1.6 Water in Molecular-Dynamic Simulations
41
proposed by Vega and Abascal [92]. The test of different models showed that the
scores (out of a maximum score of 10) range from about 3 (for TIP3P) to about
7 (for TIP4P/2005). None of the water models is perfect. The TIP4P/2005 model
gets the maximum score and can be regarded as a variation on the early model of
Bernal and Fowler (see Fig. 1.2), which, after 90 years of tests, is still used to model
water, although it is becoming obvious that water cannot be “built” using the longlived molecular species only. We should search for a model which accounts for the
intermolecular dynamics in the form of local chemical reactions.
DC conductivity, the dielectric constant, the infrared spectrum, and some geometric parameters of water and ice have been modeled separately. However, these
models are highly specialized and very complex. The dynamics of various forms of
excess protons, such as H 3 O
+ , H 9 O
+
4 , or proton holes such as OH
− allows the reproduction of parts of the water dielectric response. For the further developments of
computational methods and to account for quantum effects that do not follow from
the classical model of Bernal and Fowler, the interconversion of ions and neutral
water molecules should be taken into account.
1.7 Summary of the “Structure” of Water and Ice
Analysis has shown that the current structural models follow the original ideas of
Kohlrausch [8], Röntgen [7], Bernal and Fowler [9], which are based on static conductometric measurements and early X-ray diffraction data, with two basic assumptions: that water consists of long-lived H 2 O molecules with a small concentration of
intrinsic ions and that the structure of water is similar to that observed in quartz. All
later models, except a few alternative ideas [48], are based on these assumptions.
The standard view on the structure of water can be described as follows (see
Fig. 1.30). There is a three-dimensional network of bounded H 2 O molecules. The
network is based on the tetrahedral coordination of water molecules caused by their
polarity and structure. There are defects in the hexagonal structure corresponding to
the tetrahedral coordination. Hydrogen atoms do not necessarily occupy the positions
according to Bernal–Fowler ice rules. In water, there is significant proton disorder.
Molecules are arranged, but they constantly change neighbors in such a way that
the average lifetime of the stationary states is about 1 ps. The translational diffusion
of molecules occurs via the interstitial mechanism, when a molecule temporally
occupies the cavity in the nearest hexagonal ring.
30 A spontaneous fluctuation-born
proton transfer between water molecules leads to the formation of ionic species,
30 In normal conditions, in 1 second, molecules of ice and water were displaced by 0.1 mm and
0.2 µm, respectively. Distances are calculated using the Nernst–Einstein relation and the selfdiffusion coefficients D W = 2.3· 10 −9 (298 K) and D I = 1.0·10 −14 (272 K) m 2 /s for water and
ice, respectively. These macroscopic distances are much larger than the molecular diameter, and
assume continuous molecular shuffling that destroys any long-living molecular clusters.
41
proposed by Vega and Abascal [92]. The test of different models showed that the
scores (out of a maximum score of 10) range from about 3 (for TIP3P) to about
7 (for TIP4P/2005). None of the water models is perfect. The TIP4P/2005 model
gets the maximum score and can be regarded as a variation on the early model of
Bernal and Fowler (see Fig. 1.2), which, after 90 years of tests, is still used to model
water, although it is becoming obvious that water cannot be “built” using the longlived molecular species only. We should search for a model which accounts for the
intermolecular dynamics in the form of local chemical reactions.
DC conductivity, the dielectric constant, the infrared spectrum, and some geometric parameters of water and ice have been modeled separately. However, these
models are highly specialized and very complex. The dynamics of various forms of
excess protons, such as H 3 O
+ , H 9 O
+
4 , or proton holes such as OH
− allows the reproduction of parts of the water dielectric response. For the further developments of
computational methods and to account for quantum effects that do not follow from
the classical model of Bernal and Fowler, the interconversion of ions and neutral
water molecules should be taken into account.
1.7 Summary of the “Structure” of Water and Ice
Analysis has shown that the current structural models follow the original ideas of
Kohlrausch [8], Röntgen [7], Bernal and Fowler [9], which are based on static conductometric measurements and early X-ray diffraction data, with two basic assumptions: that water consists of long-lived H 2 O molecules with a small concentration of
intrinsic ions and that the structure of water is similar to that observed in quartz. All
later models, except a few alternative ideas [48], are based on these assumptions.
The standard view on the structure of water can be described as follows (see
Fig. 1.30). There is a three-dimensional network of bounded H 2 O molecules. The
network is based on the tetrahedral coordination of water molecules caused by their
polarity and structure. There are defects in the hexagonal structure corresponding to
the tetrahedral coordination. Hydrogen atoms do not necessarily occupy the positions
according to Bernal–Fowler ice rules. In water, there is significant proton disorder.
Molecules are arranged, but they constantly change neighbors in such a way that
the average lifetime of the stationary states is about 1 ps. The translational diffusion
of molecules occurs via the interstitial mechanism, when a molecule temporally
occupies the cavity in the nearest hexagonal ring.
30 A spontaneous fluctuation-born
proton transfer between water molecules leads to the formation of ionic species,
30 In normal conditions, in 1 second, molecules of ice and water were displaced by 0.1 mm and
0.2 µm, respectively. Distances are calculated using the Nernst–Einstein relation and the selfdiffusion coefficients D W = 2.3· 10 −9 (298 K) and D I = 1.0·10 −14 (272 K) m 2 /s for water and
ice, respectively. These macroscopic distances are much larger than the molecular diameter, and
assume continuous molecular shuffling that destroys any long-living molecular clusters.