The mechanism of proton translocation along linear hydrogen-bonded wat
er chains is investigated. Classical and discretized Feynman path inte
gral molecular dynamics simulations are performed on protonated linear
chains of 4, 5, and 9 water molecules. The dissociable and polarizabl
e water model PM6 of Stillinger and co-workers is used to represent th
e potential energy surface of the systems. The simulations show that q
uantum and thermal effects are both important because the height of th
e barriers opposing proton transfer are strongly coupled to the config
uration of the chain, which is, in turn, affected by the presence of a
n excess proton. For characterization of the quantum effects, the ener
gy levels of the hydrogen nucleus located at the center of a protonate
d tetrameric water chain are calculated by solving the Schroedinger eq
uation for an ensemble of configurations which were generated with pat
h integral simulations. Analysis shows that the first excitation energ
ies are significantly larger than the thermal energy k(B)T and that qu
antum effects are dominated by the zero-point energy of the proton. Th
e quantum correlations between the different proton nuclei are found t
o be negligibly small, suggesting that an effective one-particle descr
iption could be valid. Potential of mean force surfaces for proton mot
ion in relation to the donor-acceptor separation are calculated with c
lassical and path integral simulations for tetrameric and pentameric w
ater chains. The mechanism for long-range proton transfer is illustrat
ed with a simulation of a hydrogen-bonded chain of nine water molecule
s, During the simulation, cooperative fluctuations which modulate the
asymmetry of the chain enable the spontaneous translocation of protons
over half of the length of the chain.