^{1,a)}

### Abstract

We perform molecular dynamics simulations of supercritical water (SCW) with a wide range of densities along a near critical isotherm using the simple point charge extended (SPC/E) pair potential in order to study the entropy and the solvation shell structure around a central water molecule. It is shown that both the translational and orientational two-particle correlationentropy terms can serve as the metrics of the translational-orientational structural orders in water and it is revealed that the translational structural order is very sensitive to the density variation in the gas-like and liquid-like region, while the orientational structural order is much more dependent upon compression in the medium-density SCW region. The comparison of the magnitudes of the full thermodynamic excess entropy and two-particle correlationentropy confirms the recent findings that the many-body terms other than two-body ones also present significant and non-neglectable contributions to the full excess entropy for the highly anomalous fluids like water. The analysis of entropy terms as a function of intermolecular distance and the orientational distribution functions as well as the three-dimensional spatialdistribution functions indicate that the structural order occurs only in a much more diffused first solvation shell due to the elongated hydrogen bonds under supercritical conditions. It is revealed that no obvious second or higher neighbor shells occur in SCW, in contrast with the feature of normal liquid water that the anomalous decrease of translational order upon compression occurs mainly in the second shell.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 21003072 and 91122019), National Basic Research Program (Grant No. 2011CB808604), and the Fundamental Research Funds for the Central Universities.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

IV. SUMMARY AND CONCLUSION

### Key Topics

- Entropy
- 55.0
- Hydrogen bonding
- 14.0
- Particle distribution functions
- 10.0
- Molecular dynamics
- 6.0
- Spatial analysis
- 6.0

## Figures

Calculated O–O RDFs with different box sizes and various simulated time lengths at ρ = 1.1441ρ_{ c } and *T* = 666 K.

Calculated O–O RDFs with different box sizes and various simulated time lengths at ρ = 1.1441ρ_{ c } and *T* = 666 K.

Isothermal variation of the two-particle correlation entropy with the density (*T* = 666 K).

Isothermal variation of the two-particle correlation entropy with the density (*T* = 666 K).

Isothermal variation of the thermodynamic excess entropy and two-particle correlation entropy with the density (*T* = 666 K).

Isothermal variation of the thermodynamic excess entropy and two-particle correlation entropy with the density (*T* = 666 K).

Calculated oxygen-oxygen RDF *g* _{O–O} and cumulative translational order integral *I* _{ s(tr)} as a function of the oxygen-oxygen distance *r* _{O–O} under various conditions.

Calculated oxygen-oxygen RDF *g* _{O–O} and cumulative translational order integral *I* _{ s(tr)} as a function of the oxygen-oxygen distance *r* _{O–O} under various conditions.

Calculated O–O orientational distribution functions *g*(θ, ϕ|*r*) of water in the *r* ⩽ 0.32 nm region under various conditions, where θ, ϕ are the polar angle and the azimuthal angle in the spherical coordinate system, respectively. (a) *g*(θ, ϕ|*r*) for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) in the *r* ⩽ 0.32 nm region. (b) *g*(θ, ϕ|*r*) for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) in the *r* ⩽ 0.32 nm region. The position of the oxygen atom of the central water molecule is set as the origin of the coordinates and the central water molecule is set to locate within the XZ plane and symmetric about the Z axis.

Calculated O–O orientational distribution functions *g*(θ, ϕ|*r*) of water in the *r* ⩽ 0.32 nm region under various conditions, where θ, ϕ are the polar angle and the azimuthal angle in the spherical coordinate system, respectively. (a) *g*(θ, ϕ|*r*) for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) in the *r* ⩽ 0.32 nm region. (b) *g*(θ, ϕ|*r*) for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) in the *r* ⩽ 0.32 nm region. The position of the oxygen atom of the central water molecule is set as the origin of the coordinates and the central water molecule is set to locate within the XZ plane and symmetric about the Z axis.

Calculated O–O orientational distribution functions *g*(θ, ϕ|*r*) of water in the 0.32 nm < *r* ⩽ 0.56 nm region under various conditions, where θ, ϕ are the polar angle and the azimuthal angle in the spherical coordinate system, respectively. (a) *g*(θ, ϕ|*r*) for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) in the 0.32 nm < *r* ⩽ 0.56 nm region. (b) *g*(θ, ϕ|*r*) for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) in the 0.32 nm < *r* ⩽ 0.56 nm region. The position of the oxygen atom of the central water molecule is set as the origin of the coordinates and the central water molecule is set to locate within the XZ plane and symmetric about the Z axis.

Calculated O–O orientational distribution functions *g*(θ, ϕ|*r*) of water in the 0.32 nm < *r* ⩽ 0.56 nm region under various conditions, where θ, ϕ are the polar angle and the azimuthal angle in the spherical coordinate system, respectively. (a) *g*(θ, ϕ|*r*) for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) in the 0.32 nm < *r* ⩽ 0.56 nm region. (b) *g*(θ, ϕ|*r*) for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) in the 0.32 nm < *r* ⩽ 0.56 nm region. The position of the oxygen atom of the central water molecule is set as the origin of the coordinates and the central water molecule is set to locate within the XZ plane and symmetric about the Z axis.

Calculated O–O spatial distribution functions of water under various conditions. (a) *g*(*x*, *y*, *z*) ⩾ 1.5 for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) with XZ plane is in the plane. (b) *g*(*x*, *y*, *z*) ⩾ 1.5 for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) with YZ plane is in the plane. (c) *g*(*x*, *y*, *z*) ⩾ 1.3 for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) with XZ plane is in the plane. (d) *g*(*x*, *y*, *z*) ⩾ 1.3 for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) with YZ plane is in the plane. The position of the oxygen atom of the central water molecule is set as the origin of the coordinates and the central water molecule is set to locate within the XZ plane and symmetric about the Z axis.

Calculated O–O spatial distribution functions of water under various conditions. (a) *g*(*x*, *y*, *z*) ⩾ 1.5 for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) with XZ plane is in the plane. (b) *g*(*x*, *y*, *z*) ⩾ 1.5 for ambient water (ρ = 1.0 g/cm^{3}, *T* = 298 K) with YZ plane is in the plane. (c) *g*(*x*, *y*, *z*) ⩾ 1.3 for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) with XZ plane is in the plane. (d) *g*(*x*, *y*, *z*) ⩾ 1.3 for SCW (ρ = 1.14ρ_{ c }, *T* = 1.03*T* _{ c } = 666 K) with YZ plane is in the plane. The position of the oxygen atom of the central water molecule is set as the origin of the coordinates and the central water molecule is set to locate within the XZ plane and symmetric about the Z axis.

Calculated average hydrogen bond lengths at various densities (*T* = 1.03*T* _{ c } = 666 K).

Calculated average hydrogen bond lengths at various densities (*T* = 1.03*T* _{ c } = 666 K).

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