  Density-functional theory may be used to predict both the frequency and the
dipole moment of the fundamental oscillations of molecular crystals. Suitably
polarized photons at those frequencies excite such oscillations. Thus, in
principle, terahertz spectroscopy may confirm the calculated fundamental modes
of amino acids. However, reports to date have multiple shortcomings: (a)
material of uncertain purity and morphology and diluted in a binder material is
employed; (b) consequently, vibrations along all crystal axes are excited
simultaneously; (c) data is restricted to room temperature, where resonances
are broad and the background dominant; (d) comparison with theory has been
unsatisfactory (in part because the theory assumes zero temperature). Here, we
overcome all four obstacles, in reporting detailed low-temperature polarized
THz spectra of single-crystal L-alanine, assigning vibrational modes using
density-functional theory, and comparing the calculated dipole moment vector
direction to the electric field polarization of the measured spectra. Our
direct and detailed comparison of theory with experiment corrects previous mode
assignments for L-alanine, and reveals unreported modes, previously obscured by
closely-spaced spectral absorptions. The fundamental modes are thereby
determined.
