Vibrational sum frequency (VSF) spectroscopy has been increasingly used in
recent years to measure the vibrational spectroscopy of molecules at surfac
es. Some of the more important systems examined in such studies involve the
surface of liquid water. Unfortunately, obtaining spectral fits to vibrati
onal spectra acquired in these studies can be challenging. The difficulty a
rises from the wide range of contributing vibrational modes, the breadth of
the spectral peaks for hydrogen-bonded water molecules, and the complex in
terference effects that can arise between adjacent vibrational modes becaus
e of the coherent nature of the sum frequency process. In this paper, we de
scribe a detailed method for obtaining spectral fits to such VSF data, that
takes into account a range of water species present at a water surface and
die possible interference between these contributing modes. The relationsh
ip between the spectral information derived and the molecular orientation i
s also given. This analysis is applied to two cases, VSF spectra of water m
easured at the CCl4/H2O interface and at the air/H2O interface.