Models, interaction site

PRISM (polymer reference interaction-site model) method for modeling homopolymer melts... 

One important class of integral equation theories is based on the reference interaction site model (RISM) proposed by Chandler [77]. These RISM theories have been used to smdy the confonnation of small peptides in liquid water [78-80]. However, the approach is not appropriate for large molecular solutes such as proteins and nucleic acids. Because RISM is based on a reduction to site-site, solute-solvent radially symmetrical distribution functions, there is a loss of infonnation about the tliree-dimensional spatial organization of the solvent density around a macromolecular solute of irregular shape. To circumvent this limitation, extensions of RISM-like theories for tliree-dimensional space (3d-RISM) have been proposed [81,82],... 

The integral equation method is free of the disadvantages of the continuum model and simulation techniques mentioned in the foregoing, and it gives a microscopic picture of the solvent effect within a reasonable computational time. Since details of the RISM-SCF/ MCSCF method are discussed in the following section we here briefly sketch the reference interaction site model (RISM) theory. 

If each polymer is modeled as being composed of N beads (or sites) and the interaction potential between polymers can be written as the sum of site-site interactions, then generalizations of the OZ equation to polymers are possible. One approach is the polymer reference interaction site model (PRISM) theory [90] (based on the RISM theory [91]) which results in a nonlinear integral equation given by... 

PRISM polymer-reference-interaction-site model... 

F. O. Raineri, Y. Zhou and H. L. Friedman, Ion solvation dynamics in an interaction-site model solvent, Chem. Phys., 152 (1991) 201-20. 

The original OZ equation can be applied only to liquids composed of spherically symmetrical particles, namely atoms. Chandler and Andersen proposed one of the possible extensions to treat general polyatomic cases, referred to as the reference interaction site model (RISM) or site-site OZ (SSOZ) theory [4], This has been further extended by Hirata and Rossky to be applicable to polar molecules such as water [5], In the RISM theory,... 

Sato presents an alternative method to both continuum solvation models and hybrid QM/MM or ONIOM approaches. This is represented by the reference interaction site model (RISM) formalism when combined to a QM description of the solute to give the RISM-SCF theory. 

The PRISM (Polymer-Reference-Interaction-Site model) theory is an extension of the Ornstein-Zernike equation to molecular systems [20-22]. It connects the total correlation function h(r)=g(r) 1, where g(r) is the pair correlation function, with the direct correlation function c(r) and intramolecular correlation functions (co r)). For a primitive model of a polyelectrolyte solution with polymer chains and counterions only, there are three different relevant correlation functions the monomer-monomer, the counterion-counterion, and the monomer-counterion correlation function [23, 24]. Neglecting chain end effects and considering all monomers as equivalent, we obtain the following three PRISM equations for a homogeneous and isotropic system in Fourier space ... 

Radial Distribution Functions and Reference Interaction Site Model... 

The equations depend essentially on six coordinates in the Cartesian space, and it includes a sixfold integral. This integral is the one that prevents the theory from applications to polyatomic molecules. It is the interaction-site model and the RISM approximation proposed by Chandler and Andersen [16] that enabled one to solve the equations. The idea behind the model is to project the functions onto the one-dimensional space along the distance between the interaction sites, usually placed on the center of atoms, by taking the statistical average over the angular coordinates of the molecules with fixation of the separation between a pair of interaction site. 

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