## 5 Conclusions  
We conducted a detailed spectroscopic study of seven saccharides (GLU, GAL, \(\alpha\)LM, \(\alpha\)LA, \(\beta\)LA, CBS, and CEL) by using a THz-TDS system. The THz-TDS data analysis was carefully performed to eliminate the FP interference effect, and the actual volume fraction of samples within the pellets was evaluated to recover the absorption coefficient (cm\({}^{-1}\)) and refractive index of the saccharides. The experimental results were compared with the theoretical spectra obtained by ab initio techniques based on DFT considering H-bonding interactions with an enhanced version of the van der Waals non-local density functional vdW-DF2. The analysis of the saccharides' low-energy vibrational modes followed the methodology introduced by [PERSON] et al. [7]. This facilitated the calculation of the proportional contributions of intermolecular translations, intermolecular librations, and intramolecular vibrations for every mode within the saccharides. The low-energy vibrations of the studied saccharides are mainly due to intermolecular librations and intramolecular vibrations, with a small percentage of intermolecular translations. The convergence of the characteristic frequency ranges between intermolecular librations and intramolecular vibrations implies the flexibility of the molecular backbone and a significant amalgamation of these two vibration classes within these frequency domains. Saccharides, and in particular, lactose, are one of the most used pharmaceutical excipients. In fact, approximately 70% of pharmaceutical dosage forms contain lactose as a filler, carrier, excipient, or binder agent. Therefore, we believe that our analysis of the vibrational modes in the THz region could be used in the design and synthesis pharmaceutical processes. **Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13179719/s1](https://www.mdpi.com/article/10.3390/app13179719/s1)]([https://www.mdpi.com/article/10.3390/app13179719/s1](https://www.mdpi.com/article/10.3390/app13179719/s1)). Figure S1: Sketch of the THz beamline used for the experiments with the multiple sample holder. TPX1 to TPX4 are polymethylpentene lenses with 50 mm focal length; Figure S2: Time traces (left) and Fourier transform of the THz signal (right) propagating through the dry N2 (black lines) and the noise floor of the system (red lines); Figure S3: The DR (left) and highest measurable absorbance \((\alpha d)_{max}\) (right) of the THz-TDS system; Table S1: Typical nominal density of the investigated saccharides and PET, as reported in the literature [39; 57; 60; 61; 62]; Table S2: Experimental THz frequencies modes associated with the simulated ones and the correspondent mode number; Figure S4-S10: Ball and stick representation of CBS, \(\beta\)LA, \(\alpha\)LM, GLU, CEL, \(\alpha\)LA, and GAL, molecular crystals. The unit cell is indicated with a box. Black, red, and white spheres represent, respectively, carbon, oxygen and hydrogen atoms, and the azure dotted lines the H-bonds; Table S3: Unit cell parameters for all simulated systems. a, b, and c are the primitive vectors lengths, and \(\alpha\), \(\beta\), and \(\gamma\) are the axial angles; Figure S11: Refractive index, ns, of (a) GLU, (b) GAL, (c) \(\alpha\)LA, (d) \(\beta\)LA, (e) \(\alpha\)LM, (f) CBS, (g) CEL; Figure S12-S18: Atomic displacement vectors of CBS, \(\beta\)LA, \(\alpha\)LM, GLU, CEL, \(\alpha\)LA, and GAL, for the main vibrational modes. Black, red, and white spheres represent, respectively, carbon, oxygen and hydrogen atoms, and the red dotted lines the H-bonds. **Author Contributions:** Conceptualization, A.A.P. and M.M. ; methodology, A.A.P. and M.M. ; software, A.A.P., N.L. and A.M.C. ; validation, A.A.P., N.L., O.P. and M.M. ; formal analysis, A.A.P., N.L. and M.M. ; investigation, A.A.P. and M.M. ; resources, M.M. ; data curation, A.A.P. and N.L. ; writing--original draft preparation, A.A.P. and A.M.C. ; writing--review and editing, A.A.P., N.L., O.P., A.M.C. and M.M.