Proton transfer reactions and dynamics were theoretically studied using the hydrogen-bond (H-bond) complexes formed from H(3)O(+) and nH(2)O, n = 1-4, as model systems. The investigations began with searching for characteristics of transferring protons in the gas phase and continuum aqueous solution using DFT method at the B3LYP/TZVP level, followed by Born-Oppenheimer molecular dynamics (BOMD) simulations at 350 K. B3LYP/TZVP calculations revealed the threshold asymmetric O-H stretching frequencies (ν(OH)*) for the proton transfers in the Zundel complex (H(5)O) in the gas phase and continuum aqueous solution at 1984 and 1881 cm(-1), respectively. BOMD simulations suggested lower threshold frequencies (ν(OH,MD)* = 1917 and 1736 cm(-1), respectively), with two characteristic ν(OH,MD) being the IR spectral signatures of the transferring protons. The low-frequency band could be associated with the "oscillatory shuttling motion" and the high-frequency band with the "structural diffusion motion". These can be regarded as the spectroscopic evidences of the formations of the shared-proton structure (O···H(+)···O) and the H(3)O(+)-H(2)O contact structure (O-H(+)···O), respectively. Since the quasi-dynamic equilibrium between the Zundel and Eigen complexes was suggested to be the rate-determining step, in order to achieve an "ideal" maximum efficiency of proton transfer, a concerted reaction pathway should be taken. The most effective interconversion between the two proton states, the shared-proton structure and the H(3)O(+)-H(2)O contact structure, can be reflected from comparable intensities of the oscillatory shuttling and structural diffusion bands. The present results iterated the previous conclusions that static proton transfer potentials cannot provide complete description of the structural diffusion process and it is essential to incorporate thermal energy fluctuations and dynamics in the model calculations.

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