  Vibrational spectroscopy is key for probing the interplay between the
structure and dynamics of aqueous systems. In order to map different regions of
experimental spectra to the microscopic structure of a system, it is important
to combine them with first-principles atomistic simulations that incorporate
the quantum nature of nuclei. Here, we show that the large cost of calculating
quantum vibrational spectra of aqueous systems can be dramatically reduced
compared to standard path integral methods by using approximate quantum
dynamics based on high-order path integrals. Together with state-of-the-art
machine-learned electronic properties, our approach gives an excellent
description of the infrared and Raman spectra of bulk water, but also of 2D
correlation and more challenging sum-frequency generation spectra of the
water-air interface. This paves the way for understanding complex interfaces
such as water encapsulated between or in contact with hydrophobic and
hydrophilic materials, through robust and inexpensive surface sensitive and
multidimensional spectra with first-principles accuracy.
