1.6 Water in Molecular-Dynamic Simulations
37
using so-called functionals.
26 Although the approach is very useful for the study of the
structure that corresponds to the potential energy minimum, the DFT fails to describe
the intermolecular interactions of water, account for intermolecular charge transfer,
the transition states of protons and proton holes, or find any far-from-equilibrium
potential energy surface [99]. Moreover, with current computers, a sufficiently accurate simulation is possible only for processes shorter than a few picoseconds [100]
(see Fig. 1.26). Nevertheless, the DFT method continues to provide useful information on the local structure of water and ice, including nuclear quantum effects [101],
which are beyond the consideration in conventional MD-potential models, but seems
crucial for the electrodynamics of water (see Chap. 4).
The most popular among ab initio approaches which have been successfully
applied to water and ice is Car–Parrinello molecular dynamics [102]. This is based
on the symbiosis of DFT and Kohn–Sham functions [91]. This method does not
require any potentials in an analytical form. Instead, wave functions are specified.
The parameters of water molecules in neutral [95, 103, 104], protonated [105], and
deprotonated [106, 107] states, as well as in ice [108] have been carefully modeled
by the Car–Parrinello method for the past several decades. Many atomic-molecular
mechanisms have been modeled by introducing adjustable parameters. However, the
universal parameters of interacting water molecules which can describe all the properties of water have not yet been found. There are some interesting examples below,
which are related to the electrodynamic properties of ice and water.
1.6.2 The Simulation of the Electrodynamic Parameters
of Water and Ice
Geissler et al. [77] analyzed the autodissociation of water by sampling ab initio
molecular-dynamic trajectories. Identifying the rare fluctuations in solvation energies, the authors studied the transfer of protons between molecules. This is an important process for the electrodynamics of water. Calculations showed that the proton
“wire” (the chain of proton-transfer events) reaches a length of at least three molecular diameters. This result coincides with a previous study [109], and additionally
shows that if the proton wire remains unbroken, the ions recombine rapidly within
100 fs.
27 This time interval was later confirmed by Marx [50]. In accounting for the
concentration of ionic species that appear/disappear due to autoionization events,
Geissler et al. rely on the classic paper of Eigen who states, on the basis of the early
conductivity measurements (see Sect. 1.3.1), that the average H 2 O molecule lifetime
26 Hybrid functionals are a class of approximations of the exchange-correlation energy functional
in DFT which incorporate a portion of the exact exchange from Hartree–Fock theory with the rest
of the exchange-correlation energy from other sources (ab initio or empirical).
27 Note that this time corresponds to the so-called OH-band (3,600 cm −1 ) of the infrared spectrum
of liquid water.
37
using so-called functionals.
26 Although the approach is very useful for the study of the
structure that corresponds to the potential energy minimum, the DFT fails to describe
the intermolecular interactions of water, account for intermolecular charge transfer,
the transition states of protons and proton holes, or find any far-from-equilibrium
potential energy surface [99]. Moreover, with current computers, a sufficiently accurate simulation is possible only for processes shorter than a few picoseconds [100]
(see Fig. 1.26). Nevertheless, the DFT method continues to provide useful information on the local structure of water and ice, including nuclear quantum effects [101],
which are beyond the consideration in conventional MD-potential models, but seems
crucial for the electrodynamics of water (see Chap. 4).
The most popular among ab initio approaches which have been successfully
applied to water and ice is Car–Parrinello molecular dynamics [102]. This is based
on the symbiosis of DFT and Kohn–Sham functions [91]. This method does not
require any potentials in an analytical form. Instead, wave functions are specified.
The parameters of water molecules in neutral [95, 103, 104], protonated [105], and
deprotonated [106, 107] states, as well as in ice [108] have been carefully modeled
by the Car–Parrinello method for the past several decades. Many atomic-molecular
mechanisms have been modeled by introducing adjustable parameters. However, the
universal parameters of interacting water molecules which can describe all the properties of water have not yet been found. There are some interesting examples below,
which are related to the electrodynamic properties of ice and water.
1.6.2 The Simulation of the Electrodynamic Parameters
of Water and Ice
Geissler et al. [77] analyzed the autodissociation of water by sampling ab initio
molecular-dynamic trajectories. Identifying the rare fluctuations in solvation energies, the authors studied the transfer of protons between molecules. This is an important process for the electrodynamics of water. Calculations showed that the proton
“wire” (the chain of proton-transfer events) reaches a length of at least three molecular diameters. This result coincides with a previous study [109], and additionally
shows that if the proton wire remains unbroken, the ions recombine rapidly within
100 fs.
27 This time interval was later confirmed by Marx [50]. In accounting for the
concentration of ionic species that appear/disappear due to autoionization events,
Geissler et al. rely on the classic paper of Eigen who states, on the basis of the early
conductivity measurements (see Sect. 1.3.1), that the average H 2 O molecule lifetime
26 Hybrid functionals are a class of approximations of the exchange-correlation energy functional
in DFT which incorporate a portion of the exact exchange from Hartree–Fock theory with the rest
of the exchange-correlation energy from other sources (ab initio or empirical).
27 Note that this time corresponds to the so-called OH-band (3,600 cm −1 ) of the infrared spectrum
of liquid water.