^{1}and José L. F. Abascal

^{1,a)}

### Abstract

A new flexible water model, TIP4P/2005f, is developed. The idea was to add intramolecular degrees of freedom to the successful rigid model TIP4P/2005 in order to try to improve the predictions for some properties, and to enable the calculation of new ones. The new model incorporates flexibility by means of a Morse potential for the bond stretching and a harmonic term for the angle bending. The parameters have been fitted to account for the peaks of the infrared spectrum of liquid water and to produce an averaged geometry close to that of TIP4P/2005. As for the intermolecular interactions, only a small change in the σ parameter of the Lennard-Jones potential has been introduced. The overall predictions are very close to those of TIP4P/2005. This ensures that the new model may be used with the same confidence as its predecessor in studies where a flexible model is advisable.

This work has been funded by grants FIS2010/16159 of the MEC, P2009/ESP-1691 of CAM and UCM-Banco de Santander GR35/10-A-910570.

I. INTRODUCTION

II. THE MODEL

III. RESULTS

A. Liquid densities at normal pressure

B. Structure: Radial distribution function

C. Enthalpy of vaporization

D. Isothermal compressibility

E. Self-diffusion coefficient

F. Melting temperature of ice Ih

G. Relative stability of ices

H. Static dielectric constant

I. Power spectrum

IV. CONCLUSIONS

### Key Topics

- Ice
- 21.0
- Numerical modeling
- 11.0
- Dielectric constant
- 9.0
- Enthalpy
- 9.0
- Electric dipole moments
- 7.0

## Figures

Four alternative functions to describe the bond stretching in a flexible water model.

Four alternative functions to describe the bond stretching in a flexible water model.

Distribution of bond distances at different conditions. The area of both histograms is normalized. The red (broader) histogram corresponds to liquid water at 1 bar, 298 K while the blue one corresponds to the results for a single molecule at 2 K (zoomed at the inset).

Distribution of bond distances at different conditions. The area of both histograms is normalized. The red (broader) histogram corresponds to liquid water at 1 bar, 298 K while the blue one corresponds to the results for a single molecule at 2 K (zoomed at the inset).

Densities of the TIP4P/2005f model (full circles) at *p* = 1 bar compared to the values of the same property of TIP4P/2005 model (open squares) and experimental data (full line).

Densities of the TIP4P/2005f model (full circles) at *p* = 1 bar compared to the values of the same property of TIP4P/2005 model (open squares) and experimental data (full line).

Oxygen-oxygen radial distribution function at *T* = 298 K, *p* = 1 bar.

Oxygen-oxygen radial distribution function at *T* = 298 K, *p* = 1 bar.

Evolution of the total energy of a system made of liquid water in contact with ice Ih. The results are averages over 20 ps simulation blocks for three *NpT* simulation runs at 1 bar and *T* = 256 K, 254 K, and 252 K, respectively.

Evolution of the total energy of a system made of liquid water in contact with ice Ih. The results are averages over 20 ps simulation blocks for three *NpT* simulation runs at 1 bar and *T* = 256 K, 254 K, and 252 K, respectively.

Spectrum of densities of state of water. Vertical lines signal the position of the peaks in the experimental spectra of liquid water.

Spectrum of densities of state of water. Vertical lines signal the position of the peaks in the experimental spectra of liquid water.

## Tables

Potential parameters of the TIP4P/2005f and TIP4P/2005 water models. Notice that and define the rigid geometry of TIP4P/2005.

Potential parameters of the TIP4P/2005f and TIP4P/2005 water models. Notice that and define the rigid geometry of TIP4P/2005.

Average value of the parameters related to the molecular geometry in a simulation at *T* = 298 K and *p* = 1 bar. The corresponding values for TIP4P/2005 are also given for comparison.

Average value of the parameters related to the molecular geometry in a simulation at *T* = 298 K and *p* = 1 bar. The corresponding values for TIP4P/2005 are also given for comparison.

A summary of the properties of TIP4P/2005f compared to the corresponding values for TIP4P/2005 and with experimental data. Density, ρ, isothermal compressibility, κ_{ T }, (relative) static dielectric constant, ɛ_{ r } = ɛ/ɛ_{0}, and self-diffusion coefficient, *D* _{ s }, have been calculated at *T* = 298 K, *p* = 1 bar. The melting temperature, T_{ m }, and the enthalpy of vaporization, Δ_{ v } *H*, also correspond to a pressure of 1 bar. Δ_{ v } *H* includes the self-polarization correction —Eq. (6)— while the values in parenthesis are the result of Eq. (5) without any further correction.

A summary of the properties of TIP4P/2005f compared to the corresponding values for TIP4P/2005 and with experimental data. Density, ρ, isothermal compressibility, κ_{ T }, (relative) static dielectric constant, ɛ_{ r } = ɛ/ɛ_{0}, and self-diffusion coefficient, *D* _{ s }, have been calculated at *T* = 298 K, *p* = 1 bar. The melting temperature, T_{ m }, and the enthalpy of vaporization, Δ_{ v } *H*, also correspond to a pressure of 1 bar. Δ_{ v } *H* includes the self-polarization correction —Eq. (6)— while the values in parenthesis are the result of Eq. (5) without any further correction.

Liquid densities (g/cm^{3}) at *p* = 1 bar.

Liquid densities (g/cm^{3}) at *p* = 1 bar.

Properties of several ice polymorphs at *T* = 0 K and *p* = 0 bar for flexible water models and their rigid counterparts. The results marked in bold correspond to the more stable phase.

Properties of several ice polymorphs at *T* = 0 K and *p* = 0 bar for flexible water models and their rigid counterparts. The results marked in bold correspond to the more stable phase.

Dielectric constant at different thermodynamics states.

Dielectric constant at different thermodynamics states.

Wavenumbers (in cm^{−1}) at the peak of the bands of the power spectrum for the TIP4P/2005f model and liquid water. Experimental results have been taken from Refs. 37 and 64–66.

Wavenumbers (in cm^{−1}) at the peak of the bands of the power spectrum for the TIP4P/2005f model and liquid water. Experimental results have been taken from Refs. 37 and 64–66.

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