Reaction field INDEX

In all cases the dielectric constant used is that of the pure solvent. Neglect of the solute is usually justified by its low concentration and the assumption that any necessary correction would be additive. In at least a few cases where the first two expressions have been employed the linearity of the results is to some extent dependent on how closely the refractive index of the solute meets the conditions n2 = 2.0 or 2.5 a situation not always recognized by the investigators. In one instance attempts have been made to clarify the role of solvent reaction field by examining solutes with different dipole moment orientations relative to the bonds involving coupled atoms. 

Ihrig and Smith extended their study by running a regression analysis including reaction field terms, dispersion terms and various combinations of the solvent refractive index and dielectric constant. The best least squares fit between VF F and solvent parameters was found with a linear function of the reaction field term and the dispersion term. The reaction field term was found to be approximately three times as important as the dispersion term and the coefficients of the terms were opposite in sign. 

The Kamlet-Taft u polarity/polarizability scale is based on a linear solvation energy relationship between the n it transition energy of the solute and the solvent polarity ( 1). The Onsager reaction field theory (11) is applicable to this type of relationship for nonpolar solvents, and successful correlations have previously been demonstrated using conventional liquid solvents ( 7 ). The Onsager theory attempts to describe the interactions between a polar solute molecule and the polarizable solvent in the cybotatic region. The theory predicts that the stabilization of the solute should be proportional to the polarizability of the solvent, which can be estimated from the index of refraction. Since carbon dioxide is a nonpolar fluid it would be expected that a linear relationship... 

This approach is based on the introduction of molecular effective polarizabilities, i.e. molecular properties which have been modified by the combination of the two different environment effects represented in terms of cavity and reaction fields. In terms of these properties the outcome of quantum mechanical calculations can be directly compared with the outcome of the experimental measurements of the various NLO processes. The explicit expressions reported here refer to the first-order refractometric measurements and to the third-order EFISH processes, but the PCM methodology maps all the other NLO processes such as the electro-optical Kerr effect (OKE), intensity-dependent refractive index (IDRI), and others. More recently, the approach has been extended to the case of linear birefringences such as the Cotton-Mouton [21] and the Kerr effects [22] (see also the contribution to this book specifically devoted to birefringences). 

Hie polarizability a(-o) a)) is involved in several linear optical experiments including refractive index measurements. Equation (93) shows that the solute molecule experiences a local field which is larger than the macroscopic field by the cavity field factor/ " and by the reaction field factor For typical media the magnitude of the product is of the order of 1.3-1.4. In the case of... 

The spectral position of absorption and fluorescence are influenced by the dielectric properties of the medium in which observations are made. Figure 5 shows that the vapour phase 0-0 bands in absorption and fluorescence of a molecule are identical, whereas in solution with solvent of static dielectric constant e, refractive index n, the bands are no longer coincident. The differences can be rationalized as follows. From Onsager theory, a solute molecule of dipole moment ju in a spherical cavity of radius a polarizes the dielectric of the solvent, producing a reaction field. This is given for the ground-state of the solute molecule (of dipole moment iiq), by (22). Upon excitation, and invoking the Franck-Condon principle, the electronic excitation is much more rapid than the dielectric relaxation time of... 

HB interactions, is claimed to lie in different responses to solvent polarizability effects. Likewise, in the relationship between the Ji scale and the reaction field functions of the refractive index (whose square is called the optical dielectric constant e ) and the dielectric constant, the aromatic and the halogenated solvents were found to constitute special cases." This feature is also reflected by die polarizability correction term in eq. [13.1.2] below. For the select solvents, the various polarity scales are more or less equivalent. A recent account of the various scales has been given by Marcus, and in particular of by Laurence et al., and of Ey by Reichardt. ... 

A UV-visible spectroscopic study of 3 and related substances revealed a strong solvatochromic effect, which served as the basis of the establishment of a solvent polarity scale (Buncel and Rajagopal, 1989, 1990,1991). The theoretical study of Rauhut et al. (1993) was based on AMI methodology (Dewar and Storch, 1985,1989) but used a double electrostatic reaction field in a cavity, dependent on both the relative permittivity and the refractive index. Nuclear motions interact with the medium through the relative permittivity, but electronic motions are too fast only the extreme high-frequency part of the dielectric constant is relevant. These authors were able to evaluate solvent-specific dispersion contributions to the solvation energy. The calculations reproduced satisfactorily the experimental solvatochromic results for 3 in 29 different solvents. The method has also been successfully applied to other solvatochromic dyes, including Reichardt s .j,(30) betaine. 

Now suppose that excitation of the chromophore changes its dipole moment to Uhl,. Although the solvent molecules cannot reorient instantaneously in response, the dielectric constant includes electronic polarization of the solvent in addition to orientational polarization, and changes in electronic polarization can occur essentially instantaneously in response to changing electric fields. The high-frequency component of the dielectric constant is the square of the refractive index (n) (Sects. 3.1.4 and 3.1.5). If we subtract the part of the reaction field that is attributable to electronic polarization, the part due to orientation of the solvent Eor) can be written... 

Several theoretical approaches to the description of dynamical solvent effects have been proposed within the framework of PCM of other continuum models [41]. The simplest, and most commonly used, treatment involves the definition of two limit time regimes equilibrium (EQ) and nonequilibrium (NEQ). In the former all the solvent degrees of freedom are in equilibrium with the electron density of the excited-state density, and the solvent reaction field depends on the static dielectric constant of the embedding medium. In the latter, only solvent electronic polarization (fast degrees of freedom) is in equilibrium with the excited-state electron density of the solute, while the slow solvent degrees of freedom remain equilibrated with the groimd-state electron density. In the NEQ time regime the fast solvent reaction field is ruled by the dielectric constant at optical frequency (Copt, usually related to the square of the solvent refractive index). 

Various models have been developed for explaining the solvent-induced changes in the Xe shielding. For example, it has been proposed, based on the reaction field theory of Onsager, that the medium shift is proportional to the function f(n) = [ n - 1)/ 2n +l)] (this is called the van der Waals continuum model), where n is the refractive index of the solvent. Part of the experimental data indeed follows this... 

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