Reference interaction-site model integral equation

Kezic, B. and A. Perera. 2011. Towards a more aceurate reference interaction site model integral equation theory for molecular liquids. Journal of Chemical Physics. 135, 234104. Kim, J. I. 1978. A critical study of the Ph4AsPh4B assumption for single ion thermodynamics in amphiprotic and dipolar-aprotic solvents Evaluation of physical parameters relevant to theoretical consideration. Zeitschriftfur Physikalische Chemie. 113,129. 

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... 

RISM integral equation reference-interaction-site model... 

Integral equation ideas on the structure of monatomic liquids were first modified and applied to molecular liquids by Chandler and Andersen, Their classic work is now referred to as the reference interaction site model (RISM) of molecular liquids. Polymer RISM (PRISM) is essentially an extension of RISM theory that successfully describes the structure of flexible polymer chains in the liquid state. 

In this section we introduce integral equation theories (IETs) and approximate closures applicable for various models of polyelectrolyte solutions. A theory for linear polyelectrolytes based on the polymer reference interaction site model has also been proposed [58, 59], but this approach will not be reviewed here. 

In the weak-segregation regime, the phase behavior of a polymer melt composed of flexible-chain macromolecules can be described on the basis of the random-phase approximation (RPA) or the polymer integral equation reference interaction site model (pRISM) theory that allow finding the conditions under which the spatially homogeneous state of the system becomes unstable. 

ID Reference Interaction Site Model The ID RISM approach [78] and its extension to dipolar liquids (XRISM [79]) require a solution of a systan of site-site Omstein-Zemike (SSOZ) ID integral equations that operate with the... 

Over the p t several years we and our collaborators have pursued a continuous space liquid state approach to developing a computationally convenient microscopic theory of the equilibrium properties of polymeric systems. Integral equations method [5-7], now widely employed to understand structure, thermodynamics and phase transitions in atomic, colloidal, and small molecule fluids, have been generalized to treat macromolecular materials. The purpose of this paper is to provide the first comprehensive review of this work referred to collectively as Polymer Reference Interaction Site Model (PRISM) theory. A few new results on polymer alloys are also presented. Besides providing a unified description of the equilibrium properties of the polymer liquid phase, the integral equation approach can be combined with density functional and/or other methods to treat a variety of inhomogeneous fluid and solid problems. 

These integral equation ideas of monatomic liquids were generalized and applied to molecular liquids by Chandler and Andersen [6,8] to formulate the Reference Interaction Site Model or RISM theory of molecular fluids. In the RISM approach, each molecule is subdivided into spherically symmetric, interaction sites. The intermolecular pair structure of a uniform molecular liquid of M molecules is now specified through a site-site radial distribution function matrix gaY(r) ... 

Among the applications of integral equation theory to solutions, Koga et al. (1996) used a reference interaction-site model (RISM), an approximation due to Chandler and Andersen (1972), to calculate the local solvation behavior of naphthalene in supercritical carbon dioxide. They used a ten-site model for naphthalene and a three-site model for carbon dioxide, in which partial charges were placed on the sites in addition to Lennard-Jones potentials acting between sites on different molecules. Their potential function was a sum over the ten naphthalene sites and the three carbon dioxide sites of terms of the form of Equation 5.11 ... 

In the 1970s Chandler, Andersen, and co-workers initiated the pioneering extension of atomic integral equation concepts to molecular liquids based on the Reference Interaction Site Model, or RISM,... 

MC and MD simulations could be replaced by other less expensive methods. We shall quote the use of the integral equation methods called RISM (reference interaction site model) explored by Ten-no et al. RISM methods give solute-solvent site-site correlations functions as MC and MD simulations do. The RISM procedure is inserted into an SCF QM cycle as for combined QM/MM methods based on simulations. We have no direct experience on computational costs of these procedures, but in general RISM calculations are faster by some orders of magnitude than MC simulations. This is paid for by a greater sensitivity of RISM to some features of the integral equation methods, such as the closure expressions one has to use. 

An alternative approach that combines the Gaussian thread model of polymers with liquid-state theory is known as the polymer reference interaction site model (PRISM) approach [34-38[. This approach has the merit that phenomena such as the de Gennes [3] correlation hole phenomena and its consequences are incorporated in the theoretical description, and also one can go beyond the Gaussian model for the description of intramolecular correlations of a polymer chain, adding chemical detail (at the price of a rather cumbersome numerical solution of the resulting integral equations) [37,38[. An extension to describe the structure of colloid-polymer mixtures has also become feasible [39, 40]. On the other hand, we note that this approach shares vhth other approaches based on liquid state theories the difficulty that the hierarchy of exact equations for correlation functions needs to be decoupled via the so-called closure approximation [34—38]. The appropriate choice of this closure approximation has been a formidable problem [34—36]. A further inevitable consequence of such descriptions is the problem that the critical behavior near the critical points of polymer solutions and polymer blends is always of mean-field character ... 

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