In fitting the experimental spectra, we assumed a known frequency difference between the symmetric and asymmetric stretches of water ( ) to further constrain the fitting. Leaving as a free parameter of the fit often produced nonphysical results (e.g., values so large that the peaks in the pair were completely independent, or so small that the fit curve was flat due to cancelation of the two peaks that are equal in amplitude but opposite in sign). To address this issue, the initial value can be selected based on our theoretical studies. In principle, the value depends on the fundamental water O-H stretching frequencies and the intramolecular coupling strength, which can be calculated by the ensemble average for a subset of vibrational chromophores. The initial value can then be taken as the separation of the calculated symmetric and asymmetric stretches of the first hydration shell with the assumption that water molecules even in different subsets have values of similar magnitude. This assumption is validated by the analysis of the simulated symmetric and asymmetric stretches of the subsets shown in Figures S1-S7 using a value of ranging from 30 to 100 cm -1 . Therefore, our theoretical studies can guide setting the constraints of the value in fitting the experimental spectra.