The radial distribution function of water

Perhaps some of the most important information on the mode of molecular packing of water in the liquid state is contained in the radial distribution function, which, in principle, can be obtained by processing X-ray or neutron scattering data. There are, however, several difficulties in extracting the proper information from the experimental data. First, it should be kept in mind that the full orientation-dependent pair correlation function cannot be obtained from such an experiment. Instead, only information on the spatial pair correlation function is accessible. We recall the definition of this function, 

Furthermore, water, as a heteroatomic liquid, produces a diffraction pattern that reflects the combined effects of 0-0, O-H, and H-H correlations. Thus, in principle, we have three distinct atom pair-correlation functions oo( ), and Experimental data cannot, at 

The most important differences between the two curves in Fig. 6.8 are the following (1) The first coordination number, defined by 

These two features of the radial distribution function lead to the following conclusion The basic geometry around a single molecule in 

The temperature dependence of g R) of water is shown in Fig. 6.10. It has been noted by Narten and Levy (1972) that there is a gradual shift in the location of the first peak, from 2.84 A at 4°C to about 2.94 A at 

The most important experimental information on the mode of packing of water molecules in the liquid state is contained in the radial distribution function, which is obtained from X-ray 

If we could sit at the center of one of the particles and observe our surroundings, we would not see any regular pattern that we could call a structure. But if we counted the number of particle centers that appeared within a spherical shell of width dR at a distance R, we would find the following regularities. 

Having this qualitative definition of g(R), we now turn to describing some of its salient features for spherical particles  

The reason for this is that at distances R a, the two particles exert strong repulsive forces hence, they are effectively impenetrable. (In fact, the diameter a is defined as the distance below which the repulsive forces are so large that the two particles practically cannot approach each other to a distance shorter than a.) 

The typical concentric and approximately equidistant peaks observed in g R) are a result of the spherical-symmetrical interaction between the particles. This information provided by g R) is sometimes called the structure of the liquid, but when applied to liquid water g R) is not a good measure of structure. 

as a heteroatomic liquid, produces a diffraction pattern that reflects the combined effects of O—O, O—H, and H—H correlations. Thus, in principle, we have three distinct atom-atom pair correlation functions goo(R), goH(T ), and gmiR). Experimental data cannot, at present, be resolved to obtain these three functions separately. Therefore, the only information obtained is a weighted average of these three functions. In all our future reference to the experimental radial distribution function, we shall always refer to goo(. ) or simply to g R). In some simulation calculations, more detailed information on goo( ), oh( ), and gHnCi ) have been obtained. 

The average coordination number as defined above slightly increases with an increase in temperature. This is in contrast to the normal behavior of argon, where the average coordination number decreases with the increase of temperature, as in Fig. 7.7. We shall see that this fact indicates an important feature of the correlation between local density and local binding energy (see section 7.9). 

FIGURE 7.7. The average coordination number of argon ( ) and of water (x) as a function of temperature, above the melting temperature (r ,). 

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Sorenson, J. M., Hura, G., Glaeser, R. M., Head-Gordon, T., What can x-ray scattering tell us about the radial distribution functions of water J. Chem. Phys. 2000, 113, 9149-9161. 

Soper AK (2000) The radial distribution functions of water and ice from 220-673 K at pressures up to 400 MPa. Chem Phys 258 121-137 Soper AK (2010) Recent water myths. Pure Appl Chem 82 1855-1867... 

Fig. 1.34 The radial distribution function of water and heavy water at 4 C.

In contrast to the behavior of noble gases, the radial distribution functions of water around the infinitely dilute anion (C/ ) and cations (Na and Lt) exhibit a rather strong re-structuring, Le,y relative to unperturbed water there is a substantial increase in the local water density around the ions due to strong ion-dipole interactions (Figure 13). The presence of an ion induces an increase in the solvent... 

This structural feature has affected almost all subsequent attempts to theorize about the properties of liquid water and aqueous solutions. Bernal and Fowler were also the first to attempt a theoretical calculation of the radial distribution function of water. Such an undertaking could not have been feasible without a detailed characterization of the structure of the various components presumed to exist in the liquid. 

The center of the oxygen nucleus is usually chosen as the center of the molecule (which is slightly different from the center of mass of the molecule). Figure 7.1 depicts the water molecule according to the van der Waals radii assigned to the oxygen (1.4 A) atoms. It is sometimes convenient to view a water molecule as a sphere of radius 1.41 A. (This is about half of the average distance between two closest water molecules, as manifested by the first peak of the radial distribution function of water see below.)... 

In Figures 14 and 15 we show the radial distribution functions of water surrounding the infinitely dilute He and Ne in comparison to that of the surrounding water (ideal solution) at the two state conditions. Beyond the small differences in strength, there are clear indications that water forms a cavity around these solutes, i.e., the water local density around each solute is much smaller than that found around any water molecule (ideal solution). Moreover, due to the closeness to the water critical conditions, these distribution functions show the characteristic slow-decaying (compressibility driven) tails, from above unity and below unity for... 

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