Modified hypernetted-chain

A closure similar to the RHNC is the modified hypernetted chain (MHNC), introduced by Rosenfeld and Ashcroft [67]. This approximation is based on the empirical observation that the bridge functions for a wide variety of pair potentials belong to the same family of curves. This means that the bridge functions calculated for a suitable reference fluid can be used to a good approximation for another fluid. The reference fluid is usually... 

One should perhaps mention some other closures that are discussed in the literature. One possibility is to combine the PY approximation for the hard core part of the potential and then use the HNC approximation to compute the corrections due to the attractive forces. Such an approach is called the reference hypernetted chain or RHNC approximation [48,49]. Recently, some new closures for a mixture of hard spheres have been proposed. These include one by Rogers and Young [50] (RY) and the Martynov-Sarkisov [51] (MS) closure as modified by Ballone, Pastore, Galli and Gazzillo [52] (BPGG). The RY and MS/BPGG closure relations take the forms... 

Table I. Values of the Hard-Sphere g (r) Calculated from the Exact, the Modified Born-Green-Yvon (BGY2), the Unmodified Born-Green-Yvon (BGY), the Percus-Yevick (PY), and the Convolution-Hypernetted-Chain (CHNC) Theories ...

Simulation results were compared with the predictions of the Ornstein-Zernike (OZ) equation with the hypernetted chain (HNC) closure approximation and the non-linear Poisson-Boltzmann equation, both augmented by pertinent Lifshitz NES potentials. We show in Fig. 1 that there is very good agreement between modified Poisson-Boltzmann theory, MC simulations, and HNC calculations when the counterions and co-ions are monovalent. There is also good agreement between the different approaches with divalent co-ions (not shown here). However, the results from MPBE cannot account for ion correlation effects that occur in Fig. 2 when the counterions are divalent. The reason is simply that the... 

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