Quantum Mechanical Interpretation of Intermolecular Vibrational Modes of Crystalline Poly-(R)-3-Hydroxybutyrate Observed in Low-Frequency Raman and Terahertz Spectra

Low-frequency vibrational bands observed in the Raman and terahertz (THz) spectra in the region of 50-150 cm(-1) of crystalline powder poly-(R)-3-hydroxybutyrate (PHB) were assigned based on comparisons of the Raman and THz spectra, polarization directions of THz absorption spectra, and their congruities to quantum mechanically (QM) calculated spectra. This combination, Raman and THz spectroscopies and the QM simulations, has been rarely adopted in spite of its potential of reliable assignments of the vibrational bands. The QM simulation of a spectrum has already been popular in vibrational spectroscopies, but for low-frequency bands of polymers it is still a difficult task due to its large scales of systems and a fact that interactions among polymer chains should be considered in the calculation. In this study, the spectral calculations with the aid of the Cartesian-coordinate tensor transfer (CCT) method were applied successfully to the crystalline PHB, which include the explicit consideration of an intermolecular interaction among helical polymer chains. The agreements between the calculations and the experiments are good in both the Raman and THz spectra in terms of spectral shapes, frequencies, and intensities. A Raman active band at 79 cm(-1) was assigned to the intermolecular vibrational mode of the out-of-plane C=O + CH3 vibration. A polarization state of the corresponding far-infrared absorption band at similar to 82 cm(-1), perpendicular to the helix-elongation direction of PHB, was reproduced only under the explicit correction, which indicates that this polarized band originates from the interaction among the polymer chains. The calculation explored that the polarization direction of this band was along the a axis, which is consistent with the direction in which weak intermolecular hydrogen bonds are suggested between the C=O and CH3 groups of two parallel polymer chains. The results obtained here have confirmed sensitivity of the low-frequency vibrational bands to the weak hydrogen bonds among the polymer chains.