RISM theory radial distribution functions

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... 

This is another type of solvated Fock operator in the combination method of RISM and ab initio MO theory. It should be noted that the first order derivatives of radial distribution functions with respect to the effective charges are required to construct the Fock matrix. 

Figure flf. Potential of mean force between the Na" " and Cl ions in ambient water at infinite dilution. Results following from the 3D-RISM/HNC and 3D-RISM/KH approach (solid and short-dashed hnes, respectively), and from the ion-ion radial distribution function obtained by the site-site DRISM/HNC theory (dash dotted Une). Molecular simulation data [115] (open squares). Prediction of the primitive continuum model of solvent (long dashed line). 

Figure 4-26. Radial distribution functions between water oxygen and hydrogen sites and the Cl and Na+ ions in ambient aqueous solution at infinite dilution. Orientational averages of the 3D water-ion distributions obtained from the SC-3D-RISM/HNC theory (sohd hnes), results following from the site-site RISM/HNC approach (dash dotted lines), and molecular simulation data [112] (short dashed lines).

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) ... 

Fig. 3. Intennolecular radial distribution functions from theory (lines) and MD simulations (symbols) for melts of freely jointed polymers of varying chain length. The lines correspond to PY theory (N = ), RISM theory (N = 2), and SC/PRISM theory (N > 2)...

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],... 

To obtain the PMF between ions in solution at a finite salt concentration, the 3D-RISM description is applied to two labelled ions considered as a composite solute immersed in solvent of all other ions and molecular species constituting the solution. The ion-ion as well as all other site-site radial distributions input to the 3D-RISM equation are follow from the site-site DRISM theory. The PMFs following from Eq. (4.36) would be same as those corresponding to the distribution functions yielded by... 

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