Nuclear quantum effects on the vibrational dynamics of the water-air interface

We have applied path integral molecular dynamics simulations to investigate nuclear quantum effects on the vibrational dynamics of water molecules at the water-air interface. The instantaneous fluctuations in the frequencies of the O-H stretch modes are calculated using the wavelet method of time series analysis, while the time scales of vibrational spectral diffusion are determined from frequency-time correlation functions and joint probability distributions, as well as the hydrogen bond number correlation functions. We find that the inclusion of nuclear quantum effects leads not only to a redshift in the vibrational frequency distribution by about 120~cm$^{-1}$ for both the bulk and interfacial water molecules, but also to an acceleration of the vibrational dynamics on the water-air interface by as much as 60$\%$. In addition, a blueshift of about 30 ~cm$^{-1}$ is seen in the vibrational frequency distribution of interfacial water molecules compared to that of the bulk. Furthermore, the dynamics of water molecules beyond the topmost two molecular layers was found to be essentially similar to that of bulk water.