Dispersive solvation energy

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. 

For solvent models where the cavity/dispersion interaction is parameterized by fitting to experimental solvation energies, the use of a few explicit solvent molecules for the first solvation sphere is not recommended, as the parameterization represents a best fit to experimental data without any explicit solvent present. 

Given the diversity of different SCRF models, and the fact that solvation energies in water may range from a few kcal/mol for say ethane to perhaps 100 kcal/mol for an ion, it is difficult to evaluate just how accurately continuum methods may in principle be able to represent solvation. It seems clear, however, that molecular shaped cavities must be employed, the electiostatic polarization needs a description either in terms of atomic charges or quite high-order multipoles, and cavity and dispersion terms must be included. Properly parameterized, such models appear to be able to give absolute values with an accuracy of a few kcal/mol." Molecular properties are in many cases also sensitive to the environment, but a detailed discussion of this is outside the scope of this book. ... 

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)). 

Floris, F.M. Tomasi, J. Pascal-Ahuir, J.L., Dispersion and repulsion contributions to the solvation energy refinements to a simple computational model in the continuum approximation, J. Comp. Chem. 1991,12, 784-791... 

Large anions, such as I- and CIO4, have a relatively weak tendency to accept hydrogen bonds. However, they are highly polarizable and interact to a fair extent by dispersion forces (London forces) with the molecules of aprotic solvents, which are also considerably polarizable. Thus, for large anions, the solvation energies in protic solvents (water, alcohols) and those in dipolar aprotic solvents (AN, DMF, DMSO) are not as different as in the case of small anions (Table 2.4). 

Christopher J. Cramer and their co-workers during the last decade [61,100, 55, 56], In SMx, terms responsible for cavity foimation. dispersion, solvent structure and local field polarization are present [51,57], The solvation energy is obtained via the usual approximation that the solute, treated at the quantum mechanical level, is immersed in an isotropic polarizable continuum representing the solvent. Therefore the standard free energy of the solute in solution can be expressed as ... 

Electrostatics is certainly the most important interaction between a dielectric medium and a molecular species. Therefore, it has also been investigated extensively for interfaces as shown in the previous section. Nonelectrostatic forces are often neglected in the bulk solution since their contribution to the solvation energy is often limited because of reciprocal cancellation and their effect on molecular properties is small [16] (repulsion and particularly dispersion) or zero (the present understanding of cavitation is strictly empirical). 

The electrostatic solvation energy is only a part of the total solvation energy. Cavitation, dispersion and repulsion terms must be added. We show below that the MPE method leads to similar electrostatic energies than the polarizable continuum model (PCM) of Tomasi and co-workers [10], provided the same cavities are used. Therefore, non-electrostatic terms in these methods may be computed using the same computational strategies [15]. We emphasize the fact that accurate non-electrostatic contributions are often difficult to compute since they are based on parameterized formulae that cannot be directly compared to experiment. The obtained data must therefore be used with prudence, especially if they are expected to play a major role in the process under study. Fortunately, in many circumstances, non-electrostatic terms are small and/or vary little, so that they can be neglected. Tunon et al. [80] developed a parameterized expression for the MPE method using an expression of the type... 

The remaining portion of the solvation energy, energies attributable to cavitation, dispersion, and other short-range forces, is usually treated in an empirical fashion. All of these effects are usually grouped together, in a term called AG ds, and computed as... 

F. Floris and J. Tomasi, /. Comput. Chem., 10, 616 (1989). Evaluation of the Dispersion Contribution to the Solvation Energy. A Simple Computational Model in the Continuum Approximation. 

F. M. Floris, A. Tani, and J. Tomasi, Chem. Phys. 169, 11 (1993). Evaluation of the Dispersion-Repulsion Contributions to the Solvation Energy. Calibration of the Uniform Approximation with the Aid of RISM Calculations. 

The effect of the solvent on the abundance of the conformers of 2-meth-oxyoxane is demonstrated in Table XIV, where molar fractions of the axial form are compared with available experimental data already shown in Table VI. For a number of solvents, the agreement is remarkably good. Although the results indicate a decreased abundance of the a form of 2-methoxyoxane with increase in the dielectric constant of the solvent, the dependence is not a simple one. The calculations also reproduce such subtle factors as the pronounced effect of chloroform when compared with other solvents of similar polarity and, conversely, a relatively weak effect of dimethyl sulfoxide in comparison to less-polar solvents. The analysis of the role of individual solvation energy terms in the total energy suggests that the conformationally most important term is the contribution of electrostatic interactions that stabilize the ap conformations. Conversely, the dispersion term shows only a shght conformational dependence. 

A short overview of the quantum chemical and statistical physical methods of modelling the solvent effects in condensed disordered media is presented. In particular, the methods for the calculation of the electrostatic, dispersion and cavity formation contributions to the solvation energy of electroneutral solutes are considered. The calculated solvation free energies, proceeding from different geometrical shapes for the solute cavity are compared with the experimental data. The self-consistent reaction field theory has been used for a correct prediction of the tautomeric equilibrium constant of acetylacetone in different dielectric media,. Finally, solvent effects on the molecular geometry and charge distribution in condensed media are discussed. 

Figure 1. Dependence of the AMI SCa SCRF Calculated Electrostatic Solvation Energies (E), INDO/1 SCa Calculated Dispersion Energies (D) and SPT Spherical Cavity Formation Free Energies (C) on the Cavity Radius for Methanol (a) and Acetonitrile (b).

AMI SCRF Calculated Electrostatic Solvation Energies, Eei, INDO/1 Calculated Dispersion Energies, Edisp, SPT Cavity Formation Free Energies, AGcav, and Experimental Solvation Free Energies, AG(exp) (kcal/mol), [63] of 30 Organic Compounds in Aqueous Solution. 

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