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The dielectric spectrum of liquid water, $10^{4} - 10^{11}$ Hz, is interpreted in terms of diffusion of charges, formed as a result of self-ionization of H$_{2}$O molecules. This approach explains the Debye relaxation and the dc conductivity as two manifestations of this diffusion. The Debye relaxation is due to the charge diffusion with a fast recombination rate, $1/tau_{2}$, while the dc conductivity is a manifestation of the diffusion with a much slower recombination rate, $1/tau_{1}$. Applying a simple model based on Brownian-like diffusion, we find $tau_{2} simeq 10^{-11}$ s and $tau_{1} simeq 10^{-6}$ s, and the concentrations of the charge carriers, involved in each of the two processes, $N_{2} simeq 5 times 10^{26}$ m$^{-3}$ and $N_{1} simeq 10^{14}$ m$^{-3}$. Further, we relate $N_{2}$ and $N_{1}$ to the total concentration of H$_{3}$O$^{+}$--OH$^{-}$ pairs and to the pH index, respectively, and find the lifetime of a single water molecule, $tau_{0} simeq 10^{-9}$ s. Finally, we show that the high permittivity of water results mostly from flickering of separated charges, rather than from reorientations of intact molecular dipoles.
One of the many peculiar properties of water is the pronounced deviation of the proton momentum distribution from Maxwell-Boltzmann behaviour. This deviation from the classical limit is a manifestation of the quantum mechanical nature of protons. Its
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A comprehensive microscopic understanding of ambient liquid water is a major challenge for $ab$ $initio$ simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as