Dielectric medium effects

J. Jortner, Mol. Phys., 5, 257 (1962). Dielectric Medium Effects on Loosely Bound Electrons. 

While this result confirmed the feasibility of the general approach, it did not precipitate wider exploration of dielectric medium effects. Recently, however, Wiberg et al. have incorporated the Onsager self-consistent reaction-field model into ab initio MO theory in an implementation which provides analytical gradients and second derivatives. The model considers just the dipole of the solute molecules and a spherical cavity whose radius is chosen for a given solute molecule from the molecular volume estimated at the 0.001 eB electron-density contour (B is the Bohr radius), plus an empirical constant 0.5 A to account for the nearest approach of solvent molecules [164]. Cieplak and Wiberg have used this model to probe solvent effects on the transition states for nucleophilic additions to substituted acetaldehydes [165]. For each... 

Onsager s SCRF is the simplest method for taking dielectric medium effects into account and more accurate approaches have been developed such as polarizable continuum modes, " continuum dielectric solvation models, - explicit-solvent dynamic-dielectric screening model, - and conductor-like screening model (COSMO). Extensive refinements of the SCRF method (spherical, elliptical, multicavity models) in conjunction with INDO/CIS were introduced by Zerner and co-workers ° as well. 

The isotropic magnetizabUities are in general very little affected by nonelectronic contributions such as zero-point vibrational corrections, dielectric medium effects, or weak intermolec-ular forces. The situation is very different for the magnetizabUity anisotropy, which may display both fairly large electron correlation effects as well as sizeable contributions from nonelectronic contributions. 

Greater deviations which are occasionally observed between two reference electrodes in a medium are mostly due to stray electric fields or colloid chemical dielectric polarization effects of solid constituents of the medium (e.g., sand [3]) (see Section 3.3.1). Major changes in composition (e.g., in soils) do not lead to noticeable differences of diffusion potentials with reference electrodes in concentrated salt solutions. On the other hand, with simple metal electrodes which are sometimes used as probes for potential controlled rectifiers, certain changes are to be expected through the medium. In these cases the concern is not with reference electrodes, in principle, but metals that have a rest potential which is as constant as possible in the medium concerned. This is usually more constant the more active the metal is, which is the case, for example, for zinc but not stainless steel. 

Sn2 reactions with anionic nucleophiles fall into this class, and observations are generally in accord with the qualitative prediction. Unusual effects may be seen in solvents of low dielectric constant where ion pairing is extensive, and we have already commented on the enhanced nucleophilic reactivity of anionic nucleophiles in dipolar aprotic solvents owing to their relative desolvation in these solvents. Another important class of ion-molecule reaction is the hydroxide-catalyzed hydrolysis of neutral esters and amides. Because these reactions are carried out in hydroxy lie solvents, the general medium effect is confounded with the acid-base equilibria of the mixed solvent lyate species. (This same problem occurs with Sn2 reactions in hydroxylic solvents.) This equilibrium is established in alcohol-water mixtures ... 

Many approaches have been used to correlate solvent effects. The approach used most often is based on the electrostatic theory, the theoretical development of which has been described in detail by Amis [114]. The reaction rate is correlated with some bulk parameter of the solvent, such as the dielectric constant or its various algebraic functions. The search for empirical parameters of solvent polarity and their applications in multiparameter equations has recently been intensified, and this approach is described in the book by Reich-ardt [115] and more recently in the chapter on medium effects in Connor s text on chemical kinetics [110]. 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

Effect of off-diagonal dynamic disorder (off-DDD). The interaction of the electron with the fluctuations of the polarization and local vibrations near the other center leads to new terms VeP - V P, Vev - Vev and VeAp - VAPd, VA - VAd in the perturbation operators V°d and Vfd [see Eqs. (14)]. A part of these interactions corresponding to the equilibrium values of the polarization P0l and Po/ results in the renormalization of the electron interactions with ions A and B, due to their partial screening by the dielectric medium. However, at arbitrary values of the polarization P, there is another part of these interactions which is due to the fluctuating electric fields. This part of the interaction depends on the nuclear coordinates and may exceed the renormalized interactions of the electron with the donor and the acceptor. The interaction of the electron with these fluctuations plays an important role in processes involving solvated, trapped, and weakly bound electrons. 

A subject not treated here is the use of distance-dependent effective dielectric constants as a way to take account of the structure in the dielectric medium when a solute is present. This subject has recently been reviewed [120], In the approaches covered in the present chapter, deviations of the effective dielectric constant from the bulk value may be included in terms of physical effects in the first solvation shell, as discussed in Section 2.2. 

As a final topic in this section, we briefly consider the effect of electrolyte concentration on the solvent properties. The linearized Poisson-Boltzmann equation [31,121] can be used instead of (2) and (3) when the dielectric medium... 

If one is interested in changes of the solute molecule, or if the structure of the surrounding solvent can be neglected, it may be sufficient to regard the solvent as a homogeneous dielectric medium, as was done in the older continuum theories, and to perform a quantum mechanical calculation on the molecule with a modified Hamiltonian which accounts for the influence of the solvent as has been done by Hylton et al. 18 5>. Similarly Yamabe et al. 186> substituted dipole-moment operators for the solvent in their perturbational treatment of solvent effects on the activation energy in the NH3 + HF reaction. 

Usually, the most general nonspecific effects of dipole-orientational and electronic polarization of the medium are discussed, and the results of the theory of relaxational shifts developed under the approximation of a continuous dielectric medium may be used.(86 88) The shift of the frequency of the emitted light with time is a function of the dielectric constant e0, the refractive index n, and the relaxation time xR ... 

Studies of medium effects on hexacyanoferrate(II) reductions have included those of dioxygen,iodate, peroxodisulfate, - [Co(NH3)5(DMSO)] +, and [Co(en)2Br2]+. Rate constants for reaction with dioxygen depended strongly on the electron-donor properties of the organic cosolvent. Rate constants for reduction of peroxodisulfate in several binary aqueous media were analyzed into their ion association and subsequent electron transfer components. Rate constants for reduction of [Co(en)2Br2] in methanol water and dioxan water mixtures were analyzed by a variety of correlatory equations (dielectric constant Grunwald-Winstein Swain Kamlet-Taft). 

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