DFT-Based Calculation of the Vibrational Sum Frequency Generation Spectrum of Noncentrosymmetric Domains Interspersed in an Amorphous Matrix

Vibrational sum frequency generation (SFG) spectroscopy can selectively probe noncentrosymmetric arrangements of molecules or crystalline domains buried in amorphous bulk phases. This attribute makes SFG useful for detecting molecules at interfaces between bulk phases that are random or that have inversion symmetry. The same principle can also be utilized for selective detection of crystalline domains of biopolymers interspersed inside amorphous bulk phases of natural materials, but quantitative interpretation of SFG spectral features of such systems has been challenging due to the difficulty of how the spectral features can vary as a function of various structural parameters. Here, we present a theoretical simulation-based approach utilizing polarizability and dipole derivative tensors obtained from density functional theory (DFT), circumventing the difficulty and limitation of assuming the local symmetry of specific vibrational modes. One of the main challenges in using this DFT-based method is how to choose, among all possible modes predicted from model structures, proper modes that can be compared with the experimentally observed vibrational peaks. In this work, we show that the orientation of the infrared (IR) dipole moment with respect to a reference axis, which can be obtained from polarized IR analysis, can be used to identify the representative normal modes predicted from a DFT geometry-optimized structure. Using those representative modes only, the experimental spectral features can be simulated reliably through a numerical algorithm, taking into account the random quasi-phase matching principle. This approach is demonstrated for cellulose samples prepared with certain structural orders.