  Canonical ensemble molecular dynamics simulations of liquid methanol, modeled
using a rigid-body, pair-additive potential, are used to compute static
distributions and temporal correlations of tagged molecule potential energies
as a means of characterising the liquid state dynamics. The static distribution
of tagged molecule potential energies shows a clear multimodal structure with
three distinct peaks, similar to those observed previously in water and liquid
silica. The multimodality is shown to originate from electrostatic effects, but
not from local, hydrogen-bond interactions. An interesting outcome of this
study is the remarkable similarity in the tagged potential energy power spectra
of methanol, water and silica, despite the differences in the underlying
interactions and the dimensionality of the network. All three liquids show a
distinct multiple time scale (MTS) regime with a 1/f dependence with a clear
positive correlation between the scaling exponent alpha and the diffusivity.
The low-frequency limit of the MTS regime is determined by the frequency of
crossover to white noise behaviour which occurs at approximately 0.1 cm{-1} in
the case of methanol under standard temperature and pressure conditions. The
power spectral regime above 200 cm{-1} in all three systems is dominated by
resonances due to localised vibrations, such as librations. The correlation
between $\alpha$ and the diffusivity in all three liquids appears to be related
to the strength of the coupling between the localised motions and the larger
length/time-scale network reorganizations. Thus the time scales associated with
network reorganization dynamics appear to be qualitatively similar in these
systems, despite the fact that water and silica both display diffusional
anomalies but methanol does not.
