DFT-Based Calculation of Molecular Hyperpolarizability and SFG Intensity of Symmetric and Asymmetric Stretch Modes of Alkyl Groups.

Vibrational sum frequency generation (SFG) spectroscopy has been extensively used for obtaining structural information of molecular functional groups at two-dimensional (2D) interfaces buried in the gas or liquid medium. Although the SFG experiment can be done elegantly, interpreting the measured intensity in terms of molecular orientation with respect to the lab coordinate is quite complicated. One of the main reasons is the difficulty of determining the hyperpolarizability tensors of even simple molecules that govern their SFG responses. The single-bond polarizability derivative model has been proposed to estimate the relative magnitude of SFG-active hyperpolarizability by assuming that the perturbation associated to each vibration is negligible. In this study, density functional theory was used to calculate the polarizability and dipole derivative tensors of the CH 3 stretch mode of CH 3 I, CH 3 CH 2 I, CH 3 OH, and CH 3 CH 2 OH. Then, the hyperpolarizability tensors of symmetric and asymmetric vibration modes were calculated considering the Boltzmann distribution of representative conformers, which allowed us to theoretically calculate their SFG intensities at all polarization combinations as a function of the tilt angle of the CH 3 group with respect to the surface normal direction. Then, the ratios of the calculated SFG intensities for the CH 3 symmetric and asymmetric stretch peaks used in experimental studies for the CH 3 tilt angle determination were compared. This comparison clearly showed that the effect of vibrational coupling among neighboring functional groups is significant and cannot be assumed to be negligible. This study presents new parameters that can be used in determining the average tilt angle of the CH 3 group at the 2D interface with SFG measurements as well as limitations of the method.