Pair potential models properties

M. Hemmati et al., in Comparison of Pair-Potential Models for the Simulation of Liquid Si02 Thermodynamic, Angular-Distribution, and Dijfusional Properties, in Physics Meets Mineralogy Condensed-Matter Physics in Geosciences, ed. by H. Aoki, Y. Syono, R.J. Hemley (Cambridge University Press, Cambridge, 2000), p. 325 M. Benoit et al., Europhys. Lett. 60(2), 269-275 (2002)... 

The intennolecular forces between water molecules are strongly non-additive. It is not realistic to expect any pair potential to reproduce the properties of both the water dimer and the larger clusters, let alone liquid water. There has therefore been a great deal of work on developing potential models with explicit pairwise-additive and nonadditive parts [44, 50, 51]. It appears that, when this is done, the energy of the larger clusters and ice has a nonadditive contribution of about 30%. 

Results have shown that the properties of solids can usually be modeled effectively if the interactions are expressed in terms of those between just pairs of atoms. The resulting potential expressions are termed pair potentials. The number and form of the pair potentials varies with the system chosen, and metals require a different set of potentials than semiconductors or molecules bound by van der Waals forces. To illustrate this consider the method employed with nominally ionic compounds, typically used to calculate the properties of perfect crystals and defect formation energies in these materials. 

One of the most important developments in the theory of water is the invention of a realistic effective intermolecular pair potential. Although others had made similar suggestions earlier 59>, it is Stillinger and co-workers 60> who have shown, with the aid of molecular dynamics calculations 3>, how satisfactory such a potential can be. The availability of a water-water potential drastically reduces the scope for parameterization in model based theories, and permits investigation of such concepts as "broken hydrogen bond. We shall frequently have occasion to call upon its properties in the following discussion. 

When the results of a molecular dynamics study are being judged, the question, Is the potential realistic is often asked. This can be the incorrect approach to evaluating the validity of a computer simulation. The appropriate question to be addressed should be, Ts the potential used appropriate for the phenomena being modeled . In the same vein, it is common for a potential developed to model one property of a system to be arbitrarily extended to phenomena for which it may be inappropriate. In this way, interaction potentials are often misjudged. For example, pair potentials with tails that mimic the oscillations present in an electron gas due to ion cores can be used to understand the properties of bulk metals. It is obvious that these potentials, however, would not realistically describe the interaction between three metal atoms, where an electron gas is not well defined. It is the rare interaction potential which works well for all properties of a particular system and so one needs to understand why a particular potential works well for a given property. 

Pair Potentials and Modelling of Spectroscopic, Collisional, and Thermodynamic Properties of Binary Complexes... 

A key question about the use of any molecular theory or computer simulation is whether the intermolecular potential model is sufficiently accurate for the particular application of interest. For such simple fluids as argon or methane, we have accurate pair potentials with which we can calculate a wide variety of physical properties with good accuracy. For more complex polyatomic molecules, two approaches exist. The first is a full ab initio molecular orbital calculation based on a solution to the Schrddinger equation, and the second is the semiempirical method, in which a combination of approximate quantum mechanical results and experimental data (second virial coefficients, scattering, transport coefficients, solid properties, etc.) is used to arrive at an approximate and simple expression. 

Why should one go to all this trouble and do all these integrations if there are other, less complex methods available to theorize about ionic solutions The reason is that the correlation function method is open-ended. The equations by which one goes from the gs to properties are not under suspicion. There are no model assumptions in the experimental determination of the g s. This contrasts with the Debye-Htickel theory (limited by the absence of repulsive forces), with Mayer s theory (no misty closure procedures), and even with MD (with its pair potential used as approximations to reality). The correlation function approach can be also used to test any theory in the future because all theories can be made to give g(r) and thereafter, as shown, the properties of ionic solutions. 

One consequence of using the pairwise additive approximation is that if a true pair potential is used to calculate the properties of a liquid or solid, there will be an error due to the omission of the nonadditive contributions. Conversely, if the pairwise additive approximation is made in deriving the pair potential U b, the latter will have partially absorbed some form of average over the many-body forces present, producing an error in the calculated properties of the gas phase where only two-body interactions are important. Because the effective pair potential Uab cannot correctly model the orientation and distance dependence of the absorbed nonadditive contributions, there will also be errors in transferring the effective potential to other condensed phases with different arrangements of molecules. 

Table 3 Anisotropic Atom—Atom Models for the Intermolecular Pair Potential, Which Can Be Quantified Using Ab Initio Monomer Properties, and Lead References... 

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