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[Display omitted] • THz spectra of three xanthine alkaloids (2.0–17.0 THz) were obtained using THz spectroscopy. • The accuracy of different computational methods in resolving the vibrational properties of xanthine alkaloids was evaluated. • Common and unique THz peaks of caffeine, theobromine, and theophylline were analyzed. • The correlation between their structural properties and characteristic absorption frequencies was investigated. Caffeine, theophylline and theobromine are representative xanthine alkaloids, commonly used as stimulants due to their effects on the central nervous system. Despite their similar molecular structures, they have different pharmacological effects, necessitating a rapid and accurate identification method. In this study, terahertz time-domain spectroscopy (THz-TDS) was used to measure the absorption spectra of these three xanthine alkaloids within the range of 2.0–17.0 THz. The characteristic absorption peaks were visualized and analyzed basing on the quantum chemical calculations using Hartree-Fock (HF), Møller–Plesset perturbation theory (MP2) and density functional theory (DFT). Caffeine exhibited unique absorption peaks at 4.24, 5.00, and 11.13 THz. Theophylline showed characteristic peaks at 9.25, 12.20, and 15.09 THz. While theobromine exhibited characteristic peaks at 4.45, 7.68, and 11.21 THz. The results demonstrate that combining THz-TDS with DFT calculation can non-destructively, efficiently, and accurately identify these xanthine alkaloids, and providing valuable information for further understanding their pharmacological functions. [ABSTRACT FROM AUTHOR]