Investigation of (1R,2S)‐(−)‐Ephedrine by Cryogenic Terahertz Spectroscopy and Solid‐State Density Functional Theory

The terahertz (THz) spectrum of the pharmaceutical (1R,2S)‐(?)‐ephedrine from 8.0 to 100.0 cm^?1 is investigated at liquid‐nitrogen (78.4 K) temperature. The spectrum exhibits several distinct features in this range that are characteristic of the crystal form of the compound. A complete structural analysis and vibrational assignment of the experimental spectrum is performed using solid‐state density functional theory (DFT) and cryogenic single‐crystal X‐ray diffraction. Theoretical modeling of the compound includes an array of density functionals and basis sets with the final assignment of the THz spectrum performed at a PW91/6‐311G(d,p) level of theory, which provides excellent solid‐state simulation agreement with experiment. The solid‐state analysis indicates that the seven experimental spectral features observed at low temperature consist of 13 IR‐active vibrational modes. Of these modes, nine are external crystal vibrations and provide approximately 57 % of the predicted spectral intensity. This study demonstrates that the THz spectra of complex pharmaceuticals may be well reproduced by solid‐state DFT calculations and that inclusion of the crystalline environment is necessary for realistic and accurate simulations.