Solvent Framework

Implicit solvent models have several advantages over explicit water representations, especially in molecular dynamics simulations. These include the following. 

Lower computational costs tor many molecular systems, and better scaling on parallel machines. The effective cost reduction may be particularly signiticant it one takes into account the improved sampling in contrast to explicit solvent models, solvent viscosity that slows down conformational transitions can be turned off completely within implicit representations. 

Effective ways to estimate tree energies since solvent degrees ot treedom are taken into account implicitly, estimating tree energies ot solvated structures is much more straightforward than with explicit water models. 

Since implicit solvent models correspond to instantaneous dielectric response trom solvent, there is no need tor the lengthy equilibration ot water that is typically necessary in explicit water simulations. This teature ot implicit solvent models becomes key when charge state ot the system is changed many times during the course ot a simulation, as, tor example, in constant pH simulations. 

Finally, the implicit solvent approach has a clear advantage over explicit solvent in computing and making physical sense ot energy landscapes ot molecular structures. Ftere, implicit averaging over solvent degrees ot treedom eliminates the noise —an astronomical number ot local minima arising trom small variations in solvent structure. 

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For molecular systems in the vacuum, exact analytical derivatives of the total energy with respect to the nuclear coordinates are available [22] and lead to very efficient local optimization methods [23], The situation is more involved for solvated systems modelled within the implicit solvent framework. The total energy indeed contains reaction field contributions of the form ER(p,p ), which are not calculated analytically, but are replaced by numerical approximations Efp(p,p ), as described in Section 1.2.5. We assume from now on that both the interface Y and the charge distributions p and p depend on n real parameters (A, , A ). In the geometry optimization problem, the A, are the cartesian coordinates of the nuclei. There are several nonequivalent ways to construct approximations of the derivatives of the reaction field energy with respect to the parameters (A1 , A ) ... 

FIGURE 7.1 An approximations tree of the implicit solvent framework. 

Protein folding. Exploring large conformational transitions is one of several areas where the advantages of implicit solvent framework, and the GB model in particular, become apparent. Several all-atom MD simulations of ah initio folding of small proteins have been reported. Examples include 20-residue "trpcage" protein [40],... 

An accurate description of the solvent environment is essential for realistic biomolecular modeling, but often becomes prohibitively expensive computationally if water is treated explicitly. Implicit solvent framework is an attractive alternative that offers several significant advantages over the explicit water representation, including lower computational costs, faster conformational search, and very effective ways to estimate relative free energies of conformational ensembles. However, these advantages come at a price of making several fundamental. 

At the same time, examples where the GB model breaks down are also well known. Part of the overall error in these cases is attributable to the PB GB approximation, while the remainder comes from the more fundamental limitations of the general implicit solvent framework itself. These examples are extremely important for defining the current boundaries of applicability of the GB model they also suggest directions for future improvements. 

In summary, the use of implicit solvation models in molecular simulations offers considerable rewards, both at conceptual and practical levels. However, compared to the more established explicit solvent approach, less is known about the domain of applicability of these models, and so extra care must be taken when using them in practice. Drawing on the analogy with the development of the empirical explicit solvent force-fields over the past 30 years, it is likely that improvements in the implicit solvent framework accompanied by accumulation of practical experience will eventually make the framework a standard approach within its reasonably well-defined domain. 

Feng, G., J. Huang, B. G. Sumpter, V. Meunier, and R. Qiao. 2011. A countercharge layer in generalized solvents framework for electrical double layers in neat and hybrid ionic liquid electrolytes. Physical Chemistry Chemical Physics 13 14723-14734. 

This chapter is organized as follows. Section 18.2 describes the theoretical foundation of Marcus theory, formulated in a molecular rather than dielectric continuum solvent framework. Its non-Gaussian extension is presented in section 18.3 and its implications for rate calculations are discussed in section 18.4. The theory is then confronted to various molecular simulation results in section 18.5 and a conclusion is proposed in section 18.6. 

The reason for this enliancement is intuitively obvious once the two reactants have met, they temporarily are trapped in a connnon solvent shell and fomi a short-lived so-called encounter complex. During the lifetime of the encounter complex they can undergo multiple collisions, which give them a much bigger chance to react before they separate again, than in the gas phase. So this effect is due to the microscopic solvent structure in the vicinity of the reactant pair. Its description in the framework of equilibrium statistical mechanics requires the specification of an appropriate interaction potential. 

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Many additional refinements have been made, primarily to take into account more aspects of the microscopic solvent structure, within the framework of diffiision models of bimolecular chemical reactions that encompass also many-body and dynamic effects, such as, for example, treatments based on kinetic theory [35]. One should keep in mind, however, that in many cases die practical value of these advanced theoretical models for a quantitative analysis or prediction of reaction rate data in solution may be limited. 

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

Calculations within tire framework of a reaction coordinate degrees of freedom coupled to a batli of oscillators (solvent) suggest tliat coherent oscillations in the electronic-state populations of an electron-transfer reaction in a polar solvent can be induced by subjecting tire system to a sequence of monocliromatic laser pulses on tire picosecond time scale. The ability to tailor electron transfer by such light fields is an ongoing area of interest [511 (figure C3.2.14). 

Practical Solubility Concepts. Solution theory can provide a convenient, effective framework for solvent selection and blend formulation (3). When a solute dissolves in a solvent, a change in free energy occurs as a result of solvent—solute interactions. The change in free energy of mixing must be negative for dissolution to occur. In equation 1,... 

Kamlet-Taft Linear Solvation Energy Relationships. Most recent works on LSERs are based on a powerfiil predictive model, known as the Kamlet-Taft model (257), which has provided a framework for numerous studies into specific molecular thermodynamic properties of solvent—solute systems. This model is based on an equation having three conceptually expHcit terms (258). 

A refined grade of MTBE is used ia the solvents and pharmaceutical iadustries. The main advantage over other ethers is its uniquely stable stmctural framework that contains no secondary or tertiary hydrogen atoms, which makes it very resistive to oxidation and peroxide formation. In addition, its higher autoignition temperature and narrower flammabihty range also make it relatively safer to use compared to other ethers (see Table 3). 

Another way is to reduce the magnitude of the problem by eliminating the explicit solvent degrees of freedom from the calculation and representing them in another way. Methods of this nature, which retain the framework of molecular dynamics but replace the solvent by a variety of simplified models, are discussed in Chapters 7 and 19 of this book. An alternative approach is to move away from Newtonian molecular dynamics toward stochastic dynamics. 

A statistical mechanical fonnulation of implicit solvent representations provides a robust theoretical framework for understanding the influence of solvation biomolecular systems. A decomposition of the free energy in tenns of nonpolar and electrostatic contributions, AVF = AVF " + AVF ° , is central to many approximate treatments. An attractive and widely used treatment consists in representing the nonpolar contribution AVF " by a SASA surface tension term with Eq. (15) and the electrostatic contribution by using the... 

In many cases, it is possible to replace environmentally hazardous chemicals with more benign species without compromising the technical and economic performance of the process. Examples include alternative solvents, polymers, and refrigerants. Group contribution methods have been conunonly used in predicting physical and chemical properties of synthesized materials. Two main frameworks have... 

The isoquinoline framwork is derived from the corresponding acyl derivatives of P-hydroxy-P phenylethylamines. Upon exposure to a dehydrating agent such as phosphorous pentaoxide, or phosphorous oxychloride, under reflux conditions and in an inert solvent such as decalin, isoquinoline frameworks are formed. 

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