The Solvation Energy Term

Under this imperfect assumption, these interactions will be mono- or di-polar in nature and are listed below. 

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It is especially interesting to examine the thermodynamics of reaction (i) for the trityl and dityl (diphenylmethyl) cations as initiating salts for isobutylene because we can thus provide a theoretical explanation of the experimental fact that trityl salts do not initiate isobutylene polymerisation, but dityl salts do Table 2 shows the relevant data. The solvation energy terms have been omitted since on the basis of a... 

Equation 17 may be viewed as an explicit form of the Forster cycle. It depends on both intramolecular and intermolecular factors which determine the extent of the photoacidity. The first factor is the difference between the excited-state and the ground-state proton affinities of the photobase. This difference will be equal to the difference in the intramolecular stabilization of the proton upon the electronic excitation of the acid, and will depend, in general, on the quantum-mechanical properties of the first excited electronic state of the photoacid. The second factor is the difference in the solvation energies of the base and the photoacid upon electronic excitation. The magnitude of the solvation-energy terms will depend in general both on the solvent and the solutes and will depend on the nature of the first electronic state of the photoacid and its conjugate base. 

Stabilization of the syn conformer in the gas phase is explained rather intuitively in terms of the extra stabilization due to increased interactions between the H atom in the OH group and the O atom in C=0 group. As one can see in Figure 5, the extra stabilization in the anti confonner in aqueous solution arises from the solvation energy, especially at the carbonyl oxygen site. 

The continuum models represent a real alternative to the supermolecule approach. In this cases the solvation energy Esolv is assumed to be a sum of individual terms which can be calculated separately (see Eq. (6)). 

Table 5. Portions of individual terms in the solvation energy of different species (see Eq. (6) solvent CH2C12 values inkJ mol-1)...

Hence, the solvation energy change accompanying the disproportionation can compensate the repulsion term. In weakly solvating media, association with counter ions occurs and the disproportionation equilibrium should be considered, for example, as follows ... 

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

The article is organized as follows in Section 2, a general discussion concerning the definition of electrostatic potentials in the frame of DFT is presented. In Section 3, the solvation energy is reformulated from a model based on isoelectronic processes at nucleus. The variational formulation of the insertion energy naturally leads to an energy functional, which is expressed in terms of the variation of the electron density with respect to... 

Using this expression for the induced electron density, expression (83) giving the solvation energy may be transformed as follows from Eqs (71) and (72), the first term of Eq (83) may be rewritten as ... 

On the other hand, Equation (91) may be easily used in conextion with an orbital theory with the electron density and the electrostatic potential obtained from a standard SCRF wavefunction. The third term may be also evaluated from finite difference approximation formula. The charm of Eq (91) comes from the fact that it introduces for the first time, the natural reactivity indices of DFT in the expression of the solvation energy. This feature should be of great importance for the study of solvation effects in... 

In chapter 2, Profs. Contreras, Perez and Aizman present the density functional (DF) theory in the framework of the reaction field (RF) approach to solvent effects. In spite of the fact that the electrostatic potentials for cations and anions display quite a different functional dependence with the radial variable, they show that it is possible in both cases to build up an unified procedure consistent with the Bom model of ion solvation. The proposed procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy. Especially interesting is the introduction of local indices in the solvation energy expression, the effect of the polarizable medium is directly expressed in terms of the natural reactivity indices of DF theory. The paper provides the theoretical basis for the treatment of chemical reactivity in solution. 

In the original James and Healy model, the magnitude of the adjustable chemical term usually swamped the other two terms. By using a much smaller value of the solvation energy as suggested by Levine [27], it was found that the adjustable chemical term could be eliminated in the simulation of a number of metal cation/silica systems [26],... 

The reorganization energy term derives from the solvent being unable to reorient on the same timescale as the electron transfer takes place. Thus, at the instant of transfer, the bulk dielectric portion of the solvent reaction field is oriented to solvate charge on species A, and not B, and over the course of the electron transfer only the optical part of the solvent reaction field can relax to the change in tire position of the charge (see Section 14.6). If the Bom formula (Eq. (11.12)) is used to compute the solvation free energies of the various equilibrium and non-equilibrium species involved, one finds that... 

At this stage, very little is known about the stabilities of various isomers in coordination chemistry and obviously much less about the reasons for them. It is not clear in many instances whether the chelate conformations have any great influence on isomer stability, or how the influence is exerted in the few instances where it has been established. It is conceivable that the conformation exerts its influence through the entropy term rather than as a AH effect. On the other hand, the conformers may have quite different effects on the solvation energies of the complex isomers, and the stability difference may be reflected through this term. 

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