40
1 A Historical Review of the Structures of Water and Ice
hydrated ions H 9 O
+
4 and H 7 O
−
4 lay in the 2–3 ps time interval, which correspond to
that found by means of dielectric spectroscopy [118] (see Chap. 4 for details).
Markovich et al. [119] analyzed the dissociation–association rate of water dimer
(H 2 O–H 2 O) and calculated the self-diffusion coefficient D w of water molecules. They
obtained the value of D w = 2.27·10
−9 m
2 /s, which coincides with the experimental
result (see Sect. 1.4). They also found that the dimer recombination–relaxation time is
4.8 ps, which coincides with the second relaxation time of water at room temperature
(see Sect. 2.6.2). Similar values for the self-diffusion coefficient were obtained by
Liang et al. [117], who also showed that the proton diffusion coefficient is pHdependent and varies from D p = 1.0·10
−9 m
2 /s at pH = 1 to D p = 9.3·10
−9 m
2 /s
at pH = 6. The latter coincides with the proton diffusion coefficient obtained by
the equivalent conductivity measurement (see Sect. 1.3.1). The simulated proton
exchange rate k pt = 0.47 ps
−1 is close to the experimental value of 0.67 ps
−1 [120].
It is also approximately equal to the rate k d = 0.4 ps
−1 that corresponds to the
dissociation constant pK w of water (see Sect. 1.3.2).
There is no standard schematic for the modeling of proton transport and the
electrodynamic properties of water and ice. The search for the optimal model is
continuing. The limitation of the ab initio approaches is the small number of particles
that can be taken into consideration, while DFT requires a priori knowledge of
potential. Therefore, a full comparison of the models with the real properties of
bulk water is complicated, because a condensed medium is something more than
just an ensemble of interacting molecules. Although the qualitative and quantitative
description of some properties of water and ice has been achieved [121] and we know
how to describe each molecule and the bonds between the pairs of them and how
to simulate their motion in a corresponding potential, there is still no real theory of
water [122, 123] underpinning a fully predictive model [124], and a universal model
of the water molecule has yet to be found [125].
Figure 1.29 illustrates the current status of the search for a universal potential. It
shows the ranks of the performance of different water models based on the analysis
Fig. 1.29 An image with the scores from different molecular models for the description of the main
electrical, thermodynamic, and structural properties of water. For details, see the text. Reproduced
from [92] with permission from the PCCP Owner Societies
1 A Historical Review of the Structures of Water and Ice
hydrated ions H 9 O
+
4 and H 7 O
−
4 lay in the 2–3 ps time interval, which correspond to
that found by means of dielectric spectroscopy [118] (see Chap. 4 for details).
Markovich et al. [119] analyzed the dissociation–association rate of water dimer
(H 2 O–H 2 O) and calculated the self-diffusion coefficient D w of water molecules. They
obtained the value of D w = 2.27·10
−9 m
2 /s, which coincides with the experimental
result (see Sect. 1.4). They also found that the dimer recombination–relaxation time is
4.8 ps, which coincides with the second relaxation time of water at room temperature
(see Sect. 2.6.2). Similar values for the self-diffusion coefficient were obtained by
Liang et al. [117], who also showed that the proton diffusion coefficient is pHdependent and varies from D p = 1.0·10
−9 m
2 /s at pH = 1 to D p = 9.3·10
−9 m
2 /s
at pH = 6. The latter coincides with the proton diffusion coefficient obtained by
the equivalent conductivity measurement (see Sect. 1.3.1). The simulated proton
exchange rate k pt = 0.47 ps
−1 is close to the experimental value of 0.67 ps
−1 [120].
It is also approximately equal to the rate k d = 0.4 ps
−1 that corresponds to the
dissociation constant pK w of water (see Sect. 1.3.2).
There is no standard schematic for the modeling of proton transport and the
electrodynamic properties of water and ice. The search for the optimal model is
continuing. The limitation of the ab initio approaches is the small number of particles
that can be taken into consideration, while DFT requires a priori knowledge of
potential. Therefore, a full comparison of the models with the real properties of
bulk water is complicated, because a condensed medium is something more than
just an ensemble of interacting molecules. Although the qualitative and quantitative
description of some properties of water and ice has been achieved [121] and we know
how to describe each molecule and the bonds between the pairs of them and how
to simulate their motion in a corresponding potential, there is still no real theory of
water [122, 123] underpinning a fully predictive model [124], and a universal model
of the water molecule has yet to be found [125].
Figure 1.29 illustrates the current status of the search for a universal potential. It
shows the ranks of the performance of different water models based on the analysis
Fig. 1.29 An image with the scores from different molecular models for the description of the main
electrical, thermodynamic, and structural properties of water. For details, see the text. Reproduced
from [92] with permission from the PCCP Owner Societies