The amount of energy in natural gas hydrates is thought to be equivalent to twice that of all other fossil fuels combined. However, economic and safe energy recovery has remained a challenge till now. To develop a novel method of breaking the hydrogen bonds (HBs) surrounding the trapped gas molecules, we investigated the vibrational spectra of the HBs of gas hydrates with structure types II and H. Two models of 576-atom propane-methane sII hydrate and 294-atom neohexane-methane sH hydrate were built. A first-principles density functional theory (DFT) method was employed using the CASTEP package. The simulated spectra were in good agreement with the experimental data. Compared with the partial phonon density of states of guest molecules, we confirmed that the experimental infrared absorption peak in the terahertz region mainly arose from HB vibrations. By removing the components of guest molecules, we found that the theory of two kinds of hydrogen bond vibrational modes applies. The use of a terahertz laser to enable resonance absorption of HBs (at about 6 THz, to be tested) may therefore lead to the rapid melting of clathrate ice and release of guest molecules.