First-Principles Prediction of Vibrational Sum Frequency Generation Features of Phenyl Groups at the 2D Interface with <i>C</i>_∞ Symmetry

Vibrational sum frequency generation (SFG) spectroscopy is capable of probing the orientation of the interfacial molecules. A conventional approach assumes that hyperpolarizability tensors governing the SFG signal intensity can be determined based on the point group symmetry of individual functional groups. However, vibrational coupling among neighboring groups breaks the normal mode symmetry. This makes it difficult to accurately interpret SFG spectra, particularly for phenyl (C₆H₅-) groups. In this study, we employed density functional theory (DFT) calculations to predict the SFG spectral features of C₆H₅ groups at two-dimensional interfaces with <i>C</i>_∞ symmetry. Using model compounds such as iodobenzene (C₆H₅-I) and various substituted phenyl derivatives, we systematically investigated the effect of vibrational coupling with neighboring atoms on the aromatic C-H stretching modes presented in the 3000-3100 cm^-1 region. If the substituent group lacks C-H bonds capable of coupling with the phenyl ring vibrations, the computed polarizability and dipole derivative tensors align well with the A1 and B1 symmetries expected from the <i>C</i>_2<i>v</i> point group. However, when the substituent contains C-H groups in the nearest or next-nearest positions to the phenyl ring, significant deviations from <i>C</i>_2<i>v</i> symmetry arise, leading to shifts in peak positions and intensity variations in SFG spectra. These findings underscore the limitations of conventional <i>C</i>_2<i>v</i>-based SFG analyses in determining the tilt angle of phenyl groups at polymer interfaces and emphasize the necessity of incorporating vibrational coupling effects for accurate SFG spectral interpretation. The approach presented in this work provides a more rigorous framework for accurately predicting and characterizing interfacial molecular orientations and can be extended to other complex systems, where vibrational interactions play a crucial role.