Weeks-Chandler-Andersen potential

The Weeks-Chandler-Andersen potential given in Equation 15.7, acts to divide the LJ potential into attractive and repulsive potentials [32]. Only the repulsive potential is shown below. 

In case of tetrahedral non polar liquid i.e. methane) each molecule in CG level represented by one bead and atomistically the molecule consisted of four atoms. The non-bonded interactions between the atoms were treated by Weeks-Chandler-Andersen potential (potential form is given in equation 38) and bonded interaction of all the atoms of a molecules by finitely extensible nonlinear elastic bonds as given in equation 39. 

The first step towards the development of appropriate expressions is the decomposition of the nonassociative pair potential into repulsive and attractive terms. In this work we apply the Weeks-Chandler-Andersen separation of interactions [117], according to which the attractive part of the Lennard-Jones potential is defined by... 

As we have already pointed out, the theoretical basis of free energy calculations were laid a long time ago [1,4,5], but, quite understandably, had to wait for sufficient computational capabilities to be applied to molecular systems of interest to the chemist, the physicist, and the biologist. In the meantime, these calculations were the domain of analytical theories. The most useful in practice were perturbation theories of dense liquids. In the Barker-Henderson theory [13], the reference state was chosen to be a hard-sphere fluid. The subsequent Weeks-Chandler-Andersen theory [14] differed from the Barker-Henderson approach by dividing the intermolecular potential such that its unperturbed and perturbed parts were associated with repulsive and attractive forces, respectively. This division yields slower variation of the perturbation term with intermolecular separation and, consequently, faster convergence of the perturbation series than the division employed by Barker and Henderson. 

At this stage, undiscutable data, external of the IETs, were necessarily required to shed some light on these peculiar behaviors, which provides exact reference data for more realistic potentials. First, Nicolas et al. [33] derived an EOS for the Lennard-Jones fluid and Johnson et al. [34] provided MD results for the classical thermodynamic quantities. Notice that Heyes and Okumura [35] recently derived an EOS of the Weeks-Chandler-Andersen fluid. 

To address this, Liem, Brown, and Clarke ° simulated in excess of 40,000 particles interacting via a Weeks-Chandler-Andersen (WCA) potential. While the x and z directions were treated normally, the y direction was divided into three regions two atomistic walls separated by a fluid region. The walls consisted of three hexagonally close-packed layers of particles. The wall atoms interacted with the fluid particles and with each other through the same WCA potential used for the fluid-fluid interactions. Additionally, each wall particle felt a harmonic potential centered at its triangular lattice site. This setup allowed heat transfer from the fluid to the wall while allowing the wall to remain crystalline. The momenta of the wall particles were rescaled to keep the total... 

Figure 19 Shear-induced microstructure in a Weeks-Chandler-Andersen fluid of 500 particles under low shear (T = 0.722, p = 0.844, and y = 0.6). The unit of length is the WCA potential a. The direction of flow (x) is out of the page, and the particles are projected on the yz plane.

Figure 5. Weeks-Chandler-Andersen pair potential (solid line). The Lennard-Jones pair potential is shown for comparison (dashed line).

Most investigations in this area have been concerned with the Weeks-Chandler-Andersen division of the potential. For the molecular potential, the reference system is defined by... 

The eelebrated Pratt-Chandler (PC) theory is usually the starting point of any diseussion on the hydrophobie effeet. This theory ean be regarded as an application of the Weeks-Chandler-Andersen (WCA) perturbative theory of liquids to the solvation of one and a pair of non-polar solute moleeules. While Stillinger discussed the ehemieal potential involved in ereating a hard-sphere cavity in water using the scaled partiele theory, the Pratt-Chandler theory used an integral equation deserip-tion and showed how to properly discuss the effect within a general statistieal mechanical theory. 

Accordingly, the methane simulations have been supplemented with a series of simulations of attractive or repulsive guest molecules. These "molecules" were defined by breaking the methane potential into its attractive and repulsive branches according to the Weekes/Chandler/Andersen partition [51]... 

A very successfiil first-order perturbation theory is due to Weeks, Chandler and Andersen pair potential u r) is divided into a reference part u r) and a perturbation w r)... 

Similarly in the perturbation theory of Weeks, Chandler and Andersen [5,28] (WCA) the Lennard-Jones potential is decomposed according to... 

J. D. Weeks, D. Chandler, H. C. Andersen. Role of repulsive forces in determining the equilibrium structure of simple liquids. J Chem Phys 54 5237, 1971. R. L. Rowley, M. W. Schuck, J. Perry. A direct method for determination of chemical potential with molecular dynamics simulations. 2. Mixtures. Mol Phys 55 125, 1995. 

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