell diatomic system. Its dominating isotopologue 51V16O has non-zero nuclear spin, I = 7/2. The interaction between the spin of unpaired electrons and the nuclear spin yields a very pronounced hyperfine structure. The widely used effective Hamiltonian method for hyperfine structure is not applicable to give accurate line list of VO, as the interactions between the electronic states of VO reshape its line positions and intensities. This thesis presents a variational algorithm for the calculation of hyperfine structure and spectra of diatomic molecules. The hyperfine-resolved IR spectra of VO has been computed from first principles, considering necessary nuclear hyperfine coupling curves.