Solvation dispersion energy

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

One may easily see that the quantities Eaq represent the generalization of the expressions for the electrostatic contribution to the solvation free energy for the case of spatial dispersion of the dielectric function e(k, w). Thus, it has been shown in Ref. 5 that the quantity A/ in Eqs. (9) and (10) for the transition probability represents the free energy of the transition. A similar result was obtained later in Ref. 10. 

Part of the motivation behind so straightforward an approach derives from its ready application to certain simple systems, such as the solvation of alkanes in water. Figure 11.8 illustrates the remarkably good linear relationship between alkane solvation free energies and their exposed surface area. Insofar as the alkane data reflect cavitation, dispersion, and the hydrophobic effect, this seems to provide some support for the notion that these various terms, or at least their sum, can indeed be assumed to contribute in a manner proportional to solvent-accessible surface area (SASA). 

C. Amovilli and B. Mennucci, Self-consistent-field calculation of Pauli repulsion and dispersion contributions to the solvation free energy in the polarizable continuum model, J. Phys. Chem. B, 101 (1997) 1051. 

Support to these assumptions has recently come from the analysis of the coupling between electrostatic and dispersion-repulsion contributions to the solvation of a series of neutral solutes in different solvents [31]. It has been found that the explicit inclusion of both electrostatic and dispersion-repulsion forces have little effect on both the electrostatic component of the solvation free energy and the induced dipole moment, as can be noted from inspection of the data reported in Table 3.1. These results therefore support the separate calculation of electrostatic and dispersion-repulsion components of the solvation free energy, as generally adopted in QM-SCRF continuum models. 

Table 3.1 Electrostatic contribution (Ge/e kcal moC1) to the solvation free energy and dipole moment (p Debye) for a series of representative neutral compounds in water (determined from QM-SCRF B3LYP/ aug-cc-pVDZ calculations with and without coupling between electrostatic and dispersion-repulsion components...

C. Curutchet, M. Orozco, F. J. Luque, B. Mennucci and J. Tomasi, Dispersion and repulsion contributions to the solvation free energy comparison of quantum mechanical and classical approaches in the polarisable continuum model, J. Comput. Chem. 27 (2006) 1769-1780. 

Fig. 7 shows the behaviour of these charges with variation of the CC1 distance. As was to be expected in going towards the products, namely CH3NH3 and Cl-, Qn tends to a minimal value while qci tends to unity. The effect of water, the solvent, results in a further enhancement of qci and in a further reduction of qjy with the increase of CC1 distance. This effect is completely due to the solvent polarization when the ionic products begin to form. It is important to note that such small changes in the Mulliken charges (27) and (28) correspond instead to a strong change in the value of the energy along the reaction path (see Fig. 6). Repulsion and dispersion contributions to the solvation free energy do not have any visible effects on the solute wavefunction in this reaction.

The nonpolar solvation free energy is given by the sum of two terms the free energy to form the cavity in solvent filled by the solute and the dispersion attraction between solute and solvent [65,113]. The nonpolar free energy is written as [27]... 

Dispersion forces give rise to an interaction energy in which the potential energy of interaction varies as r , where r is the distance between the centers of the two substances interacting. Thus, the equation for the dispersive energy of interaction may be written as A/r , where A is a constant independent of r. The rapid decrease of such forces with increase of distance from the origin makes it unnecessary to consider dispersion interactions outside the primary solvation shell by then, they have already decreased to an extent that they no longer warrant consideration. Inside the primary hydration sheath, the dispersion interaction can be treated in the same way as the ion-dipole interaction. That is, in the replacement of a water molecule by a nonelectrolyte molecule, one must take into account not only the difference in ion-dipole... 

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).

The calculated individual contributions to the total aqueous solvation free energies of 30 organic compounds are given in Table 1. The electrostatic (SCRF) contributions were calculated using semiempirical AMI (Austin Model 1 [60,61]) method. The dispersion energies were calculated using INDO/1 parameterization [62] and AMI optimized molecular geometries in solution. A comparison of different columns in Table 1 with the experimental solvation... 

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. 

The data presented above demonstrate that the total solvation free energy of organic compounds in aqueous solution can be calculated with some confidence using a minimum number of parameters (the dielectric constant and the solute cavity size contibution for the solvent) and provided that appropriate quantum chemical and statistical physical models are used for the description of the reaction field and dispersion interactions, and the cavity formation in solution. 

The constants K depend upon the volume of the solvent molecule (assumed to be spherical in shape) and the number density of the solvent. a-i2 is the average of the diameters of a solvent molecule and a spherical solute molecule. This equation may be applied to solutes of a more general shape by calculating the contribution of each atom and then scaling this by the fraction of that atom s surface that is actually exposed to the solvent. The dispersion contribution to the solvation free energy can be modelled as a continuous distribution function that is integrated over the cavity surface [Floris and Tomasi 1989]. 

The calculations have been performed using a standard 6-31IG basis set with one more Gaussian d set with exponent 0.2 and one more Gaussian/set with exponent 0.3 added on the chlorine atom for the calculation of the dispersion contribution to the solvation free energy. 

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