Interaction hypemetted chain

We will describe integral equation approximations for the two-particle correlation fiinctions. There is no single approximation that is equally good for all interatomic potentials in the 3D world, but the solutions for a few important models can be obtained analytically. These include the Percus-Yevick (PY) approximation [27, 28] for hard spheres and the mean spherical (MS) approximation for charged hard spheres, for hard spheres with point dipoles and for atoms interacting with a Yukawa potential. Numerical solutions for other approximations, such as the hypemetted chain (EfNC) approximation for charged systems, are readily obtained by fast Fourier transfonn methods... 

An extension of the HNC approach is the reference hypemetted chain (RHNC) approximation [52-54]. In this approach, studying a system preliminarily requires that we determine the properties of a reference fluid (RF). Usually, it has to be assumed that the properties of the actual system are closed to those of the RF. For example, the interaction potential of the system under study can be written as the sum of the RF potential and of a small perturbation, namely, u r) = wRF(r) + Au(r). Correspondingly, one has y(r) = yKF(r) + Ay(r), and the direct correlation function is given by... 

The free energy profile for the electron transfer reaction in a polar solvent is examined based on the extended reference interaction site method (ex-RISM) applying it to a simple model of a charge separation reaction which was previously studied by Carter and Hynes with molecular dynamics simulations. Due to the non-linear nature of the hypemetted chain (HNC) closure to solve the RISM equation, our method can shed light on the non-linearity of the free energy profiles, and we discuss these problems based on the obtained free energy profile. 

Both closures have been employed for determining the distribution functions for liquids 182 the Percus-Yevick equation tends to yield better results for nonpolar systems, while the hypemetted-chain equation (with the appropriate renormalization of long-range interactions)113,183 is found to be more appropriate for polar and ionic liquids.184... 

Kovalenko A, Ten-No S, Hirata F Solution of three-dimensional reference interaction site model and hypemetted chain equations for simple point charge water by modified method of direct inversion in iterative subspace, J Comput Chem 20(9) 928-936, 1999. 

FH = Flory-Huggins GF = generalized Flory GFD = generalized Flory dimer HNC = hypemetted chain HTA = high temperature approximation IFJC = ideal freely joined chain ISM = interaction site model LCT = lattice cluster theory MS = Martynov-Sarkisov PMMA = polymethyl methacrylate PRISM = polymer reference interaction site model PVME = polyvinylmethylether PS = polystyrene PY = Percus-Yevick RMMSA = reference molecule mean spherical approximation RMPY = reference molecular Percus-Yevick SANS = small angle neutron scattering SFC = semiflexible chain TPT = thermodynamic perturbation theory. 

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