Argon pair potential

This atom-atom potential is essentially modelling the interaction between molecules as the sum of the interactions between spherical atomic charge distributions. The 6-exp form is a simple realistic model for the repulsion and dispersion forces, which can give a qualitatively reasonable description of the properties of argon, but lacks the flexibility to represent accurately the argon pair potential (Maitland et al., 1981). 

Comparison of the Lennard-]ones potential for argon with the Barker-Fisher-Watts pair potential kg is .mann s constant. 

Alder and Wainwright gave MD treatments of particles whose pair potential was very simple, typically the square well potential and the hard sphere potential. Rahman (1964) simulated liquid argon in 1964, and the subject has shown exponential growth since then. The 1970s saw a transition from atomic systems... 

In the case of fluids which consist of simple non-polar particles, such as liquid argon, it is widely believed that Ui is nearly pairwise additive. In other words, the functions for n > 2 are small. Water fails to conform to this simplification, and if we truncate the series after the term, then we have to understand that the potential involved is an effective pair potential which takes into account the higher order-terms. 

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. 

For the solid it is assumed that the total potential energy (i.e., lattice energy) is the sum of all pair potentials Ujj(rjj). The result of this summation for a face-centered cubic lattice (such as argon) is ... 

The dispersion energy is the universal attractive glue that leads to the formation of condensed phases. It is additive at second order in perturbation theory, and the form of the three-body term that arises at third order (the tripledipole dispersion term) is also well known from perturbation theory. This Axilrod-Teller term " was the only addition to the pair potential for argon that was required to quantitatively account for its solid and liquid state properties. This may be grounds for optimism that other nonadditive dispersion terms are negligible. Whether this can be extended to less symmetrical organic molecules and their typical crystalline and liquid environments has not yet been established however. 

Figure 1 Comparison of argon interaction-potentials. The solid line is the empirical pair potential 100 the dashed line is the van der Waals + dispersion model of Dion et al. 485 the dot-dashed line is a CCSD(T) ab initio potential 77 and the dotted lines with circle and square symbols are the SAPT (DFT) potentials of Podeszwa and Szalewicz97 with different functionals. Reprinted from, 97, Copyright (2005) with permission from Elsevier...

Lennard-Jones (LJ) particles are model particles, the behavior of which resembles the behavior of real, simple spherical particles such as argon. In this section, we present some further information on the behavior of g(R) and its dependence on density and on temperature. The LJ particles are defined by means of their pair potential as... 

For simple solute a, such as argon, one can separate each of the solute-solvent pair potentials into two contributions (see section 7.7)... 

Fig. 1.4 The pair potential for neon, argon, krypton, and xenon.

Similar considerations apply to the prediction of the most likely location of the second minimum in the potential of mean force for the pair of Hsolute molecules. Consider two methane molecules (or neon, argon, etc.) in water. We have already noted that the first peak of gAA(R) is expected at Ri crA- The main reason is that R cta corresponds to the minimum of the direct pair potential between two solute molecules. For two spherical solutes in a normal solvent, the location of the second peak is expected at about R2 cta+(Tw In Sec. 4.11, we shall see that the simulated curve of the potential of mean force for methane in water has a second minimum either at ]l2 6 A or at J 2 7 A (with a choice of molecular diameters of 4.4 A and 2.8 A for methane and water, respectively). 

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