Integral equation theory of molecular liquids

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

B. C. Eu and H. Farhat, J. Chem. Phys., 104, 300 (1996). Integral Equation Theory of Molecular Liquids Kirkwood Hierarchy Approach to Diatomic and Polyatomic Liquids. 

Hirata, F., Chemical processes in solution studied by an integral equation theory of molecular liquids. Bull. Chem. Soc. Jap. 71, 1483- 1499 (1998). 

T. Yamazaki and A. Kovalenko. Spatial decomposition of solvation free energy based on the 3D integral equation theory of molecular liquid Application to mini proteins. 

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. 

Comparison between Integral Equation Theory and Molecular Dynamics Simulations of Dense, Flexible Polymer Liquids. 

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) ... 

Curro JG, Schweizer KS, Grest GS, Kremer K A comparison between integral equation theory and molecular dynamics simulations of dense, flexible polymer liquids, J Chem Phys 91(2) 1357-1364, 1989. 

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],... 

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. 

Here we briefly outline the methrxl for obtaining the free energy profiles of ET reactions based on ex-RISM, an integral equation theory developed for molecular liquids. (For more detailed description of the method, see Ref. I.) We denote the charge distribution of the solute ions, the donor (A) and the acceptor (B) ions, at the reactant state as (ca, Cb). The distance between A and B is fixed. Let z denote a fraction of the electronic charge transferred from A to B. We define a reaction coordinate as. 

Experimental determination of excess molar quantities such as excess molar enthalpy and excess molar volume is very important for the discussion of solution properties of binary liquids. Recently, calculation of these thermodynamic quantities becomes possible by computer simulation of molecular dynamics (MD) and Monte Carlo (MC) methods. On the other hand, the integral equation theory has played an essential role in the statistical thermodynamics of solution. The simulation and the integral equation theory may be complementary but the integral equation theory has the great advantage over simulation that it is computationally easier to handle and it permits us to estimate the differential thermodynamic quantities. 

During the 1950s and the 1960s, two important theories of the liquid state were developed, initially for simple liquids and later applied to mixtures. These are the scaled-particle theory, and integral equation methods for the pair correlation function. These theories were described in many reviews and books. In this book, we shall only briefly discuss these theories in a few appendices. Except for these two theoretical approaches there has been no new molecular theory that was specifically designed and developed for mixtures and solutions. This leads to the natural question why a need for a new book with the same title as Prigogine s ... 

Other melting rules are formulated in terms of properties of the saturated liquid phase, focusing in particular on some feature of the structure as quantified by the radial distribution function g r). Ideally, these rules could be applied to predict the freezing transition of a molecular model using a correlation function given by (say) an integral equation theory for g r). 

Computer simulations are not the only methods which can be used to calculate the dielectric constant of pure liquids. Other approaches are given by the use of integral equations, in particular, the hypemetted chain (HNC) molecular integral equation and the molecular Omstein-Zemike (OZ) theory (see Section 8.7.1 for details on such methodologies). 

An analytical method for applying Polanyi s theory at temperatures near the critical temperature of the adsorbate is described. The procedure involves the Cohen-Kisarov equation for the characteristic curve as well as extrapolated values from the physical properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Rad/ush-kevich equation was a limiting case of the Cohen-Kisarov s equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. 

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