Theoretical Study of the Two-Dimensional Vibrational Sum Frequency Generation Spectroscopy of the Air-Water Interface at Varying Temperature and Its Connections to the Interfacial Structure and Dynamics

We performed a theoretical study of the temperature variation of two-dimensional vibrational sum frequency generation (2D-VSFG) spectra of the OH stretch modes at air-water interfaces in the mid-IR region. The calculations are performed at four different temperatures from 250 to 325 K by using a combination of techniques involving response function formalism of nonlinear spectroscopy, electronic structure calculations, and molecular dynamics simulations. Also, the calculations are performed for isotopically dilute solutions so that the intra- and intermolecular coupling between the vibrational modes of interest can be ignored. We have established the connections of temperature variation of various frequency- and time-dependent features of the calculated spectra to the changes in the underlying structure and dynamics of the interfaces. The results reveal that interfacial water is dynamically more heterogeneous than bulk water, with three dominant dynamical processes exhibiting their corresponding time-dependent features in the 2D-VSFG spectrum. These are the spectral diffusion of hydrogen-bonded OH groups at the interface, conversion of an initially hydrogen-bonded OH group to a dangling OH which is a stable state for surface water, unlike the bulk water, and the third one, which involves the conversion of an initially free or dangling OH group to its hydrogen-bonded state at the interface. The temporal appearance of the cross peaks corresponding to interconversion of the hydrogen-bonded state to the dangling state or vice versa of an interfacial OH group is found to take place at a slower rate than the dynamics of spectral diffusion of hydrogen-bonded molecules at the interface, which, in turn, is slower than the corresponding spectral diffusion of bulk water molecules. The temperature variation of these dynamic processes can be linked to the decay of appropriate hydrogen-bond and non-hydrogen-bond time correlation functions of interfacial water molecules for the different air-water systems studied in this work.