Vibrational spectroscopy is one of the most powerful techniques for characterizing molecular interactions. While it is widely used in science and technology, interpreting spectroscopic signals remains a challenge - particularly in liquids, aqueous solutions, and amorphous materials, where signals stem from mixed origins and overlapping contributions. In the most general case, a spectroscopic signal arises from two distinct origins: the response of individual molecules, and the collective response from interacting molecules. The superposition of these two types of contributions limits the interpretability of spectra in terms of direct, quantifiable, and physically meaningful observables.

In this thesis, we introduce correlated vibrational spectroscopy (CVS), a hyper-Raman scattering based method that exploits nonlinear light-scattering to disentangle these contributions in a model-free manner. We derive polarization selection rules that separately isolate the single-molecule response and the collective response from interacting molecules, and we demonstrate an easily implementable protocol covering a wide spectral range (60 - 4000 cm-1).

Using CVS, we address key questions about intermolecular structure and interactions in liquids and solutions, demonstrating the capabilities of the method. In solvents, CVS allows to retrieve information such as intermolecular bond angles. In acidic and basic solutions, it enables quantification of charge transfer between excess protons or hydroxide ions and water. In neat water, CVS reveals the impact of nuclear quantum effects on hydrogen (H) bonding, shedding light on their influence on charge transfer and on the balance of forces within H-bonds. In electrolyte solutions, CVS provides a comprehensive picture of how ions modify the H-bond network of water, uncovering multiple pathways through which ions are "making" or "breaking" the structure of water. Together, these findings reveal molecular mechanisms that were unsuspected from macroscopic quantities and from traditional methods. CVS opens a new window into molecular interactions.