Second harmonic generation (SHG) has been proven a uniquely effective technique in the investigation of molecular structure and conformations, as well as dynamics of molecular interfaces. The ability to apply SHG to molecular interface studies depends on the ability to abstract quantitative information from the measurable quantities in the actual SHG experiments. In this review, we try to assess recent developments in the SHG experimental methodologies towards quantitative analysis of the nonlinear optical properties of the achiral molecular interfaces with rotational isotropy along the interface normal. These developments include the methodology for orientational analysis of the SHG experimental data, the experimental approaches for more accurate SHG measurements, and a novel treatment of the symmetry properties of the molecular polarizability tensors in association with the experimentally measurable quantities. In the end, the recent developments on the problem of surface versus bulk contribution in SHG surface studies is discussed. These developments can put SHG on a more solid foundation for molecular interface studies, and to pave the way for better understanding and application of SHG surface studies in general.

Knowledge of the ratios between different polarizability betai'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 betai'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.

It has been generally accepted that there are significant quadrupolar and bulk contributions to the second harmonic generation (SHG) reflected from the neat air/water interface, as well as common liquid interfaces. Because there has been no general methodology to determine the quadrupolar and bulk contributions to the SHG signal from a liquid interface, this conclusion was reached based on the following two experimental phenomena. Namely, the broken of the macroscopic Kleinman symmetry, and the significant temperature dependence of the SHG signal from the neat air/water interface. However, because sum frequency generation vibrational spectroscopy (SFG-VS) measurement of the neat air/water interface observed no apparent temperature dependence, the temperature dependence in the SHG measurement has been reexamined and proven to be an experimental artifact. Here we present a complete microscopic analysis of the susceptibility tensors of the air/water interface, and show that dipolar contribution alone can be used to address the issue of broken of the macroscopic Kleinman symmetry at the neat air/water interface. Using this analysis, the orientation of the water molecules at the interface can be obtained, and it is consistent with the measurement from SFG-VS. Therefore, the key rationales to conclude significantly quadrupolar and bulk contributions to the SHG signal of the neat air/water interface can no longer be considered as valid as before. This new understanding of the air/water interface can shed light on our understanding of the nonlinear optical responses from other molecular interfaces as well.