DFT-based calculation of vibrational sum frequency generation spectral features of crystalline β-sheets in silk: Polarization and azimuth angle dependences.

Sum frequency generation (SFG) necessitates both noncentrosymmetry and coherence over multiple length scales. These requirements make vibrational SFG spectroscopy capable of probing structural information of noncentrosymmetric organic crystals interspersed in polymeric matrices and their three-dimensional spatial distributions within the matrices without spectral interferences from the amorphous components. However, this analysis is not as straightforward as simple vibrational spectroscopy or scattering experiments; it requires knowing the molecular hyperpolarizability of SFG-active vibrational modes and their interplay within the coherence length. This study demonstrates how density function theory (DFT) calculations can be used to construct the molecular hyperpolarizability of a model system and combine it with the SFG theory to predict the polarization and azimuth angle dependences of SFG intensities. A model system with short peptide chains mimicking β-sheet domains in Bombyx mori silk was chosen. SFG signals of the amide-I, II, III, and A bands and one of the CH deformation modes were simulated and compared with the experimental results and the predictions from the group theory. The SFG features of amide-I and A bands of antiparallel β-sheet could be explained with DFT-based theoretical calculations. Although vibrational coupling with neighboring groups breaks the symmetry of the D2 point group, the group theory approach and DFT calculations gave similar results for the amide-I mode. The DFT calculation results for amide-II did not match with experimental data, which suggested vibrational coupling within a larger crystalline domain may dominate the SFG spectral features of these modes. This methodology can be applied to the structural analysis of other biopolymers.