Abstract: Terahertz (THz) absorption is a fingerprint property of materials, due to the underlying low-frequency vibration/phonon modes being strongly dependent on the chemical constitutions and microscopic structures. The low excitation energies (0.414-41.4 meV) are related to two intrinsic properties of THz vibrations: the potential energy surfaces (PESs) are shallow, and the vibrationally excited states are usually populated via thermal fluctuations. The shallow PESs make the vibrations usually anharmonic, leading to redshifted vibrational excited state absorption; combined with considerable vibrational excited states population, characteristic THz signals are usually redshifted and congested with varying degrees at different temperatures. Combining existing experimental THz spectra at low temperatures, first principles vibration analysis, and the Morse potential, we developed a semi-empirical model to evaluate the anharmonicity of the low-frequency modes. The model was benchmarked with purine molecular crystal to generate THz spectra at different temperatures, the results were consistent with experiments. The good agreement suggests this model would facilitate the application of THz spectroscopy in molecular crystal characterization.