Implicit solvent/solvation

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... 

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. 

A key element of many simplified free energy methods is the use of an implicit description of the solvent. Implicit solvent models are based on the concept of a PMF, presented briefly in this section see [11] for a detailed review see Chap. 4 for applications of the PMF concept that are not related to implicit solvation. 

Solvation Free Energies Using Implicit Solvent... 

The most common approach to solvation studies using an implicit solvent is to add a self-consistent reaction field (SCRF) term to an ab initio (or semi-empirical) calculation. One of the problems with SCRF methods is the number of different possible approaches. Orozco and Luque28 and Colominas et al27 found that 6-31G ab initio calculations with the polarizable continuum model (PCM) method of Miertius, Scrocco, and Tomasi (referred to in these papers as the MST method)45 gave results in reasonable agreement with the MD-FEP results, but the AM1-AMSOL method differed by a number of kJ/mol, and sometimes gave qualitatively wrong results. 

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.). 

Having identified the strongest points of the explicit and implicit solvent models, it seems an obvious step to try to combine them in a way that takes advantage of the strengths of each. For instance, to the extent first-solvation-shell effects are qualitatively different from those deriving from the bulk, one might choose to include the first solvation shell explicitly and model the remainder of the system with a continuum (see, for instance, Chahnet, Rinaldi, and Ruiz-Lopez, 2001). 

DFT was employed to study the mechanism of ammonolysis of phenyl formate in the gas phase, and the effect of various solvents on the title reaction was assessed by the polarizable continuum model (PCM). The calculated results show that the neutral concerted pathway is the most favourable one in the gas phase and in solution.24 The structure and stability of putative zwitterionic complexes in the ammonolysis of phenyl acetate were examined using DFT and ab initio methods by applying the explicit, up to 7H20, and implicit PCM solvation models. The stability of the zwitterionic tetrahedral intermediate required an explicit solvation by at least five water molecules with stabilization energy of approximately 35 kcalmol-1 25... 

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 ) ... 

In recent years many attempts have been made to extend the implicit solvent models to the description of time-dependent phenomena. One of these phenomena is nonequilibrium solvation [3] and it can be described effectively in a very simplified way, despite the fact that it actually depends on the details of the full frequency spectrum of the dielectric constant. Typical examples of nonequilibrium solvation are the absorption of light by the solute which produces an excited state which is no longer in equilibrium with the surrounding polarization of the medium [11-13], Another example is intermolecular charge transfer within the solute, also leading to a nonequilibrium polarization [14],... 

Influence of the molecular environment on the structure and dynamics of molecular subsystems will be outlined referring to the solvation free energy (Chapter 4). Implicit solvent models based on the Poisson-Boltzmann (PB) equation and the Generalized Born (GB) model is discussed in 5 and 6. The PB or GB models are used for studies of molecular electrostatic properties and allow proper assignments of positions of protons (hydrogen atoms) within the given (bio)molecular structure. 

Once the computational model of the molecule is created, it is of most interest to study its properties in the natural environment, in particular, water solvent. Surrounding the molecule with water, allows us to study the solvation process. Like molecules, the solvent may be also described with different levels of accuracy. Beginning with all-atom models of water,48,49 which allow for the studies of solvent structure around solutes but are time consuming and the results are model dependent, to continuous dielectric models,50- 52 which are faster but less accurate and give no knowledge about the solvent itself. Thus, the difference in the level of description for both models is either an advantage or a drawback. These models are commonly known as explicit or implicit solvent models, respectively. 

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