Reference interaction site model method

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

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. 

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. 

Between the appearance of the MD studies by Vishnyakov and Neimark [56], and that by Urata et al. [60], Khalatur, Khokhlov and co-workers published two coarse-grained molecular modelling studies of Nafion [64, 65] that utilised rather different approaches to studying the morphology of PFSIs. The first of these [64] was based on a hybrid Monte Carlo/reference interaction site model (MC/RISM). The principle behind this method was to use MC simulations, based on the rotational isomeric state (RIS)... 

As concerns the site-site approach the most important theory is the reference interaction site model , or RISM. This method applies to an intermolecular pair potential modeled by a site-site form, i.e., V(rc0iC02 ) = 5 apV p (r ) and its original intuitive derivation is based on exploring the possibility of decomposing g(r o),a)2) also in the same form, i.e., as a sum of site-site gap(r)s. 

D Reference Interaction Site Model The 3D RISM [80-82, 93] is a theoretical method for modeling solution phase systems based on classical statistical mechanics. The 3D RISM equations relate 3D intermolecular solvent site—solute total correlation functions (hjr)), and direct correlation functions (c (r)) (index a corresponds to the solvent sites) [80, 82] ... 

The infortnation provided in this chapter can be divided into four parts 1. introduction, 2. thermodynamic theories of polymer blends, 3. characteristic thermodynamic parameters for polymer blends, and 4. experimental methods. The introduction presents the basic principles of the classical equilibrium thermodynamics, describes behavior of the single-component materials, and then focuses on the two-component systems solutions and polymer blends. The main focus of the second part is on the theories (and experimental parameters related to them) for the thermodynamic behavior of polymer blends. Several theoretical approaches are presented, starting with the classical Flory-Huggins lattice theory and, those evolving from it, solubility parameter and analog calorimetry approaches. Also, equation of state (EoS) types of theories were summarized. Finally, descriptions based on the atomistic considerations, in particular the polymer reference interaction site model (PRISM), were briefly outlined. 

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. 

Kovalenko A, Ten-No S, Hirata F Solution of three-dimensional reference interaction site model and hypemetted chain equations for simple point charge water by modified method of direct inversion in iterative subspace, J Comput Chem 20(9) 928-936, 1999. 

Kovalenko A, Hirata F, Kinoshita M Hydration structure and stabdity of Met-enkephalin studied by a three-dimensional reference interaction site model with a repulsive bridge correction and a thermodynamic perturbation method, J Chem Phys 113(21) 9830—9836, 2000. 

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. 

H. Sato, F. Hirata and S. Kato. Analytical energy gradient for the reference interaction site model multiconfigurational self-consistent-field method Application to 1,2-difluoro-ethylene in aqueons solntion. J. Chem. Phys. 105,1996, 1546-1551. 

The free energy profile for the electron transfer reaction in a polar solvent is examined based on the extended reference interaction site method (ex-RISM) applying it to a simple model of a charge separation reaction which was previously studied by Carter and Hynes with molecular dynamics simulations. Due to the non-linear nature of the hypemetted chain (HNC) closure to solve the RISM equation, our method can shed light on the non-linearity of the free energy profiles, and we discuss these problems based on the obtained free energy profile. 

Reference interaction site method (RISM), 5, 8, 165 polaron, 175, 176 Resonant energy transfer in excitons, 244-246 Restricted ion hydration, 352-356 Restricted primitive model (RPM), 92-95... 

The MFA [1] introduces the perturbation due to the solvent effect in an averaged way. Specifically, the quantity that is introduced into the solute molecular Hamiltonian is the averaged value of the potential generated by the solvent in the volume occupied by the solute. In the past, this approximation has mainly been used with very simplified descriptions of the solvent, such as those provided by the dielectric continuum [2] or Langevin dipole models [3], A more detailed description of the solvent has been used by Ten-no et al. [4], who describe the solvent through atom-atom radial distribution functions obtained via an extended version of the interaction site method. Less attention has been paid, however, to the use of the MFA in conjunction with simulation calculations of liquids, although its theoretical bases are well known [5]. In this respect, we would refer to the papers of Sese and co-workers [6], where the solvent radial distribution functions obtained from MD [7] calculations and its perturbation are introduced a posteriori into the molecular Hamiltonian. 

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