132
4 The Dielectric Properties and Dynamic Structure of Water and Ice
The complexity of the concept of hydrogen bonding is obvious from the fact that
the notion of a hydrogen bond includes many types of interactions, including electrostatic attraction, polarization, dispersion, proton exchange, and covalent bonds,
2 and
that it has no strict criteria that allow one to “recognize” the hydrogen bond among
other molecular interactions [1]. The criteria are still too blurry, and the relative contribution of the individual components of hydrogen bonds that keep the species of
water together remains a matter of debate [2, 3].
The specificity of bonds between water molecules can be demonstrated in a simple
thought experiment. The amount of energy necessary for the evaporation of water
at normal pressure is Q = 2260 kJ/kg [4]. Assuming that water consists of H 2 O
species,
3 one gets their molar concentration n = m/M = 1000 g/18 g · mol
−1
=
55.5 mol/l, where m is the mass, and M is the molecular mass. Dividing Q by n,
one gets the energy per molecule, which equals q 0 = 40.7 kJ/mol. Assuming that on
average there are 3.6 “bonds” per molecule [5], one gets the energy of a single bond
between two water molecules: q H B ≈ 11.3 kJ/mol. This bond is too weak for covalent
or ionic bonds, which lie between 60 and 600 kJ/mol, and too strong for Van-derWaals interactions, which lie between 0.1 and 4.0 kJ/mol [4]. Thus, the bonds between
water molecules were assigned to a special type of intermolecular interactions, or
hydrogen bonds [6]. The value q H B is close to the value 13.6 kJ/mol of the binding
energy of the water dimer (H 2 O) 2 [7], and close to the spread of about 11 kJ/mol (0.11
eV) in the interaction energy among different isomers of the water dimer [3]. The
latter energy is obviously a minimal energy barrier of molecular diffusion.
4 In such
a way, the concept of hydrogen bonding found a logical framework and has spread
widely across different fields of science [6]. However, it has significant limitations,
which make it inapplicable at short (picosecond) timescales.
Note that the calculations provided above are based on the assumption that water
is an ensemble of sharply defined H 2 O species. The diffusion-averaged structure of
water possess a molecular nature, however, at short (picosecond) timescales, simulations of molecular dynamics, and ultrafast spectroscopic techniques (see Chap. 1),
show that molecules lose their individuality and can form the short-lived species
which are missing in the diffusion-averaged structure of water by Bernal and Fowler
(see Chap. 1). Each short-lived charged species, such as hydronium, Eigen, or Zundel cations, and their counterions (anions), are the centers of the Coulomb field,
which electrostatically affects the surrounding molecules. These kinds of intermolecular interactions are missing in the conventional concept of hydrogen bonding. For
instance, Eigen showed [8] that the heat of the hydration of the hydronium (H 3 O
+ ) or
hydroxyle (OH
− ) ions of water is relatively large and is approximately 1200 kJ/mol
2 Covalent bonding includes σ -bonding, π -bonding, metal-to-metal bonding, agostic interactions,
bent bonds, three-center two-electron bonds, and three-center four-electron bonds.
3 See the notes on the DC conductivity of water in Sect. 1.3, which show that this assumption is
not totally correct, because the small concentration of intrinsic ions (H 3 O + and OH − ) of water
was obtained neglecting their mutual interaction. Accounting for the interaction leads to a much
higher concentration of short-lived ionic species (see Sect. 3.5), which cannot be neglected when
intermolecular interaction is taken into account.
4 The experimental activation energy of self-diffusion in water is 0.18 eV (see Sect. 1.4).
4 The Dielectric Properties and Dynamic Structure of Water and Ice
The complexity of the concept of hydrogen bonding is obvious from the fact that
the notion of a hydrogen bond includes many types of interactions, including electrostatic attraction, polarization, dispersion, proton exchange, and covalent bonds,
2 and
that it has no strict criteria that allow one to “recognize” the hydrogen bond among
other molecular interactions [1]. The criteria are still too blurry, and the relative contribution of the individual components of hydrogen bonds that keep the species of
water together remains a matter of debate [2, 3].
The specificity of bonds between water molecules can be demonstrated in a simple
thought experiment. The amount of energy necessary for the evaporation of water
at normal pressure is Q = 2260 kJ/kg [4]. Assuming that water consists of H 2 O
species,
3 one gets their molar concentration n = m/M = 1000 g/18 g · mol
−1
=
55.5 mol/l, where m is the mass, and M is the molecular mass. Dividing Q by n,
one gets the energy per molecule, which equals q 0 = 40.7 kJ/mol. Assuming that on
average there are 3.6 “bonds” per molecule [5], one gets the energy of a single bond
between two water molecules: q H B ≈ 11.3 kJ/mol. This bond is too weak for covalent
or ionic bonds, which lie between 60 and 600 kJ/mol, and too strong for Van-derWaals interactions, which lie between 0.1 and 4.0 kJ/mol [4]. Thus, the bonds between
water molecules were assigned to a special type of intermolecular interactions, or
hydrogen bonds [6]. The value q H B is close to the value 13.6 kJ/mol of the binding
energy of the water dimer (H 2 O) 2 [7], and close to the spread of about 11 kJ/mol (0.11
eV) in the interaction energy among different isomers of the water dimer [3]. The
latter energy is obviously a minimal energy barrier of molecular diffusion.
4 In such
a way, the concept of hydrogen bonding found a logical framework and has spread
widely across different fields of science [6]. However, it has significant limitations,
which make it inapplicable at short (picosecond) timescales.
Note that the calculations provided above are based on the assumption that water
is an ensemble of sharply defined H 2 O species. The diffusion-averaged structure of
water possess a molecular nature, however, at short (picosecond) timescales, simulations of molecular dynamics, and ultrafast spectroscopic techniques (see Chap. 1),
show that molecules lose their individuality and can form the short-lived species
which are missing in the diffusion-averaged structure of water by Bernal and Fowler
(see Chap. 1). Each short-lived charged species, such as hydronium, Eigen, or Zundel cations, and their counterions (anions), are the centers of the Coulomb field,
which electrostatically affects the surrounding molecules. These kinds of intermolecular interactions are missing in the conventional concept of hydrogen bonding. For
instance, Eigen showed [8] that the heat of the hydration of the hydronium (H 3 O
+ ) or
hydroxyle (OH
− ) ions of water is relatively large and is approximately 1200 kJ/mol
2 Covalent bonding includes σ -bonding, π -bonding, metal-to-metal bonding, agostic interactions,
bent bonds, three-center two-electron bonds, and three-center four-electron bonds.
3 See the notes on the DC conductivity of water in Sect. 1.3, which show that this assumption is
not totally correct, because the small concentration of intrinsic ions (H 3 O + and OH − ) of water
was obtained neglecting their mutual interaction. Accounting for the interaction leads to a much
higher concentration of short-lived ionic species (see Sect. 3.5), which cannot be neglected when
intermolecular interaction is taken into account.
4 The experimental activation energy of self-diffusion in water is 0.18 eV (see Sect. 1.4).