Integral equation theory of molecular

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. 

Theories based on the solution to integral equations for the pair correlation fiinctions are now well developed and widely employed in numerical and analytic studies of simple fluids [6]. Furtlier improvements for simple fluids would require better approximations for the bridge fiinctions B(r). It has been suggested that these fiinctions can be scaled to the same fiinctional fomi for different potentials. The extension of integral equation theories to molecular fluids was first accomplished by Chandler and Andersen [30] through the introduction of the site-site direct correlation fiinction c r) between atoms in each molecule and a site-site Omstein-Zemike relation called the reference interaction site... 

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

Tsige, M., Curro, J.G., Grest, G.S., McCoy, J.D. Molecular dynamics simulations and integral equation theory of alkane chains comparison of explicit and united atom models. Macromolecules 36(6), 2158-2164 (2003). doi 10.1021/ma0212543... 

The various approaches to spatial integration of molecular simulation data described in Section 6.3 use this equation instead of the full OZ equation. While this may not be fully rigorous, it is supported by several different analyses. First, Equation 6.8 is exact in some integral equation theories of fluids with anisotropic... 

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. 

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. 

Molecular Dynamics Simulations and Integral Equation Theory of Alkane Chains Comparison of Explicit and United Atom Models. 

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],... 

Nevertheless, the concept of spatial dispersion provides a general background for a qualitative understanding of those solvation effects which are beyond the scope of local continuum models. The nonlocal theory creates a bridge between conventional and well developed local approaches and explicit molecular level treatments such as integral equation theory, MC or MD simulations. The future will reveal whether it can survive as a computational tool competitive with these popular and more familiar computational schemes. 

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. 

Fluid microstructure may be characterized in terms of molecular distribution functions. The local number of molecules of type a at a distance between r and r-l-dr from a molecule of type P is Pa T 9afi(r)dr where Pa/j(r) is the spatial pair correlation function. In principle, flr (r) may be determined experimentally by scattering experiments however, results to date are limited to either pure fluids of small molecules or binary mixtures of monatomic species, and no mixture studies have been conducted near a CP. The molecular distribution functions may also be obtained, for molecules interacting by idealized potentials, from molecular simulations and from integral equation theories. 

Computer simulations, Monte Carlo or molecular dynamics, in fact appear to be the actual most effective way of introducing statistical averages (if one decides not to pass to continuous distributions), in spite of their computational cost. Some concepts, such as the quasi-structure model introduced by Yomosa (1978), have not evolved into algorithms of practical use. The numerous versions of methods based on virial expansion, on integral equation description of correlation functions, on the application of perturbation theory to simple reference systems (the basic aspects of these... 

---