In this thesis H-bonded systems (natural gas hydrates, water clusters, and crystal ice) are studied by density functional theory (DFT) computations.Natural gas hydrates (NGHs) play an important role in energy and environmental fields: NGHs are considered as a promising backup energy resource in the near-future due to their tremendous carbon content; improper exploration of NGHs could induce geological disasters and aggravate the greenhouse effect. In addition, many technologies based on gas hydrates are being applied and developed. The thermodynamic stabilities of various water cavities in different clathrate crystalline phases occupied by hydrocarbon gas molecules are studied by dispersion-corrected hybrid functionals. The Raman spectra of C-C and C-H stretching vibrations of hydrocarbon molecules in various water cavities in the solid state are derived. The trends of C-H stretching vibrational frequencies are found to follow the prediction by the "loose cage ─ tight cage" model. In addition, the trends and origins of 13 C NMR chemical shifts of hydrocarbon molecules in various NGHs are presented. These theoretical results will enlarge the database of C-C and C-H stretching vibrational frequencies and 13 C NMR parameters of hydrocarbon molecules in NGHs, and provide valuable information to help identify the types of clathrate phases and varieties of guest molecules included in NGHs samples taken from natural sites.The behavior of water clusters may help to understand the properties of its liquid and solid states. The thermodynamic stabilities and IR spectra of a small-, medium-, and large-sized water cluster are studied in this work. After full optimization of (H 2 O) 20,54,100 using the hybrid functional B3LYP, the electronic energies, zero-point energies, internal energies, enthalpies, entropies, and Gibbs free energies of the water clusters are computed. The OH stretching vibrational IR spectra of (H 2 O) 20,54,100 are also presented and split into sub-spectra for different H-bond types based on the specific contributions from each group. It is found that the OH stretching vibrational frequencies of water are sensitive to the conformations of the H-bonds and the vibrations of the H-bonds belonging to different types are located in separated regions in the IR spectra. Thus, the spectroscopic fingerprints will reflect the H-bond topology of the water molecules in a water cluster.Ice XI has been suggested to be involved in the process of planetary formation as a considerable electric field might be formed from the ferroelectric ice XI in space. IR and Raman spectroscopic technology can be directly used to identify the occurrence of ferroelectric ice XI in laboratory or extraterrestrial settings. Due to the difficulty for DFT to describe non-covalent systems, the performance of 16 different DFT methods applied on the ice Ih, VIII, IX, and XI crystal phases are assessed. Based on the computational accuracy and cost, the II IR and Raman spectra of ice Ih and XI are derived and compared. The librational vib...