^{1}, D. Asthagiri

^{2}, L. R. Pratt

^{3}and M. E. Paulaitis

^{4}

### Abstract

A molecular theory of liquidwater is identified and studied on the basis of computer simulation of the TIP3P model of liquidwater. This theory would be exact for models of liquidwater in which the intermolecular interactions vanish outside a finite spatial range, and therefore provides a precise analysis tool for investigating the effects of longer-ranged intermolecular interactions. We show how local order can be introduced through quasichemical theory. Long-ranged interactions are characterized generally by a conditional distribution of binding energies, and this formulation is interpreted as a regularization of the primitive statistical thermodynamic problem. These binding-energy distributions for liquidwater are observed to be unimodal. The Gaussian approximation proposed is remarkably successful in predicting the Gibbs free energy and the molar entropy of liquidwater, as judged by comparison with numerically exact results. The remaining discrepancies are subtle quantitative problems that do have significant consequences for the thermodynamic properties that distinguish water from many other liquids. The basic subtlety of liquidwater is found then in the *competition* of several effects which must be quantitatively balanced for realistic results.

The authors thank H. S. Ashbaugh for pointing out that consistency of the evaluated with the other contributions could be important. This work was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. Financial support from the National Science Foundation No. (BES0555281) is gratefully acknowledged.

INTRODUCTION

STATISTICAL THERMODYNAMIC THEORY

SIMULATION DATA

RESULTS

CONCLUSIONS

### Key Topics

- Mean field theory
- 12.0
- Free energy
- 11.0
- Intermolecular forces
- 10.0
- Numerical modeling
- 6.0
- Organic liquids
- 6.0

## Figures

The internal pressure of several solvents as a function of temperature along their vapor saturation curve (Ref. 37). For van der Waals liquids . Organic solvents conform to this expectation, but water is qualitatively different.

The internal pressure of several solvents as a function of temperature along their vapor saturation curve (Ref. 37). For van der Waals liquids . Organic solvents conform to this expectation, but water is qualitatively different.

Probability density of the binding energy of a water molecule in liquid water at . , , from top to bottom with successive results shifted incrementally downward by 2 for clarity. The solid lines are the Gaussian model for each data set.

Probability density of the binding energy of a water molecule in liquid water at . , , from top to bottom with successive results shifted incrementally downward by 2 for clarity. The solid lines are the Gaussian model for each data set.

Upper panel: Dependence of the free energy predicted by the Gaussian model on the conditioning radius . The horizontal lines are the numerically exact results. The shaded areas indicate approximate 95% confidence intervals. Lower panel: Corresponding results for the entropy.

Upper panel: Dependence of the free energy predicted by the Gaussian model on the conditioning radius . The horizontal lines are the numerically exact results. The shaded areas indicate approximate 95% confidence intervals. Lower panel: Corresponding results for the entropy.

Coordination number probabilities, . Note that for , the most probable coordination number is 2 or 3 (Refs. 25 and 26). For , the most probable coordination number is . But and are nearly equally probable at , and is then 17% of the whole. With the TIP3P model, as is lowered from there is a clear tendency to enhance probability of higher coordination number cases.

Coordination number probabilities, . Note that for , the most probable coordination number is 2 or 3 (Refs. 25 and 26). For , the most probable coordination number is . But and are nearly equally probable at , and is then 17% of the whole. With the TIP3P model, as is lowered from there is a clear tendency to enhance probability of higher coordination number cases.

The fine black points are estimates of obtained from Monte Carlo simulation of TIP3P water with one water molecule centering a hard-sphere which perfectly repels other water oxygens from a sphere of radius . Upper panel: . Lower panel: . The larger composite dots were obtained directly from molecular dynamics simulations with no constraint. The solid curve is the Gaussian model for the expanded Monte Carlo data set, and confirms both the overall accuracy of the Gaussian model and the estimated conditional mean and variance of Table I. Note that the data are slightly less than the Gaussian model in the high- tail..

The fine black points are estimates of obtained from Monte Carlo simulation of TIP3P water with one water molecule centering a hard-sphere which perfectly repels other water oxygens from a sphere of radius . Upper panel: . Lower panel: . The larger composite dots were obtained directly from molecular dynamics simulations with no constraint. The solid curve is the Gaussian model for the expanded Monte Carlo data set, and confirms both the overall accuracy of the Gaussian model and the estimated conditional mean and variance of Table I. Note that the data are slightly less than the Gaussian model in the high- tail..

Distribution of water oxygen atoms radially from a distinguished water oxygen atom, evaluated with the sample corresponding to the condition , with , for O-atom neighbors of the distinguished O atom. The black, dotted curve is the running coordination number for the case.

Distribution of water oxygen atoms radially from a distinguished water oxygen atom, evaluated with the sample corresponding to the condition , with , for O-atom neighbors of the distinguished O atom. The black, dotted curve is the running coordination number for the case.

## Tables

Free energy contributions in kcal/mol associated with the Gaussian model. The bottom value of each temperature set gives the corresponding free energy evaluated by the histogram overlap method. The rightmost column is the excess entropy per particle. Note that the entropy here raises the net free energy [see Eq. (7)], and the magnitude of the entropy contribution ranges here from 60% to 75% of the magnitude of the free energy .

Free energy contributions in kcal/mol associated with the Gaussian model. The bottom value of each temperature set gives the corresponding free energy evaluated by the histogram overlap method. The rightmost column is the excess entropy per particle. Note that the entropy here raises the net free energy [see Eq. (7)], and the magnitude of the entropy contribution ranges here from 60% to 75% of the magnitude of the free energy .

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