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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.
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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 extent, which can be probed directly by Deep Inelastic Neutron Scattering (DINS) experiments, gives important insight on the potential of mean force felt by H atoms. The determination of the full distribution of particle momenta, however, is a real tour de force for both experiments and theory, which has led to unresolved discrepancies between the two. In this Letter we present comprehensive, fully-converged momentum distributions for water at several thermodynamic state points, focusing on the components that cannot be described in terms of a scalar contribution to the quantum kinetic energy, and providing a benchmark that can serve as a reference for future simulations and experiments. In doing so, we also introduce a number of technical developments that simplify and accelerate greatly the calculation of momentum distributions by means of atomistic simulations.
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Yujin Tong
, Tobias Kampfrath
, R. Kramer Campen (Fritz Habern Institute of the Max Planck Society
2017
Most properties of liquid water are determined by its hydrogen-bond network. Because forming an aqueous interface requires termination of this network, one might expect the molecular level properties of interfacial water to markedly differ from water in bulk. Intriguingly, much prior experimental and theoretical work has found that, from the perspective of their time-averaged structure and picosecond structural dynamics, hydrogen-bonded OH groups at an air/water interface behave the same as hydrogen-bonded OH groups in bulk liquid water. Here we report the first experimental observation of interfacial waters libration (i.e. frustrated rotation) using the laser-based technique vibrational sum frequency spectroscopy. We find this mode has a frequency of 834 cm$^{-1}$, $approx 165$ cm$^{-1}$ higher than in bulk liquid water at the same temperature and similar to bulk ice. Because libration frequency is proportional to the stiffness of waters rotational potential, this increase suggests that one effect of terminating bulk waters hydrogen bonding network at the air/water interface is retarding rotation of water around intact hydrogen bonds. Because in bulk liquid water the libration plays a key role in stabilizing reaction intermediates and dissipating excess vibrational energy, we expect the ability to probe this mode in interfacial water to open new perspectives on the kinetics of heterogeneous reactions at aqueous interfaces.
Nuclear quantum effects, such as zero-point energy and tunneling, cause significant changes to the structure and dynamics of hydrogen bonded systems such as liquid water. However, due to the current inability to simulate liquid water using an exact description of its electronic structure, the interplay between nuclear and electronic quantum effects remains unclear. Here we use simulations that incorporate the quantum mechanical nature of both the nuclei and electrons to provide a fully ab initio determination of the particle quantum kinetic energies, free energy change upon exchanging hydrogen for deuterium and the isotope fractionation ratio in water. These properties, which selectively probe the quantum nature of the nuclear degrees of freedom, allow us to make direct comparison to recent experiments and elucidate how electronic exchange and correlation and nuclear quantum fluctuations determine the structure of the hydrogen bond in water.
We investigate the structural similarities between liquid water and 53 ices, including 20 knowncrystalline phases. We base such similarity comparison on the local environments that consist of atoms within a certain cutoff radius of a central atom. We reveal that liquid water explores the localenvironments of the diverse ice phases, by directly comparing the environments in these phases using general atomic descriptors, and also by demonstrating that a machine-learning potential trained on liquid water alone can predict the densities, the lattice energies, and vibrational properties of theices. The finding that the local environments characterising the different ice phases are found in water sheds light on water phase behaviors, and rationalizes the transferability of water models between different phases.
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 extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for $ab$ $initio$ approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile $ab$ $initio$ based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model---a neural-network representation of the $ab$ $initio$ PES---in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H$_2$O and D$_2$O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects.
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