Theoretical basis for interpreting heterodyne chirality-selective sum frequency generation spectra of water

Chirality-selective vibrational sum frequency generation (chiral SFG) spectroscopy has emerged as a powerful technique for the study of biomolecular hydration water due to its sensitivity to the induced chirality of the first hydration shell. Thus far, water O-H vibrational bands in phase-resolved heterodyne chiral SFG spectra have been fit using one Lorentzian function per vibrational band, and the resulting fit has been used to infer the underlying frequency distribution. Here, we show that this approach may not correctly reveal the structure and dynamics of hydration water. Our analysis illustrates that the chiral SFG responses of symmetric and asymmetric O-H stretch modes of water have opposite phase and equal magnitude and are separated in energy by intramolecular vibrational coupling and a heterogeneous environment. The sum of the symmetric and asymmetric responses implies that an O-H stretch in a heterodyne chiral SFG spectrum should appear as two peaks with opposite phase and equal amplitude. Using pairs of Lorentzian functions to fit water O-H stretch vibrational bands, we improve spectral fitting of previously acquired experimental spectra of model β-sheet proteins and reduce the number of free parameters. The fitting allows us to estimate the vibrational frequency distribution and thus reveals the molecular interactions of water in hydration shells of biomolecules directly from chiral SFG spectra.