38
1 A Historical Review of the Structures of Water and Ice
is about 11 h [110].
28 In order to satisfy this huge lifetime, Geissler and co-authors
concluded that most water ions recombine quickly, without contributing to DC conductivity; however, some of them can survive for a long time, and the transient ionic
species may provide an experimentally detectable electrodynamic signal.
29
Hassanali et al. [73] analyzed the recombination of H 3 O
+ and OH
− ions in water,
taking into account nuclear quantum effects: proton tunneling and its zero point
energy. They found that the recombination of excess proton and proton hole occurs
in two stages: the compression of the chain of molecules connecting the corresponding ions in about 0.5 ps, and the neutralization of the compressed chain in 65 fs.
Thus, it was established that recombination requires the coordinated motion of several molecules, which makes this process unlikely in real temperature conditions.
However, one should note that phonons can provide the necessary conditions for
coordinated molecular dynamics even at room temperature.
Rick and Haymet [111] studied the dielectric properties of ice Ih, using a Monte
Carlo algorithm for sampling over proton configurations. They used non-polarizable
(SPC/E and TIP4P) and polarizable (TIP4P-FQ) molecular models to calculate the
static dielectric constant, (0), of ice. A good agreement with experimental data was
obtained only in the temperature range 150–270 K, and only for the polarizable
model TIP4P-FQ, which requires a phenomenological g-factor that was adjusted
to reach the required value of (0). The physical meaning of the g-factor, which
allowed the authors to fit the experimental data, is unclear, and it can be regarded as a
phenomenological parameter, the physical meaning of which is missing. For further
details, see Sect. 2.4.
Aragones et al. [112], continuing the previously mentioned study, calculated the
dielectric constants of ices Ih, III, V, VI, and VII for several water models using the
Monte Carlo method and an approximation in which proton-disordered configurations satisfy the Bernal–Fowler ice rules. Figure 1.27 shows that the SPC/E, TIP5P,
TIP4P, TIP4P/2005, and TIP4P/ice models of water are unable to reproduce simultaneously the experimental dielectric constants of water and ice Ih. The authors state
that the predictions of the Bernal–Fowler model for the dielectric constant differ,
in general, from that obtained rigorously by computer simulations because protondisordered configurations, which satisfy the Bernal–Fowler ice rules, differ in their
energies. They concluded that non-polarizable models cannot describe the dielectric
constants of different condensed phases of water because their dipole moments (about
2.3 D) are much smaller than those required for the fitting of the experimental data,
and, as estimated by the first-principles calculations, should be about 4.0 D. The predictions of TIP4P models provide an overall qualitatively correct description of the
dielectric constant of the condensed phases of water only when the dipole moment of
the model is scaled to the estimated value obtained from first-principle calculations
28 In fact, Eigen uses the adjective “apparent” for the 11-hour lifetime, and highlights that the
“true” lifetime of H 2 O molecules is determined by the intensity of proton exchange and lies in the
microsecond time interval, but, because of the indistinguishably of protons, cannot be detected.
Latter, the NMR method confirmed the short lifetime of water molecules (see Sect. 1.3).
29 These short-lived ionic species of water have been recently experimentally detected in the infrared
spectra of light and heavy water mixtures [32].
1 A Historical Review of the Structures of Water and Ice
is about 11 h [110].
28 In order to satisfy this huge lifetime, Geissler and co-authors
concluded that most water ions recombine quickly, without contributing to DC conductivity; however, some of them can survive for a long time, and the transient ionic
species may provide an experimentally detectable electrodynamic signal.
29
Hassanali et al. [73] analyzed the recombination of H 3 O
+ and OH
− ions in water,
taking into account nuclear quantum effects: proton tunneling and its zero point
energy. They found that the recombination of excess proton and proton hole occurs
in two stages: the compression of the chain of molecules connecting the corresponding ions in about 0.5 ps, and the neutralization of the compressed chain in 65 fs.
Thus, it was established that recombination requires the coordinated motion of several molecules, which makes this process unlikely in real temperature conditions.
However, one should note that phonons can provide the necessary conditions for
coordinated molecular dynamics even at room temperature.
Rick and Haymet [111] studied the dielectric properties of ice Ih, using a Monte
Carlo algorithm for sampling over proton configurations. They used non-polarizable
(SPC/E and TIP4P) and polarizable (TIP4P-FQ) molecular models to calculate the
static dielectric constant, (0), of ice. A good agreement with experimental data was
obtained only in the temperature range 150–270 K, and only for the polarizable
model TIP4P-FQ, which requires a phenomenological g-factor that was adjusted
to reach the required value of (0). The physical meaning of the g-factor, which
allowed the authors to fit the experimental data, is unclear, and it can be regarded as a
phenomenological parameter, the physical meaning of which is missing. For further
details, see Sect. 2.4.
Aragones et al. [112], continuing the previously mentioned study, calculated the
dielectric constants of ices Ih, III, V, VI, and VII for several water models using the
Monte Carlo method and an approximation in which proton-disordered configurations satisfy the Bernal–Fowler ice rules. Figure 1.27 shows that the SPC/E, TIP5P,
TIP4P, TIP4P/2005, and TIP4P/ice models of water are unable to reproduce simultaneously the experimental dielectric constants of water and ice Ih. The authors state
that the predictions of the Bernal–Fowler model for the dielectric constant differ,
in general, from that obtained rigorously by computer simulations because protondisordered configurations, which satisfy the Bernal–Fowler ice rules, differ in their
energies. They concluded that non-polarizable models cannot describe the dielectric
constants of different condensed phases of water because their dipole moments (about
2.3 D) are much smaller than those required for the fitting of the experimental data,
and, as estimated by the first-principles calculations, should be about 4.0 D. The predictions of TIP4P models provide an overall qualitatively correct description of the
dielectric constant of the condensed phases of water only when the dipole moment of
the model is scaled to the estimated value obtained from first-principle calculations
28 In fact, Eigen uses the adjective “apparent” for the 11-hour lifetime, and highlights that the
“true” lifetime of H 2 O molecules is determined by the intensity of proton exchange and lies in the
microsecond time interval, but, because of the indistinguishably of protons, cannot be detected.
Latter, the NMR method confirmed the short lifetime of water molecules (see Sect. 1.3).
29 These short-lived ionic species of water have been recently experimentally detected in the infrared
spectra of light and heavy water mixtures [32].