A three-point velocity correlation function ⟨(t1 + t2)(t1)(0)⟩ is introduced for a better understanding of the recent 2D-Raman-THz spectroscopy of the intermolecular degrees of freedoms of water and aqueous salt solutions. This correlation function reveals echoes in the presence of inhomogeneous broadening, which are coined “velocity echoes.” In analogy to the well-known two-point velocity correlation function ⟨(t)(0)⟩, it reflects the density of states (DOS) of the system under study without having to amend them with transition dipoles and transition polarizabilities. The correlation function can be calculated from equilibrium trajectories and converges extremely quickly. After deriving the theory, the information content of the three-point velocity correlation function is first tested based on a simple harmonic oscillator model with Langevin dynamics. Subsequently, velocity echoes of TIP4P/2005 water are calculated as a function of temperature, covering ambient conditions, the supercooled regime and amorphous ice, as well as upon addition of various salts. The experimentally observed trends can be reproduced qualitatively with the help of computationally very inexpensive molecular dynamics simulations.
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