How to calculate the vibration of molecules in GMX?

GROMACS version:5.1.2
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I have simulated a box of glycerol/water mixtures at 534K. Now, I want to analyze the relationship between the vibration frequency and HB lifetime of glycerol molecules.
How to define and calculate the vibration frequency of molecules in GMX?

(if I understand your question correctly), Fourier-transforming the velocity-velocity autocorrelation function of the glycerol molecules should give you the vibrational spectrum (but time is gone at that stage) - HB lifetime could be calculated with fitting the autocorrelation function of h-bonds existence. To pinpoint any relation between the two you will have to come up with some link between the two…and relate them accordingly: not an easy task. Probably relating the velocity-velocity autocorrelation function, HB-lifetime and the stress-autocorrelation function (to give you an idea of the shear viscosity) - could be a good idea. Best of luck!