Solvent continuum solvation models

A. H. Zewail I have a question for Prof. Marcus concerning the fact that, in the bulk solvation problem, there are two regimes for the description of solvation, the continuum model and the detailed molecular dynamics. Do you expect that in clusters the friction model will change as the number of solvent molecules changes from small to large ... 

Solvent continuum models are now routinely used in quantum mechanical (QM) studies to calculate solvation effects on molecular properties and reactivity. In these models, the solvent is represented by a dielectric continuum that in the presence of electronic and nuclear charges of the solute polarizes, creating an electrostatic potential, the so-called reaction field . The concept goes back to classical electrostatic schemes by Martin [1], Bell [2] and Onsager [3] who made fundamental contributions to the theory of solutions. Scholte [4] and Kirkwood [5] introduced the use of multipole moment distributions. The first implementation in QM calculations was reported in a pioneer work by Rivail and Rinaldi [6,7], Other fundamental investigations were carried out by Tapia and Goscinski [8], Hilton-McCreery et al. [9] and Miertus et al. [10], Many improvements have been made since then (for a review,... 

Ruiz-Lopez MF (2008) The multipole moment expansion solvent continuum model a brief review. In Canuto S (ed) Solvation effects on molecules and biomolecules, vol 6. Challenges and advances in computational chemistry and physics. Springer, Netherlands, pp 23-38. doi 10.1007/978-l-4020-8270-2 2... 

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]... 

The final class of methods that we shall consider for calculating the electrostatic compone of the solvation free energy are based upon the Poisson or the Poisson-Boltzmann equatior Ihese methods have been particularly useful for investigating the electrostatic properties biological macromolecules such as proteins and DNA. The solute is treated as a body of co stant low dielectric (usually between 2 and 4), and the solvent is modelled as a continuum high dielectric. The Poisson equation relates the variation in the potential (f> within a mediu of uniform dielectric constant e to the charge density p ... 

The idea of a finite simulation model subsequently transferred into bulk solvent can be applied to a macromolecule, as shown in Figure 5a. The alchemical transformation is introduced with a molecular dynamics or Monte Carlo simulation for the macromolecule, which is solvated by a limited number of explicit water molecules and otherwise surrounded by vacuum. Then the finite model is transferred into a bulk solvent continuum... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

Methods for evaluating the effect of a solvent may broadly be divided into two types those describing the individual solvent molecules, as discussed in Section 16.1, and those which treat the solvent as a continuous medium. Combinations are also possible, for example by explicitly considering the first solvation sphere and treating the rest by a continuum model. Each of these may be subdivided according to whether they use a classical or quantum mechanical description. 

The mixed solvent models, where the first solvation sphere is accounted for by including a number of solvent molecules, implicitly include the solute-solvent cavity/ dispersion terms, although the corresponding tenns between the solvent molecules and the continuum are usually neglected. Once discrete solvent molecules are included, however, the problem of configuration sampling arises. Nevertheless, in many cases the first solvation shell is by far the most important, and mixed models may yield substantially better results than pure continuum models, at the price of an increase in computational cost. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

The model process Eq. (15) has been studied by means of the MINDO/3 method to clarify the energetic conditions during the formation of cyclic reactive intermediates in cationic propagation of alkoxy-substituted monomers. The enthalpies of formation in the gas phase AH°g of both the alternative structures e and /were supplemented by the solvation energies Eso]v for transition into solvent CH2C12 with the assistance of the continuum model of Huron and Claverie which leads to heats of formation in solution AH° s. Table 13 contains the calculated results. 

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. 

It can be seen from Table 26.1 that various methods used to model the effect of a solvent can be broadly classified into three types (1) those which treat the solvent as continuous medium, (2) those which describe the individual solvent molecules (discrete/explicit solvation), and (3) combinations of (1) and (2) treatments. The following section provides a brief introduction to continuum models. 

In addition to the continuum models, the explicit solvation has also been used to quantify the reactivity [48]. In this study, the effect of solvent on the... 

It is established that a detailed understanding of chemical or biochemical systems is impossible without an accurate description of their solvent effects. Hence, tremendous effort has been made in the past to develop solvation models. In this chapter, a brief introduction to continuum solvation models and their applications are presented. Continuum models reasonably predict solvent effect on... 

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