This PDF file includes:

• section S1. Procedure of obtaining the VHF from the dynamic structure function
  
• section S2. The VHF of a simple liquid metal
  
• section S3. VHF of various models for ambient liquid water
  
• section S4. VHF and the Green function
  
• section S5. Effects of truncation over Q and E on VHF
  
• section S6. Local configurational excitations of liquid water
  
• section S7. Hydrogen dynamics
  
• fig. S1. Dynamic structure function S(Q, E) for liquid water at ambient condition.
  
• fig. S2. Intermediate scattering function F(Q, t) for liquid water at ambient condition.
  
• fig. S3. The low-Q part of F(Q, t).
  
• fig. S4. The VHF, g(r, t) – 1, of liquid iron at 2500 K by simulation.
  
• fig. S5. The calculated VHF for various water models.
  
• fig. S6. 2D plot of g(r, t) – 1 for water models at 300 K.
  
• fig. S7. The effect of a limited maximum Q in the Fourier transform of S_sim(Q, E) on the PDF g(r).
  
• fig. S8. The effect of a limited maximum Q in the FT of F(Q, t) on the g(r, t).
  
• fig. S9. The effect of a limited maximum Q in the Fourier transform of F(Q, t).
  
• fig. S10. Comparison of the total and O-O VHF for the SPC/E model.
  
• fig. S11. Correlation between τ_LC and τ_MIX for various models.
  
• References (40–49)

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