Reliable detection of energetic materials is still a formidable challenge which requires further investigation. The remote standoff detection of explosives using molecular fingerprints in the terahertz spectral range has been an evolving research area for the past two decades. Despite many efforts, identification of a particular explosive remains difficult as the spectral fingerprints often shift due to the working conditions of the sample such as temperature, crystal orientation, presence of binders, etc. In this work, we investigate the vibrational spectrum of energetic materials including RDX, PETN, AN, and 1,3-DNB diluted in a low loss PTFE host medium using terahertz time domain spectroscopy (THz-TDS) at cryogenic temperatures. The measured absorptions of these materials show spectral shifts of their characteristic peaks while changing their operating temperature from 300 to 7.5 K. We have developed a theoretical model based on first principles methods, which is able to predict most of the measured modes in 1, 3-DNB between 0.3 to 2.50 THz. These findings may further improve the security screening of explosives.