Autocorrelation function vibrational modes, hydrogen-bonded systems

The rotational relaxation of water molecules is often discussed in terms of angular momentum autocorrelation functions (e g., Stillinger and Rahman 1972 Yoshii et al. 1998). For a flexible water model, a slightly different approach can also be used. In order to separate the various modes of molecular librations (hindered rotations) and intramolecular vibrations, the scheme proposed by Bopp (1986) and Spohr et al. (1988) can be employed. The instantaneous velocities of the two hydrogen atoms of every water molecule in the molecular center-of-mass system are projected onto the instantaneous unit vectors i) in the direction of the corresponding OH bond (ui and U2) ... 

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