An empirical approach to the bond additivity model in quantitative interpretation of sum frequency generation vibrational spectra

Knowledge of the ratios between different polarizability $βi′j′k′$ tensor elements of a chemical group in a molecule is crucial for quantitative interpretation and polarization analysis of its sum frequency generation vibrational spectroscopy (SFG-VS) spectrum at interface. The bond additivity model (BAM) or the hyperpolarizability derivative model along with experimentally obtained Raman depolarization ratios has been widely used to obtain such tensor ratios for the $CH3$⁠, $CH2$⁠, and CH groups. Successfully, such treatment can quantitatively reproduce the intensity polarization dependence in SFG-VS spectra for the symmetric (SS) and asymmetric (AS) stretching modes of $CH3$ and $CH2$ groups, respectively. However, the relative intensities between the SS and AS modes usually do not agree with each other within this model even for some of the simplest molecular systems, such as the air/methanol interface. This fact certainly has cast uncertainties on the effectiveness and conclusions based on the BAM. One of such examples is that the AS mode of $CH3$ group has never been observed in SFG-VS spectra from the air/methanol interface, while this AS mode is usually very strong for SFG-VS spectra from the air/ethanol interface, other short chain alcohol, as well as long chain surfactants. In order to answer these questions, an empirical approach from known Raman and IR spectra is used to make corrections to the BAM. With the corrected ratios between the $βi′j′k′$ tensor elements of the SS and AS modes, all features in the SFG-VS spectra of the air/methanol and air/ethanol interfaces can be quantitatively interpreted. This empirical approach not only provides new understandings of the effectiveness and limitations of the bond additivity model but also provides a practical way for its application in SFG-VS studies of molecular interfaces.