A Quantitative Interpretation for the Difference of Terahertz Spectra of dl- and l-Alanine: Origins of Infrared Intensities in Terahertz Spectroscopy

The absorption spectra of l-, d-, and dl-alanine in the low-frequency region were measured by terahertz (THz) time-domain spectroscopy ( Appl. Phys. Lett. 2005, 86, 053903, DOI: 10.1063/1.1857080). 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.