Correlation between local density and binding energy

This principal feature of the water-water interaction was deemed so fundamental that I have used it for the cover design of this book. In short, it states that the most important aspect of molecular interactions between water molecules is the specific correlation between local density and binding energy. We shall encounter this principle in several places throughout this book. By invoking this principle, one can explain many properties of liquid water without ever using the concept of the structure of water. 

Fig. 2.8 The correlation between local density and binding energy in a onedimensional model for (a) normal fluid and (b) water-like particles.

The unique correlation between local density and binding energy was also found in molecular dynamics simulations by Blumberg et al. (1984), and Geiger and Stanley (1982). Interestingly, these authors concluded (belatedly) that the two views of water, the so-called continuous and the MM approach that are traditionally considered mutually exclusive, are in fact two different equivalent views of water. 

It has long been known that water is a structured liquid, and that this structure is a result of the tendency of water molecules to form hydrogen bonds. What is less recognized is that the specific correlation between local density and binding energy is a more fundamental principle of the interaction between water molecules. This feature, when implemented in a model system in any dimension can produce most of the outstanding properties of aqueous systems. 

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). 

In all of these models, the hydrogen bonds, or the structure of liquid water, were traditionally emphasized as the main molecular reasons for the anomalous behavior exhibited by liquid water. However, underlying this relatively ill-defined concept of structure (which was much later defined in statistical mechanical terms see Sec. 2.7) lies a more fundamental principle which can be defined in molecular terms, and which does not explicitly mention the concept of structure yet is responsible for the unusual properties of liquid water. This principle was first formulated in terms of generalized molecular distribution functions in 1973. It states that there exists a range of temperatures and pressures at which the water-water interactions produce a unique correlation between high local density and a weak binding energy. Clearly, this principle does not mention structure. As will be demonstrated in this section, it is this principle, not the structure per se, which is responsible for the unique properties of water as well as of aqueous solutions. ... 

The 1-D model for water described in this section is referred to as the primitive model. It has almost no other features but the principle of correlation between low local density and strong binding energy. This feature is built-in in the pair potential described in Sec. 2.5.2. A more complicated potential was published earlier as a textbook example and was shown to... 

Finally, it should be noted that the molecular reason underlying the negative temperature dependence of the volume is the same as in real liquid water, namely the unique correlation between binding energy and local density. The principle for this particular model is depicted in Fig. 2.7. 

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