Solvent implicit effect

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

In the development of solvation models, Cramer and Tmhalar have made several noteworthy contributions [8-11]. Most of the implicit solvation models do not include the effect of first solvation shell on the solute properties. This can be satisfactorily treated by finding the best effective radii within implicit models. In addition to the first-solvent-shell effects, dispersion interactions and hydrogen bonding are also important in obtaining realistic information on the solvent effect of chemical systems. 

The first term, Vs, accounts for the Coulomb-exchange direct interaction between D and A (see Eq.10), and the second, Vexpucit, describes a solvent-mediated chromophore-chromophore contribution between the transition densities. In addition to this explicit medium effect (VexpuCit), we note that another implicit effect of the environment is included in the Vs term, due to changes on the transition densities upon solvation. It is useful to define a screening factor s, conceptually equivalent to the 1/n2 term in the Forster equation, so that V = sVs ... 

Suppose that we were to average out the effects of all of the solvent molecules, effectively integrating over the coordinates describing the solvent molecules. This would dramatically simplify the description of the solvent molecules, and thereby simplify the computation of the energy of the solute-solvent system. This is the general principle behind the implicit solvent models. The solvent is described by a single term, its dielectric constant, and we just need to treat the interaction of the solute with this field. 

Thermodynamic solvent isotope effects have been utilized to evaluate the extent to which desolvation aids ligand binding [35, 36]. While the assumptions implicit in the calculations likely make precise determination of A/fsoiv impossible, the relative role of desolvation for a series of bindings is clearly accessible (Table 5). This exercise facilitates two observations that are likely general. First, a significant fraction... 

This method was introduced recently as an efficient technique to accurately model solvent and salt effects in an implicit fashion ([Gilson et al. 1993]). The forces are calculated as a sum of three terms ... 

The GB equation is suitable for the description of solvent effects in molecular mechanics and dynamics [16], as well as in quantum mechanical calculations (17,18]. An excellent review of implicit solvation models, with more than 900 references, is given by Cramer and Truhlar [19]. 

It is possible to go beyond the SASA/PB approximation and develop better approximations to current implicit solvent representations with sophisticated statistical mechanical models based on distribution functions or integral equations (see Section V.A). An alternative intermediate approach consists in including a small number of explicit solvent molecules near the solute while the influence of the remain bulk solvent molecules is taken into account implicitly (see Section V.B). On the other hand, in some cases it is necessary to use a treatment that is markedly simpler than SASA/PB to carry out extensive conformational searches. In such situations, it possible to use empirical models that describe the entire solvation free energy on the basis of the SASA (see Section V.C). An even simpler class of approximations consists in using infonnation-based potentials constructed to mimic and reproduce the statistical trends observed in macromolecular structures (see Section V.D). Although the microscopic basis of these approximations is not yet formally linked to a statistical mechanical formulation of implicit solvent, full SASA models and empirical information-based potentials may be very effective for particular problems. 

The solvent dependence of the reaction rate is also consistent with this mechanistic scheme. Comparison of the rate constants for isomerizations of PCMT in chloroform and in nitrobenzene shows a small (ca. 40%) rate enhancement in the latter solvent. Simple electrostatic theory predicts that nucleophilic substitutions in which neutral reactants are converted to ionic products should be accelerated in polar solvents (23), so that a rate increase in nitrobenzene is to be expected. In fact, this effect is often very small (24). For example, Parker and co-workers (25) report that the S 2 reaction of methyl bromide and dimethyl sulfide is accelerated by only 50% on changing the solvent from 88% (w/w) methanol-water to N,N-dimethylacetamide (DMAc) at low ionic strength this is a far greater change in solvent properties than that investigated in the present work. Thus a small, positive dependence of reaction rate on solvent polarity is implicit in the sulfonium ion mechanism. 

Another advantage of PB based pKa calculations is that effects of electrolytes are readily accounted for in the PB equation. The Coulombic contribution in conjunction with salt dependence to the abnormally depressed pAVs of histidine in staphylococcal nuclease has been experimentally tested [56], Recently, the methodology used in the PB calculations (Eqs. 10-11 and 10-12) has been combined with the generalized Born (GB) implicit solvent model [94] to offer pKa predictions at a reduced computational cost [52],... 

We present and analyze the most important simplified free energy methods, emphasizing their connection to more-rigorous methods and the underlying theoretical framework. The simplified methods can all be superficially defined by their use of just one or two simulations to compare two systems, as opposed to many simulations along a complete connecting pathway. More importantly, the use of just one or two simulations implies a common approximation of a near-linear response of the system to a perturbation. Another important theme for simplified methods is the use, in many cases, of an implicit description of solvent usually a continuum dielectric model, often supplemented by a simple description of hydrophobic effects [11]. 

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