Pair potential for water

Mas EM, Szalewicz K, Bukowski R, Jeziorski B (1997) Pair potential for water from symmetry-adapted perturbation theory. J Chem Phys 107 1207 1218... 

Morse MD, Rice SA (1982) Tfests of effective pair potentials for water predicted ice structures. J Chem Phys 76 650- 660... 

Although there have been a fairly large number of first-principle simulations of condensed phase published to date, this number is completely dwarfed by simulations based on empirical potentials. The popular empirical pair potentials for water [76-78] have been used in many (thousands) research projects. The empirical potentials are usually fitted in simulations for liquids to reproduce measured properties of this phase. Thus, these potentials mimic the nonadditive effects by distortions of two-body potentials... 

Before concluding this section it should be noted that in calculating the second virial coefficient, one needs the true pair potential for water. To study the properties of liquid water, or even the third virial coefficient, the true pair potential is not enough. The reason is that non-additive, higher order potentials are important in determining the properties of liquid water as well as of the third virial coefficient. 

This principle was first used implicitly in the construction of the first successful pair potential for water molecules. Later, it was used explicitly in constructing pair potentials that exhibit... 

It should be said that even the most seemingly realistic 3-D models for water are in fact very far from being realistic. An effective pair potential for water, even when it can lead to a perfect agreement between computed and experimental results, is far from being close to the real pair potential function between two water molecules. Conversely, even if we had a perfect pair potential between two water molecules, it is doubtful that its employment in a theory of water would reproduce the properties of water. We shall further discuss this aspect of the pair potential in Sec. 2.7. 

ST2 potential in order to obtain better agreement between the simulated and experimental results. In my opinion, the efforts to pursue this goal by Rahman and Stillinger and by many others that followed are not fully justified. As I have noted several times in this book, a better agreement between the computed and experimental results does not tell us anything about the correct or the real pair potential for water, nor does it explain any of the outstanding properties of water. All it says is that with such and such a feature of the pair potential, (the input) one obtains such and such properties similar to water (the output). Not much more than that. 

As can be seen from Fig. 4.44, there are considerable discrepancies between results obtained by different simulations and by theoretical calculations. At present, it is difficult to claim that one simulated result is better than another. This is also true for any theoretical calculations based on a specific pair potential for water. It is a fortiori true if the theory uses as an input the orientational averaged pair correlation function of water, as was done by Pratt and Chandler (1977). In my opinion, using such an input into the theory will inevitably fail to reproduce any property of water and aqueous solutions that is sensitive to the angular dependence of the pair potential — or, equivalently, that depends on the principle. For further details, see Ben-Naim (1989), Guarino and Madden (1982), and Tani (1984). 

For over 30 years, I have suggested several pair potentials for water-like particles. I have never referred to any pair potential I have devised as the Ben-Naim potential. I was dismayed to learn that through the years, authors have used these pair potentials and either presented them as their own, or simply renamed them, and as a result of which completely obliterating the roots of their origins. 

At present, there seems to be no other way but to resort to our intuition for constructing an analytical form of a pair potential for water which best describes the prominent features of the HB interaction. Of course, as time passes, more accurate data, from quantum mechanical calculations, will be accumulated. Such information may be utilized to perfect the analytical description of the pair, as well as higher-order, potentials for water. 

Simulation of the behavior of water by waterlike particles in three dimensions has all the merits discussed in the previous section. In addition, this type of computation, which may be referred to as the ab initio approach to liquid water, is of importance in establishing the most appropriate effective pair potential for water molecules. On the other hand, simulations in the three-dimensional case vastly increase the computer time required to execute a typical computation. In particular, because of the strong attractive forces operating among water molecules, the convergence of the numerical methods is usually slower than in the case of particles with relatively weak attractive forces. This aspect was discussed in the previous section, but it pertains to the three-dimensional case equally well. 

Mathematically we define the primitive pair potential for water as follows ... 

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