The
absorption spectra of l-, d-, and dl-alanine
in the low-frequency region were measured by terahertz (THz)
time-domain spectroscopy (053903Appl. Phys. Lett.200586). It has been observed that several absorption bands have a significant
difference between the enantiomers (l- and d-alanine)
and the racemic compound (dl-alanine) in their peak frequencies.
In this work, we calculate the THz spectra of dl- and l-alanine by solid-state density functional theory to quantitatively
interpret the spectral difference. The two systems give rise to similar
distributions of normal modes in the 5–80 cm–1 frequency range; however, the THz spectra of both crystals are different.
During our work, we found two critical aspects regarding the intensities
of the THz bands. One aspect, as is known for a molecular crystal,
is that the cancellation of the transition dipole moments in the unit
cell: Even if an individual molecule in a unit cell has a nonzero
transition dipole moment, the total transition dipole moment of the
unit cell is zero due to the cancellation of the contributions from
the molecules. The second aspect is that these THz normal modes of dl- and l-alanine are dominated by the intermolecular
translations, which are intrinsically infrared (IR)-inactive if the
molecules are not polarized. Our analysis shows that the IR intensities
of these “almost-pure” intermolecular translations are
due to a subtle balance between the IR activities induced by the polarization
effect of translations and the IR activities of the librations and
intramolecular vibrations, which have marginal presences in these
normal modes.