The reported anomalies of the proton mean kinetic energy,
Ke(H),
in nanoconfined water, as measured by deep inelastic neutron scattering
(DINS), constitute a longstanding problem related to proton dynamics
in hydrogen-bonded systems. A considerable number of theoretical attempts
to explain these anomalies have failed. The mean vibrational density
of states (VDOS) of protons in water nanoconfined inside single wall
carbon nanotubes (SWCNTs) is calculated as a function of temperature
and SWCNT diameter, D
CNT, by classical
molecular dynamics (MD) simulation using the TIP4P-2005f water model.
The calculated VDOS are utilized for deducing the mean kinetic energy
of the water protons, Ke(H), by treating each phonon state as a harmonic
oscillator. The calculation depicts a strong confinement effect as
reflected in the drop of the value of Ke(H) at 5 K for D
CNT < ∼12 Å, while absent for larger diameters.
The results also reveal very significant blue and red shifts of the
stretching and bending modes, respectively, compared to those in bulk
ice, in agreement with experiment.