:Vibrational spectroscopy is a valuable quantitative tool for the determination of structure at surfaces. Various techniques may be applicable and useful, depending on what is available, the transparency of the substrates, the need for in situ probes, and the degree of interfacial specificity required. We examine and compare signals in infrared absorption, Raman scattering, and vibrational sum-frequency generation spectroscopy to the underlying molecular response. In all of these experiments, varying the beam polarizations enables the orientation of specific chemical functional groups to be determined. However, the sensitivity of each technique is directly connected to the manner in which the molecular response manifests itself in the measured signal. Starting with simple distributions of a single vibrational mode, leading up to multiple vibrational bands in more complex orientation distributions, we compare these three techniques in terms of their sensitivity to features of the molecular orientation distribution. This review is aimed at guiding planned experiments when multiple techniques are available for surface structural analysis.
We provide a complete and consistent framework in which vibrational spectra may be modeled from molecular properties and molecular properties may be gleaned from vibrational spectra. This includes practical advice on how to define and use the rotation operators when moving between laboratory and molecular coordinate systems. At the same time, we provide some tips for the facile comparison of analytical orientation distributions and the construction of spectra from molecular dynamics simulations. We illustrate these approaches for infrared absorption, Raman scattering, and vibrational sum-frequency generation spectroscopy.