Time-dependent vibrational sum-frequency generation spectroscopy of the air-water interface

Vibrational sum-frequency generation spectroscopy is a powerful method to study the microscopic structure and dynamics of interfacial systems. Here we demonstrate a simple computational approach to calculate the time-dependent, frequency-resolved vibrational sum-frequency generation spectrum (TD-vSFG) of the air-water interface. Using this approach, we show that at the air-water interface, the transition of water molecules with bonded OH modes to free OH modes occurs at a time scale of ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}3 ps, whereas water molecules with free OH modes rapidly make a transition to a hydrogen-bonded state within ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}2 ps. Furthermore, we also elucidate the origin of the observed differential dynamics based on the time-dependent evolution of water molecules in the different local solvent environments.