MC/RISM

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)... 

The numerical self-consistent (SC) MC/RISM procedure [51,52] employed to solve the matrix polymer RISM equation (4) with the RMMSA closure relation (6)-(7) was used in Ref. [53] to study water-containing Nafion systems. The single-chain MC simulation was based on the realistic rotational-isomeric-state (RIS) model [54], in which the short-range intramolecular interactions depending on the details of chemical structure were taken into account via appropriate matrices of statistical weights [54]. 

Figure 15.2. Typical snapshot of single Nafion macromolecule generated in the curse of the SC-MC/RISM calculations [53]. The macromolecule consists of a fluorocarbon backbone of 98 effective units (CF2 or CF3) linked to 10 side chains OCF2CF(C-F3)0CF2CF2S03H consisting of 7 units in the main chain.

The most important achievement of the work [53] was the implementation of SC-MC/RISM technique to probe the continuum percolation in the water subphase of Nafion. The solution of such a problem is of interest for... 

Several attempts have been made to couple microscopic simulations with statistical-mechanical theories. We have demonstrated that the hybrid MC/ RISM technique combining atomistic/coarse-grained MC simulations with integral equation RISM theory is a very effective tool in the computational treatment of equilibrium properties and structural reorganizations in the weak segregation limit, when atomic level information is passed on to mesoscale level. Of course, RISM theory does not predict types of resulting nanostructures or their symmetries. It appears possible, and in fact desirable, to combine RISM or DF formalism with molecular dynamics - both classical... 

Under the circumstances it seemed desirable to obtain a pmf for TBC in water, though only the ion-pair region has been considered so far. The most closely related previous effort was by McCammon et al., who obtained a pmf for Na Cr in TIPS2 water and analyzed the dynamics for the Na Cr Na" //Cr barrier crossing. They used MD with importance sampling in this study, which is the only prior MC or MD determination of a pmf for an ion pair in water. Recently Pettitt and Rossky have calculated pmfs for several alkali halides in water via extended RISM theory. The qualitative accord with the MD results for Na Cl" is fine however, the XRISM pmf is much flatter. 

Combined RISM-MC approach for predicting peptide conformations... 

In this section, we briefly describe our hybrid approach for predicting conformations of biomolecules stabilized in solvent [15, 16, 17]. In this approach, the RISM theory is combined with the MC simulated annealing or one of the generalized-ensemble algorithms. Our approach falls into the third category, and both the biomolecule and the solvent are treated on the atomic level. The hybrid approach is implemented for two small peptides as the first step of the research. The solvent effects on the conformational stability of the peptides are discussed and the... 

In a preliminary prediction of a peptide conformation, the conformational entropy of the peptide is often neglected, and we follow this custom. Our aim is to determine the most stable conformation of a peptide molecule in solvent, and in this case the MC simulated annealing is a powerful tool. To obtain information on the average conformation by accounting for the conformational entropy, one needs to employ a generalized-ensemble algorithm. The combination of the RISM theory and the multi-canonical algorithm is considered in 1.8. 

Our approach, a combination of the RISM theory and the MC simulated annealing, is applied to Met-enkephalin. The scheme for the MC simulated annealing is the same as that employed in vacuum cases except that Ec is replaced by the total energy Et- The initial and final tern-... 

Next, we briefly summarize the result of applying our approach, in which the RISM theory is combined with the MC simulated annealing, to C-peptide in water. The initial conformation is an almost fully extended one (details of this conformation are described in 2.3). In the initial... 

They demonstrated that the RISM integral equation and MC methods gave comparable results and that the nearest CO molecules showed preferred orientations in certain positions parallel to the naphthalene molecular plane and to the long axis when above the plane but perpendicular to the plane whether abeam or ahead of the naphthalene. They also obtained the partial molal volume of naphthalene as a function of the density of solvent it is negative at low densities, owing to a number of COj molecules being attracted to naphthalene, increasing to reasonable positive values as density iuCTeases. 

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. 

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