^{1}, Masahiro Ichiki

^{2}, Katsuyuki Kawamura

^{3}and Kiyoshi Fuji-ta

^{4}

### Abstract

The physical properties of water under a wide range of pressure and temperature conditions are important in fundamental physics, chemistry, and geoscience. Molecular simulations are useful for predicting and understanding the physical properties of water at phases extremely different from ambient conditions. In this study, we developed a new five-site flexible induced point charge model to predict the density, static dielectric constant, and transport properties of water in the extremely supercritical phase at high temperatures and pressures of up to 2000 K and 2000 MPa. The model satisfactorily reproduced the density, radial distribution function, static dielectric constant, reorientation time, and self-diffusion coefficients of water above the critical points. We also developed a database of the static dielectric constant, which is useful for discussing the electrical conductivity of aqueous fluids in the earth's crust and mantle.

This research was partially supported by JSPS KAKENHI Grant No. 23740390 and a Grant-in-Aid for Scientific Research on Innovative Areas, Geofluids 2108. The authors thank E. Takahashi for useful discussions and Y. Katayama for providing his experimental results. We appreciate valuable comments by three anonymous reviewers.

I. INTRODUCTION

II. COMPUTATIONAL METHODS

A. Flexible induced point charge water model

B. Molecular dynamics simulations

III. RESULTS AND DISCUSSION

A. The parameterization strategy

B. Density

C. Radial distribution functions

D. Dielectric constant

E. Dipole moment distributions

F. Which of flexibility and induced charge is important for the change of the dipole moment?

G. Rotation of water molecules

H. Self-diffusion coefficients

I. Viscosity

J. Prediction of the static dielectric constant at extremely high temperature and pressure conditions

K. Comparisons with some of water models

IV. CONCLUSIONS

### Key Topics

- Electric dipole moments
- 41.0
- High pressure
- 41.0
- Dielectric constant
- 36.0
- Molecular dynamics
- 18.0
- Water vapor
- 16.0

## Figures

Developed five-site water model. The *x* axis is perpendicular to the molecular plane, which is represented by the *yz* plane. The permanent and induced point charges are located on two hydrogen atoms and on two lone pairs of the oxygen atom. The positions of the lone pairs are fixed along the *x* axis (*r* _{OLP} = 0.2 Å). The total charge of the H_{2}O molecule is neutralized.

Developed five-site water model. The *x* axis is perpendicular to the molecular plane, which is represented by the *yz* plane. The permanent and induced point charges are located on two hydrogen atoms and on two lone pairs of the oxygen atom. The positions of the lone pairs are fixed along the *x* axis (*r* _{OLP} = 0.2 Å). The total charge of the H_{2}O molecule is neutralized.

Comparison experimental and MD results for water density (*T* < 1000 K, *p* < 1000 MPa) and the prediction of the densities at high temperature and pressure up to *T* ≤ 2000 K and *p* ≤ 2000 MPa. The lines indicate the experimental results for IAPWS95 ^{ 11 } and sound velocity measurements. ^{ 49 }

Comparison experimental and MD results for water density (*T* < 1000 K, *p* < 1000 MPa) and the prediction of the densities at high temperature and pressure up to *T* ≤ 2000 K and *p* ≤ 2000 MPa. The lines indicate the experimental results for IAPWS95 ^{ 11 } and sound velocity measurements. ^{ 49 }

Radial distribution functions of (a) oxygen–oxygen (*g* _{OO}), (b) oxygen–hydrogen (*g* _{OH}), and (c) hydrogen–hydrogen sites (*g* _{HH}) at *T* = 573 K, *p* = 280 MPa, and *T* = 673 K, *p* = 340 MPa. MD results (solid lines) are compared with experimental neutron diffraction data (dashed lines). ^{ 50 } High-temperature and high-pressure data are shifted for comparison on the same graph.

Radial distribution functions of (a) oxygen–oxygen (*g* _{OO}), (b) oxygen–hydrogen (*g* _{OH}), and (c) hydrogen–hydrogen sites (*g* _{HH}) at *T* = 573 K, *p* = 280 MPa, and *T* = 673 K, *p* = 340 MPa. MD results (solid lines) are compared with experimental neutron diffraction data (dashed lines). ^{ 50 } High-temperature and high-pressure data are shifted for comparison on the same graph.

(a) Radial distribution functions of oxygen–oxygen sites *g* _{OO} at *T* = 673 K and *p* = 100, 340, 870, and 1190 MPa. MD results (solid lines) are compared with experimental data (dashed lines) for neutron diffraction ^{ 50 } at 340 MPa and x-ray diffraction data ^{ 51 } at 870 and 1190 MPa. The pressures for the x-ray diffraction data were calculated by conversion of the density using the IAPWS95 data. ^{ 11 } High-pressure data are shifted for comparison on the same graph. (b) Running coordination number (*rcn*) of oxygen–oxygen sites.

(a) Radial distribution functions of oxygen–oxygen sites *g* _{OO} at *T* = 673 K and *p* = 100, 340, 870, and 1190 MPa. MD results (solid lines) are compared with experimental data (dashed lines) for neutron diffraction ^{ 50 } at 340 MPa and x-ray diffraction data ^{ 51 } at 870 and 1190 MPa. The pressures for the x-ray diffraction data were calculated by conversion of the density using the IAPWS95 data. ^{ 11 } High-pressure data are shifted for comparison on the same graph. (b) Running coordination number (*rcn*) of oxygen–oxygen sites.

(a) Cumulative averages of calculated static dielectric constant of water at *p* = 2000 MPa and various temperatures. (b) Calculated static dielectric constant of water at various pressures and temperatures. Experimental values ^{ 56 } are shown as bold lines for comparison. Solid thin lines in (b) indicate fitting curves to the MD results, Eq. (20) .

(a) Cumulative averages of calculated static dielectric constant of water at *p* = 2000 MPa and various temperatures. (b) Calculated static dielectric constant of water at various pressures and temperatures. Experimental values ^{ 56 } are shown as bold lines for comparison. Solid thin lines in (b) indicate fitting curves to the MD results, Eq. (20) .

Distributions of absolute values of molecular dipole moment at *p* = (a) 340 MPa, (b) 800 MPa, (c) 1500 MPa, and (d) 2000 MPa. Arrows indicate changes in the distributions with increasing temperature.

Distributions of absolute values of molecular dipole moment at *p* = (a) 340 MPa, (b) 800 MPa, (c) 1500 MPa, and (d) 2000 MPa. Arrows indicate changes in the distributions with increasing temperature.

Mean and standard deviation of dipole moment of H_{2}O calculated by fitting a Gaussian probability density to the distribution of the dipole moment shown in Fig. 6 . Numbers indicate the temperature (K).

Mean and standard deviation of dipole moment of H_{2}O calculated by fitting a Gaussian probability density to the distribution of the dipole moment shown in Fig. 6 . Numbers indicate the temperature (K).

(a) Mean intramolecular O-H distances *r* _{OH}, (b) HOH angles, (c) increased percentage of the |**r** _{D}| (= |**r** _{OH1} + **r** _{OH2}|), and (d) the contribution of the flexibility of the water molecules into the induced dipole moments. The symbols are the same as those in Fig. 2 . (e) Distribution of intramolecular geometry among *r* _{OH} and HOH angle at *T* = 673 K and *p* = 340 MPa.

(a) Mean intramolecular O-H distances *r* _{OH}, (b) HOH angles, (c) increased percentage of the |**r** _{D}| (= |**r** _{OH1} + **r** _{OH2}|), and (d) the contribution of the flexibility of the water molecules into the induced dipole moments. The symbols are the same as those in Fig. 2 . (e) Distribution of intramolecular geometry among *r* _{OH} and HOH angle at *T* = 673 K and *p* = 340 MPa.

Rotational correlation functions (a) *C* _{2} ^{ y }(*t*) and (b) *C* _{1} ^{ z }(*t*) at *p* = 2000 MPa and the long-term exponential decay times (c) *τ* _{2} ^{ y } and (d) *τ* _{1} ^{ z }.

Rotational correlation functions (a) *C* _{2} ^{ y }(*t*) and (b) *C* _{1} ^{ z }(*t*) at *p* = 2000 MPa and the long-term exponential decay times (c) *τ* _{2} ^{ y } and (d) *τ* _{1} ^{ z }.

(a) Self-diffusion coefficients and (b) viscosity of water calculated by MD simulations. Bold lines are the experimentally obtained self-diffusion coefficients ^{ 62 } and viscosity. ^{ 65 }

(a) Self-diffusion coefficients and (b) viscosity of water calculated by MD simulations. Bold lines are the experimentally obtained self-diffusion coefficients ^{ 62 } and viscosity. ^{ 65 }

A comparison of the density at *T* = 673 K among water models and experiments. ^{ 11,49 }

A comparison of the density at *T* = 673 K among water models and experiments. ^{ 11,49 }

Radial distribution functions of (a) oxygen–oxygen (*g* _{OO}), (b) oxygen–hydrogen (*g* _{OH}), and (c) hydrogen–hydrogen sites (*g* _{HH}) at *T* = 673 K and *p* = 340 MPa. MD results using various water models are compared with experimental neutron diffraction data. ^{ 50 }

Radial distribution functions of (a) oxygen–oxygen (*g* _{OO}), (b) oxygen–hydrogen (*g* _{OH}), and (c) hydrogen–hydrogen sites (*g* _{HH}) at *T* = 673 K and *p* = 340 MPa. MD results using various water models are compared with experimental neutron diffraction data. ^{ 50 }

Static dielectric constants calculated at *T* = 673 K using various water models and the experimental data. ^{ 56 }

Static dielectric constants calculated at *T* = 673 K using various water models and the experimental data. ^{ 56 }

## Tables

Potential parameters of the FIPC model.

Potential parameters of the FIPC model.

Parameters relating to the polarization.

Parameters relating to the polarization.

Comparison of static dielectric constant of water calculated in this study and experimental values. Experimental values at *p* = 130, 140, and 340 MPa are derived from interpolation of experimental data. ^{ 56 }

Comparison of static dielectric constant of water calculated in this study and experimental values. Experimental values at *p* = 130, 140, and 340 MPa are derived from interpolation of experimental data. ^{ 56 }

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