36
1 A Historical Review of the Structures of Water and Ice
Fig. 1.26 Computer
simulation methods by the
number of particles and the
observation time of the
corresponding microscopic
processes. DPD is dissipative
particle dynamics. MD is
molecular dynamics
Monte-Carlo
DPD
Ab initio
MD
10
-3 10
-5 10
-7 10
-9 10
-11 10
-13 10
-15
10
1
10
2
10
3
10
4
10
5
Number of particles
Time (s)
adding oscillating, distributed, or variable charges, and require some additional computational cost. However, there are experiments in which such overpolarized H 2 O
molecules were not confirmed [96, 97]: in infrared spectra, the O–H stretch frequency
changes insignificantly compared to the gas phase, and neutron diffraction does not
confirm significant perturbations of the hydrogen atom positions. Thus, although
certain successes in the modeling of the water properties by MD methods have been
unambiguously achieved, there is still a question on how close these models are to
reality [98].
The growth of computer efficiency by the mid-1990s made it possible to implement quantum chemistry methods for the calculation of the electronic structure of
water molecules. Nowadays, so-called ab initio methods are widely used for the
simulation of water. This approach is based on solving the Schrödinger equation in
the Born–Oppenheimer approximation,
25 and yield electron densities, energies, and
other properties of the molecular water system. Although the method does not use
any input parameters except initial atomic coordinates, it requires high computational
costs that makes the calculation of large molecular systems difficult. That is why the
pure ab initio method is not applicable for real systems, and deals with only a few
molecules (see Fig. 1.26).
The density-functional theory (DFT) is typically used to minimize the computational costs of ab initio calculations. In hybrid ab initio-DFT simulations, the electronic structure is evaluated using the electrostatic potential of the electrons for atoms
of the molecular system. The DFT potential is constructed as the sum of external
potentials U ext , which can be determined by the X-ray spectroscopy of water vapor,
and an effective potential U e f f , which represents interelectronic interactions and is
generally unknown. Using this theory, the properties of water can be determined by
25 The assumption that the motion of atomic nuclei and electrons in a molecule can be treated
separately, as the nuclei are much heavier than the electrons.
1 A Historical Review of the Structures of Water and Ice
Fig. 1.26 Computer
simulation methods by the
number of particles and the
observation time of the
corresponding microscopic
processes. DPD is dissipative
particle dynamics. MD is
molecular dynamics
Monte-Carlo
DPD
Ab initio
MD
10
-3 10
-5 10
-7 10
-9 10
-11 10
-13 10
-15
10
1
10
2
10
3
10
4
10
5
Number of particles
Time (s)
adding oscillating, distributed, or variable charges, and require some additional computational cost. However, there are experiments in which such overpolarized H 2 O
molecules were not confirmed [96, 97]: in infrared spectra, the O–H stretch frequency
changes insignificantly compared to the gas phase, and neutron diffraction does not
confirm significant perturbations of the hydrogen atom positions. Thus, although
certain successes in the modeling of the water properties by MD methods have been
unambiguously achieved, there is still a question on how close these models are to
reality [98].
The growth of computer efficiency by the mid-1990s made it possible to implement quantum chemistry methods for the calculation of the electronic structure of
water molecules. Nowadays, so-called ab initio methods are widely used for the
simulation of water. This approach is based on solving the Schrödinger equation in
the Born–Oppenheimer approximation,
25 and yield electron densities, energies, and
other properties of the molecular water system. Although the method does not use
any input parameters except initial atomic coordinates, it requires high computational
costs that makes the calculation of large molecular systems difficult. That is why the
pure ab initio method is not applicable for real systems, and deals with only a few
molecules (see Fig. 1.26).
The density-functional theory (DFT) is typically used to minimize the computational costs of ab initio calculations. In hybrid ab initio-DFT simulations, the electronic structure is evaluated using the electrostatic potential of the electrons for atoms
of the molecular system. The DFT potential is constructed as the sum of external
potentials U ext , which can be determined by the X-ray spectroscopy of water vapor,
and an effective potential U e f f , which represents interelectronic interactions and is
generally unknown. Using this theory, the properties of water can be determined by
25 The assumption that the motion of atomic nuclei and electrons in a molecule can be treated
separately, as the nuclei are much heavier than the electrons.