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Balancing local order and long-ranged interactions in the molecular theory of liquid water
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Image of FIG. 1.
FIG. 1.

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.

Image of FIG. 2.
FIG. 2.

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.

Image of FIG. 3.
FIG. 3.

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.

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

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..

Image of FIG. 6.
FIG. 6.

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.


Generic image for table
Table I.

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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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Balancing local order and long-ranged interactions in the molecular theory of liquid water