Solvation explicit modeling

Solvent effects can be incorporated into two kinds of solvation models, either those that consider each solvent molecule as an individual molecular species (explicit models), or those that deal with the averaged effect of the solvent molecules through use of a coarse-grained description of solvent (e.g., dielectric models, implicit solvent models, etc.). 

Fig. 1. Representation of the solvation models continuum or implicit model and explicit model.

In Section 11.4.6, the limitations of continuum models in their ability to treat non-equilibrium solvation, at least in their simplest incarnations, were noted and discussed. In principle, exphcit solvent models might be expected to be more appropriate for the study of chemical processes characterized by non-equilibrium solvation. In practice, however, the situation is not much better for the explicit models than for the implicit. 

With Monte Carlo methods, the adoption of the Metropolis sampling scheme intrinsically assumes equilibrium Boltzmann statistics, so special modifications are required to extend MC methods to non-equilibrium solvation as well. Fortunately, for a wide variety of processes, ignoring non-equilibrium solvation effects seems to introduce errors no larger than those already inherent from other approximations in the model, and thus both implicit and explicit models remain useful tools for studying chemical reactivity. 

Much like the RISM method, the LD approach is intermediate between a continuum model and an explicit model. In the limit of an infinite dipole density, the uniform continuum model is recovered, but with a density equivalent to, say, the density of water molecules in liquid water, some character of the explicit solvent is present as well, since the magnitude of the dipoles and their polarizability are chosen to mimic the particular solvent (Papazyan and Warshel 1997). Since the QM/MM interaction in this case is purely electrostatic, other non-bonded interaction terms must be included in order to compute, say, solvation free energies. When the same surface-tension approach as that used in many continuum models is adopted (Section 11.3.2), the resulting solvation free energies are as accurate as those from pure continuum models (Florian and Warshel 1997). Unlike atomistic models, however, the use of a fixed grid does not permit any real information about solvent structure to be obtained, and indeed the fixed grid introduces issues of how best to place the solute into the grid, where to draw the solute boundary, etc. These latter limitations have curtailed the application of the LD model. 

The explicit modeling approach surrounds a solute molecule with solvent molecules and then examines each molecule in that solvated environment. Quantum chemical methods, both semiempiricaP and ab initio" have been used to do this however, molecular dynamics and Monte Carlo simulations using force fields are used most often.Calculations on ensembles of molecules are more complex than those on individual molecules. Dykstra et al. discuss calculations on ensembles of molecules in a chapter in this book series. Because of the many conformations accessible to both solute and solvent molecules, in addition to the great number of possible solute molecule-solvent molecule orientations, such direct QM calculations are very computer intensive. However, the information resulting from this type of calculation is comprehensive because it provides molecular structures of the solute and solvent, and takes into account the effect of the solvent on the solute. This is the method of choice for assessing specific bonding information. 

Marrone, T. J., Gilson, M. K. and McCammon, J. A. (1996). Comparison of continuum and explicit models of solvation Potential of mean force for alanine dipeptide. J. Phys. Chem., 100, 1439-1441. 

For the free energy of solvation calculation, however, it is difficult to discern the most accurate method. Recently, there have been numerous publications exploring the use of the cluster continuum method with anions. With regard to implicit solvation, there are no definite conclusions to the most accurate method, yet for the PB models the conductor-like models (COSMO CPCM) appear to be the most robust over the widest range of circumstances [23]. At this writing, the SMVLE method seems to be the most versatile, as it can be used by itself, or with the implicit-explicit model, and the error bars for bare and clustered ions are the smallest of any continuum solvation method. The ability to add explicit water molecules to anions and then use the implicit method (making it an implicit-explicit model) improves the results more often than the other implicit methods that have been used in the literature to date. 

Numerous theoretical studies on DMABN have been carried out, and many of them confirm the greater validity of the TICT model. The main body of such calculations, however, has been limited to the isolated system, while few examples including solvent effects can be quoted. " On the contrary, the phenomenon is strongly related to solvation and thus explicit considerations of solvent interactions are very important to get a more accurate understamding of the experimental evidence on the specific effects due to the presence of polar solvents. Here we summarize the results of the correlated study of DMABN both in vacuo and in solution we have published on the Journal of American Chemical Society. In this study we have used the multireference perturbation configuration interaction (Cl) method, known with the CIPSI acronym, which has been coupled to the PCM-IEF solvation continuum model. ... 

Standard computations treat isolated molecules (i.e., model the low-pressure gas phase situation). Chemistry in the condensed phase, however, can be significantly different because ionic and polar species are specifically stabilized. Computations can consider solvation explicitly by including the solvent molecules or as a continuous medium effect (reaction field methods). 

From a computational point of view, for a given theoretical level, piuely continuum solvation approaches are by far less expensive than explicit models. Such a feature is especially relevant if one is compelled to exploit QM techniques, such as those usually required to study problems in the field of computational spectroscopy. In this case, in fact, the modem implementations of continuum solvation models are able to keep the cost of the calculation for solvated systems basically the same as the corresponding calculation for the isolated system [149]. 

Semiclassical solvation models depend on parameters. Implicit models mostly depend on how the cavity that contains the solute is built, and large parameterization is required to handle a variety of different solvents. In this respect, the work of Marenich et al. for the polarizable continuum model (PCM)" has gone a long way in this direction, in the opinion of this author. Explicit models also depend on parameters that enter the definition of the individual model. However, the quality of the results obtained when employing explicit solvation models with QM methods also depends on the quality of the sampling of the solvent configuration space. This is usually accomplished with a molecular dynamics (MD) simulation, which does not need to use the same polarizable solvation model. The quality of the MD simulation will influence the reliability of the following QM results. 

For comparison with real reactions, it is usually necessary to strip the chemical system to its essentials to reduce the number of atoms in the reaction system and permit computational feasibility. Most reactions are run in solution whereas the computations apply to the gas phase thus, solvation needs to be considered at some level. Solvation is particularly important when ions are involved. It is less important for the reactions of neutral polar organometallics but these compounds generally have significant dipole moments and solvation is not insignificant. Nevertheless, most calculations of reaction systems have generally ignored solvation at least explicitly. In some recent cases solvation was modeled by coordination of one or more solvent molecules with the metal or by use of a continuum model for solvation (see Solvation Modeling). 

Operating fuel cell involves solvent environment, and it is important to study water formation reaction under solvent conditions to understand the solvation effects on overall reaction kinetics. Adding water molecules explicitly or entire water bilayer to unit cells of simulating catalyst is considered as explicit solvent model. This method, however, does not resemble fully saturated system, and water molecules are introduced during the simulation that directly participates in the ORR [148]. Poisson-Boltzmann implicit solvent model is a method to resemble solvent as a continuum rather than individual molecules in explicit models [160,162]. This method is computationally inexhaustive and accurate enough to reproduce reliable results for the atomistic energy calculations. 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

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