^{1}, Thomas E. Markland

^{1}and David E. Manolopoulos

^{1,a)}

### Abstract

Numerous studies have identified large quantum mechanical effects in the dynamics of liquid water. In this paper, we suggest that these effects may have been overestimated due to the use of rigid water models and flexible models in which the intramolecular interactions were described using simple harmonic functions. To demonstrate this, we introduce a new simple point charge model for liquid water, q-TIP4P/F, in which the O–H stretches are described by Morse-type functions. We have parametrized this model to give the correct liquid structure, diffusion coefficient, and infrared absorption frequencies in quantum (path integral-based) simulations. The model also reproduces the experimental temperature variation of the liquid density and affords reasonable agreement with the experimental melting temperature of hexagonal ice at atmospheric pressure. By comparing classical and quantum simulations of the liquid, we find that quantum mechanical fluctuations increase the rates of translational diffusion and orientational relaxation in our model by a factor of around 1.15. This effect is much smaller than that observed in all previous simulations of empirical water models, which have found a quantum effect of at least 1.4 regardless of the quantum simulation method or the water model employed. The small quantum effect in our model is a result of two competing phenomena. Intermolecular zero point energy and tunneling effects destabilize the hydrogen-bonding network, leading to a less viscous liquid with a larger diffusion coefficient. However, this is offset by intramolecular zero point motion, which changes the average water monomer geometry resulting in a larger dipole moment, stronger intermolecular interactions, and a slower diffusion. We end by suggesting, on the basis of simulations of other potential energy models, that the small quantum effect we find in the diffusion coefficient is associated with the ability of our model to produce a single broad O–H stretching band in the infrared absorptionspectrum.

This work was supported by the U.S. Office of Naval Research under Contract No. N000140510460 and by the U.K. Engineering and Physical Sciences Research Council under Grant No. E01741X. We are grateful to George Fanourgakis for providing us with his TTM3-F water simulation results and to Udo Schmitt and Gunther Zechmann for helpful discussions.

I. INTRODUCTION

II. QUANTUM WATER MODELS

III. QUANTUM SIMULATION METHODS

A. Path integral molecular dynamics

B. Ring polymer molecular dynamics

C. Partially adiabatic centroid molecular dynamics

D. Additional computational details

IV. VALIDATION OF THE q-TIP4P/F MODEL

A. Static equilibrium properties

B. Dynamical properties

C. Summary

V. COMPETING QUANTUM EFFECTS

A. Computational results

B. Analysis and discussion

VI. CONCLUDING REMARKS

### Key Topics

- Quantum effects
- 48.0
- Diffusion
- 38.0
- Polymers
- 23.0
- Absorption spectra
- 19.0
- Quantum fluctuations
- 17.0

## Figures

Oxygen-oxygen RDFs of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations at 298 K and . The experimental RDF from Ref. 48 is shown for comparison (along with its associated error bars).

Oxygen-oxygen RDFs of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations at 298 K and . The experimental RDF from Ref. 48 is shown for comparison (along with its associated error bars).

Oxygen-hydrogen RDFs of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations at 298 K and . The experimental RDF from Ref. 48 is shown for comparison (along with its associated error bars). The inset shows the intramolecular O–H peak at distances close to 1 Å.

Oxygen-hydrogen RDFs of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations at 298 K and . The experimental RDF from Ref. 48 is shown for comparison (along with its associated error bars). The inset shows the intramolecular O–H peak at distances close to 1 Å.

Hydrogen-hydrogen RDFs of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations at 298 K and . The experimental RDF from Ref. 48 is shown for comparison (along with its associated error bars).

Hydrogen-hydrogen RDFs of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations at 298 K and . The experimental RDF from Ref. 48 is shown for comparison (along with its associated error bars).

Densities at 1 atm pressure of the q-TIP4P/F and q-SPC/Fw water models obtained from PIMD simulations. The experimental density curve from Ref. 77 is shown for comparison. The red and blue curves through the calculated points are simply guides for the eye.

Densities at 1 atm pressure of the q-TIP4P/F and q-SPC/Fw water models obtained from PIMD simulations. The experimental density curve from Ref. 77 is shown for comparison. The red and blue curves through the calculated points are simply guides for the eye.

IR absorption spectra of the q-TIP4P/F and q-SPC/Fw water models obtained from PA-CMD simulations at 298 K and . The upper panel shows the experimental spectrum from Ref. 63.

IR absorption spectra of the q-TIP4P/F and q-SPC/Fw water models obtained from PA-CMD simulations at 298 K and . The upper panel shows the experimental spectrum from Ref. 63.

As in Fig. 5 but for at a temperature of 298 K and a density of . In this case the experimental spectrum is only available above (Ref. 65).

As in Fig. 5 but for at a temperature of 298 K and a density of . In this case the experimental spectrum is only available above (Ref. 65).

## Tables

Parameters in the q-TIP4P/F and q-SPC/Fw (Ref. 13) quantum water models.

Parameters in the q-TIP4P/F and q-SPC/Fw (Ref. 13) quantum water models.

Static equilibrium properties of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations. The standard errors in the final digits are given in parentheses. and are the ensemble-averaged values of the molecular dipole and tetrahedral quadrupole moments, is the liquid density at 298 K and 1 atm pressure, is the density at the temperature of maximum density, is the melting point, and is the dielectric constant.

Static equilibrium properties of the q-TIP4P/F and q-SPC/Fw quantum water models obtained from PIMD simulations. The standard errors in the final digits are given in parentheses. and are the ensemble-averaged values of the molecular dipole and tetrahedral quadrupole moments, is the liquid density at 298 K and 1 atm pressure, is the density at the temperature of maximum density, is the melting point, and is the dielectric constant.

Dynamical properties of liquid water at 298 K and (and heavy water at ) obtained from RPMD simulations of the q-TIP4P/F model. is the diffusion coefficient and is the order orientational relaxation time for molecular axis . The CMD results for the q-SPC/Fw model from Ref. 13 are provided for comparison.

Dynamical properties of liquid water at 298 K and (and heavy water at ) obtained from RPMD simulations of the q-TIP4P/F model. is the diffusion coefficient and is the order orientational relaxation time for molecular axis . The CMD results for the q-SPC/Fw model from Ref. 13 are provided for comparison.

Classical vs quantum diffusion coefficients of several liquid water models, including the q-TIP4P/F model developed in this work. The second column gives the number of water molecules used in each simulation, and the third indicates the approximate quantum dynamical method employed. Where given, the number in parentheses indicates the standard error in the final digit. The last column gives the magnitude of the quantum effect, defined as . The average quantum effect from the earlier studies in the table is 1.46.

Classical vs quantum diffusion coefficients of several liquid water models, including the q-TIP4P/F model developed in this work. The second column gives the number of water molecules used in each simulation, and the third indicates the approximate quantum dynamical method employed. Where given, the number in parentheses indicates the standard error in the final digit. The last column gives the magnitude of the quantum effect, defined as . The average quantum effect from the earlier studies in the table is 1.46.

Classical vs quantum (RPMD) orientational relaxation times for the q-TIP4P/F water model at 298 K and . The numbers in parentheses are the standard errors in the final digits. The final column gives the ratio of the classical and quantum relaxation times as a measure of the magnitude of the quantum effect in orientational relaxation.

Classical vs quantum (RPMD) orientational relaxation times for the q-TIP4P/F water model at 298 K and . The numbers in parentheses are the standard errors in the final digits. The final column gives the ratio of the classical and quantum relaxation times as a measure of the magnitude of the quantum effect in orientational relaxation.

Water monomer properties for the q-TIP4P/F model in classical and quantum (PIMD) simulations. Calculations were performed at a temperature of 298 K and density of . The standard errors in the final digits are given in parentheses.

Water monomer properties for the q-TIP4P/F model in classical and quantum (PIMD) simulations. Calculations were performed at a temperature of 298 K and density of . The standard errors in the final digits are given in parentheses.

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