Continuum dielectric theory

Consider an alchemical transformation of a particle in water, where the particle s charge is changed from 0 to i) (e.g., neon sodium q = ). Let the transformation be performed first with the particle in a spherical water droplet of radius R (formed of explicit water molecules), and let the droplet then be transferred into bulk continuum water. From dielectric continuum theory, the transfer free energy is just the Born free energy to transfer a spherical ion of charge q and radius R into a continuum with the dielectric constant e of water ... 

Chipman M (2002) Computation of pKa from Dielectric Continuum Theory. J Phys Chem A 106 7413-7422. 

Returning to x, eq 6 is available from dielectric continuum theory. In eq°6, and Dg are the optical and static... 

In turning to cases where strong, specific interactions with the solvent are expected, the picture can change considerably and it is no longer obvious that dielectric continuum theory provides a reasonable basis for calculating x It is apparent that dielectric continuum theory can not be used to account for solvent induced variations in AE but, as mentioned earlier, there is hope that a combination of dielectric continuum theory and the use of empirically determined solvent parameters can provide a framework for understanding solvent effects. The importance of specific solvent effects shows up dramatically for MLCT or LMCT transitions in complexes such as shown below (21) ... 

A third goal of the research is to measure the distance over which surface effects extend into solution. These experiments face several technical challenges, but if experf-ments are properly designed, results would provide the very distance versus strength of interaction information necessary for incorporating molecular contributions into existing dielectric continuum theories of surface solvation. 

Ao varies with (l/Z)op - 1/DS) and for polar solvents Dop 4 Ds, e.g. Dop = 2.028 and Ds = 8.9 for dichloromethane. As a consequence, dielectric continuum theory predicts electron transfer rates to be enhanced in solvents like CH2C12 which are electronically relatively highly polarizable. 

In terms of traditional Transition State Theory (TST) for solution reactions [40,41], in which e.g. the activation free energy AG can be estimated with equilibrium solvation dielectric continuum theories [42-46], the nonequilibrium or dynamical solvation aspects enter the prefactor of the rate constant k, or in terms of the ratio of k to its TST approximation kTST, k, the transmission coefficient, k and kTST are related by [41]... 

The properties of a number of these photosensitizers have been studied in aqueous and sodium lauryl sulfate micellar media,139 their electronic and emission spectra, electrochemistry and quenching of their luminescence by HgCl2 in both media.138 In some cases solvent dependence of MLCT excited state lifetimes has been observed, e.g. in [Os(bipy)2py2]2+, [Os(bipy)2(NCMe)2]2+ and [Os(bipy)j(Ph2PC6H4PPh2]2+. For these, dielectric continuum theory has been invoked to explain such solvent dependence, and it is necessary to assume that the excited electron in the excited state is localized on one ligand rather than delocalized over all three.140... 

In asymmetric complexes of the type [(bpy)2RuCl(pi-pyz)Ru-(NH3)4L]4+, studies (94) revealed that there is a solvent donor-number (DN)-dependent contribution to the Frank-Condon barrier of approximately 0.006 eV/DN, which completely overwhelms the dielectric-continuum-theory-derived (l/Dop-l/Ds) solvent dependence typically observed in symmetrical dimers. In this case, variations in MMCT Eop with solvent give linear correlations when plotted against solvent dependent AEm, the difference in potential between the two ruthenium(III/II) couples, as shown in Fig. 10. The microscopic origin of this solvent effect was described by Curtis, Sullivan, and Meyer (122) in their study of solvatochromism in the charge transfer transitions of mononuclear Ru(II) and Ru(III) ammine complexes. The dependence... 

One should also mention the work on electroreduction of t-nitrobutane in AN, DMF, DMSO and pyridine by Corrigan and Evans [182]. The results obtained were not in agreement with the dielectric continuum theory. They explained their results by ion-pairing between the anion radical product and cations of the background electrolyte. 

When the reaction coordinate // corresponds to the solvent polarization mode, the dielectric continuum theory analog of Eq. 29 is ... 

In dielectric continuum theory, the solute density is placed in a cavity embedded in a dielectric continuum solvent characterized by the electronic and inertial dielectric constants Ego and , respectively. Typically, the solvent polarization potential field is assumed to respond linearly to the change in solute charge density. The free energy of the system for fixed solute nuclei is a functional of the solvent inertial polarization potential field... 

Solvent effects have been uniquely important in ET studies. Marcus splits the vertical reorganization energy into solvation (often called /l0(uter) or s(oivent)) and internal (often called /h(nner) or /W(ibrationai)) components using dielectric continuum theory and introduced using the following equation to predict As ... 

Dielectric continuum theory obviously cannot separate ls from lv for bis(dini-trogen) radical cations, because plots of fmax ( = /.) versus y for them are far from being linear. There is an obvious effect that correlates with solvent donicity, because good donor solvents like DMF and DMSO have larger fmax values than acetonitrile, which has a larger y value. We have found that for the rather limited set of solvents that we have employed, fmax can be converted to a linear relationship with y using the following relationship ... 

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