1.5 Diffusion by Neutron Scattering
35
which it again appears in the new oscillatory state. Then the process repeats. Protons, when in oscillatory states, still undergo continuous diffusion with the center of
oscillation in a quasi-equilibrium vibrational state at the same time.
1.6 Water in Molecular-Dynamic Simulations
1.6.1 Methods of Water Modeling
Methods of computer simulation, such as molecular dynamics (MD), molecular
mechanics (MM), dissipative particle dynamics (DPD), and Monte Carlo (MC),
have been actively used for the studies of water and ice since the pioneering works
of Barker and Watts, and Rahman and Stillinger [87, 88]. Nowadays, computer simulations are an important part of studies of water and ice. Many experimental data on
water, including electrodynamic parameters, were verified by computer simulations.
The main problem of molecular-dynamic studies is to find the potential U of intraand intermolecular interactions, which would provide a description of the experimentally measured parameters of water, e.g., structural, such as density, viscosity,
surface tension; electrical, such as dielectric constant, infrared spectrum, electrical
conductivity; and thermodynamic, such as heat capacity and thermal conductivity.
Figure 1.26 shows the landscape of the main modern methods of computer simulation, which are used to study the microscopic structure of water and ice. One can see
that different methods are applicable for different time intervals, and can also account
for the different number of particles (molecules or atoms). The MC and MD methods
cover the largest range of times (including diffusion and structural relaxation), but
require knowledge of potentials, which is hard to assume a priori. That is why there
are huge variety of three-, four-, and five-point models of water molecules, which are
used to model different water properties. The most popular models are SPC/E, TIP4P,
TIP4P/Ice, and TIP5P [89]. In addition, some simple semi-classical approaches have
recently come under the spotlight again [90]. The wide range of models is a consequence of the fact that different properties are described by different potentials. To
date, there is no model that can quantitatively describe all the properties of water,
and the search for a “universal” model continues.
The MD approach is based on the idea that water is an ensemble of H 2 O molecules.
The first molecular models were built on the structure proposed by Bernal and Fowler
(see Sect. 1.3.1 and Fig. 1.2), the model that has been around since the pre-computer
era [91]. When first computers appeared, it was immediately shown that rigid nonpolarizable models fail to reproduce the basic properties of water, including electrodynamic parameters (see, for example, [92]). In order to improve the model, the
potentials that take into account the polarizability of H 2 O molecules due to the
influence of the environment have been suggested [93, 94]. In some calculations,
the molecular dipole moment μ increases by 60% compared to those observed in
the gas phase [95]. These changes to the molecular structure are usually modeled by
35
which it again appears in the new oscillatory state. Then the process repeats. Protons, when in oscillatory states, still undergo continuous diffusion with the center of
oscillation in a quasi-equilibrium vibrational state at the same time.
1.6 Water in Molecular-Dynamic Simulations
1.6.1 Methods of Water Modeling
Methods of computer simulation, such as molecular dynamics (MD), molecular
mechanics (MM), dissipative particle dynamics (DPD), and Monte Carlo (MC),
have been actively used for the studies of water and ice since the pioneering works
of Barker and Watts, and Rahman and Stillinger [87, 88]. Nowadays, computer simulations are an important part of studies of water and ice. Many experimental data on
water, including electrodynamic parameters, were verified by computer simulations.
The main problem of molecular-dynamic studies is to find the potential U of intraand intermolecular interactions, which would provide a description of the experimentally measured parameters of water, e.g., structural, such as density, viscosity,
surface tension; electrical, such as dielectric constant, infrared spectrum, electrical
conductivity; and thermodynamic, such as heat capacity and thermal conductivity.
Figure 1.26 shows the landscape of the main modern methods of computer simulation, which are used to study the microscopic structure of water and ice. One can see
that different methods are applicable for different time intervals, and can also account
for the different number of particles (molecules or atoms). The MC and MD methods
cover the largest range of times (including diffusion and structural relaxation), but
require knowledge of potentials, which is hard to assume a priori. That is why there
are huge variety of three-, four-, and five-point models of water molecules, which are
used to model different water properties. The most popular models are SPC/E, TIP4P,
TIP4P/Ice, and TIP5P [89]. In addition, some simple semi-classical approaches have
recently come under the spotlight again [90]. The wide range of models is a consequence of the fact that different properties are described by different potentials. To
date, there is no model that can quantitatively describe all the properties of water,
and the search for a “universal” model continues.
The MD approach is based on the idea that water is an ensemble of H 2 O molecules.
The first molecular models were built on the structure proposed by Bernal and Fowler
(see Sect. 1.3.1 and Fig. 1.2), the model that has been around since the pre-computer
era [91]. When first computers appeared, it was immediately shown that rigid nonpolarizable models fail to reproduce the basic properties of water, including electrodynamic parameters (see, for example, [92]). In order to improve the model, the
potentials that take into account the polarizability of H 2 O molecules due to the
influence of the environment have been suggested [93, 94]. In some calculations,
the molecular dipole moment μ increases by 60% compared to those observed in
the gas phase [95]. These changes to the molecular structure are usually modeled by