Onsager cavity radius

FL, and the difference in dipole moments determined from the plot is 2.36 D if the Onsager radius is 0.33 nm [53]. The Onsager cavity radius was obtained from molecular models where the molar volumes were calculated by CAChe WS 5.0 computer program. The simplest method to estimate the cavity radius is to assume a = (3y/47r) 3, where V is the volume of the solute. 

Kawski A, Kuklinski B, Bojarski P (2002) Z Naturforsch A 57A 716 Suppan P, Ghoneim N (1997) Solvatochromism. The Royal Society of Chemistry, London Koutek B (1978) Collect Czech Chem Common 43 2368. Onsager cavity radius ao = 4.41 A, from DPT Cam-B3LYP/6-31 + G(d)//IEF-PCM(UFF) calculations (present work) Ceron-Carrasco IP, Jacquemin D, Laurence C, Planchat A, Reichardt C, Sratdi K (2014) J Phys Chem B 118 4605... 

Optimize the two equilibrium structures in solution, using the Onsager SCRF method and the RHF/6-31G(d) model chemistry. You ll of course need to determine the appropriate cavity radius first. 

The physical significance of these variables is apparent when they are evaluated in the Onsager cavity description of solvation, which treats the solute as a sphere (which we will assume here is unpolarizable) of radius a. The solvent is modeled as a uniform dielectric medium with a static dielectric constant s and an optical dielectric constant op. The following relationships apply in the Onsager cavity description... 

The aqueous solvation free energies of the four tautomers available to the 5-(2H)-isoxazolone system have also been studied using a variety of continuum models (Table 7). Hillier and co-workers - " have provided data at the ab initio level using the Born-Kirkwood-Onsager model, the classical multipolar expansion model (up to I = 7), and an ab initio polarized continuum model. We examined the same BKO model with a different cavity radius and the AMl-SMl and AMl-SMla o- models, and Wang and Ford have performed calculations with the AMl-PCM model. 

The cavity size in the Bom/Onsager/Kirkwood models strongly influences the calculated stabilization. Unfortunately, there is no consensus on how to choose the cavity radius. In some cases, the molecular volume is calculated from the experimental density of the solvent and the cavity radius is defined by equating the cavity volume to the molecular volume. Alternatively, the cavity size may be derived from the (experimental) dielectric constant and the calculated dipole moment and polarizability. In any case, the underlying assumption of these models is that the molecule is roughly spherical or ellipsoidal, which is only generally true for small compact molecules. 

Notably, the use of the macroscopic dielectric constant s = Sq in the last formula is justified only when the lifetime of the solute molecule in a given (v-th) state is much longer than the rotational-vibrational relaxation time of the solvent at given temperature. This is not a valid assumption in the case of the Franck-Condon states, which have the lifetime much shorter than the rotational-vibrational relaxation time of the solvent. Therefore, the solvent is only partially relaxed for these states and the corresponding reaction field is characterized by the dielectric constant at infinite frequency of external electric field, 8 . By inserting the expression for the reaction field [11.1.36] into the equation [11.1.18] and assuming that the static polarizability of the solute molecule is approximately equal to the one third of the cube of Onsager s cavity radius... 

AF Lagalante, RL Hall, TJ Bruno. Kamlet-Taft solvatochromic parameters of tbe sub- and supercritical fluorinated ethane solvents. J Phys Chem B 102 6601, 1998. K Takahashi, K Abe, S Sawamura, CD Jonah. Spectroscopic study of 4-aminoben-zophenone in supercritical CF3H and CO2 local density and Onsager s reaction cavity radius. Chem Phys Lett 282 361, 1998. 

In each term of Eq. (17.39) the factors depend only on the properties of the solute m (the Onsager spherical cavity radius ao, the electric dipole moments in the ground and excited state the electric polarisabilities in the ground and... 

The simplest SCRF model is the Onsager reaction field model. In this method, the solute occupies a fixed spherical cavity of radius Oq within the solvent field. A dipole in the molecule will induce a dipole in the medium, and the electric field applied by the solvent dipole will in turn interact with the molecular dipole, leading to net stabilization. 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

R is the radius of the cavity, p and a are the dipole moment and polarizability of the solute, and s the dielectric constant of the solvent. Equation (35) does address the polarization of the solute molecule by the reaction field, although not carrying this to self-consistency. (It is interesting that Onsager s paper, the sixth-most-cited in the history of the Journal of the American Chemical Society, was rejected by the Physikalische Zeitshrift, to which it had initially been submitted.)89... 

While Onsager s formula has been widely used, there have also been numerous efforts to improve and generalize it. An obvious matter for concern is the cavity. The results are very sensitive to its size, since Eqs. (33) and (35) contain the radius raised to the third power. Within the spherical approximation, the radius can be obtained from the molar volume, as determined by some empirical means, for example from the density, the molar refraction, polarizability, gas viscosity, etc.90 However the volumes obtained by such methods can differ considerably. The shape of the cavity is also an important issue. Ideally, it should be that of the molecule, and the latter should completely fill the cavity. Even if the second condition is not satisfied, as by a point dipole, at least the shape of the cavity should be more realistic most molecules are not well represented by spheres. There was accordingly, already some time ago, considerable interest in progressing to more suitable cavities, such as spheroids91 92 and ellipsoids,93 using appropriate coordinate systems. Such shapes... 

Sules respectively, and a is the radius of the cavity in which the solute nolecule resides. The latter is defined by Onsager s reaction field Assuming the solvent as continuous dielectric. 

Within the dielectric continuum model, the electrostatic interactions between a probe and the surrounding molecules are described in terms of the interaction between the charges contained in the molecular cavity, and the electrostatic potential these changes experience, as a result of the polarization of the environment (the so-called reaction field). A simple expression is obtained for the case of an electric dipole, /a0, homogeneously distributed within a spherical cavity of radius a embedded in an anisotropic medium [10-12], by generalizing the Onsager model [13]. For the dipole parallel (perpendicular) to the director, the reaction field is parallel (perpendicular) to the dipole, and can be calculated as [10] ... 

For comparison, the results obtained using the Maier-Meier theory [4] are also shown this is a generalization of the Onsager model [13] to uniaxial media. The same dipole moment used for the calculations with the molecular shaped cavity was assumed, and the radius a was taken to be 3.9 A, a value derived from the density of the system. Improvement of the predictions, when the sphere is replaced by a molecular shaped... 

The expression most commonly used in fluorescence spectroscopy is, however, the somewhat simphfied Eq. (6-5b), first developed by Lippert [47, 488] and Mataga [14, 489]. It is based on Onsager s reaction-field theory, which assumes that the fluorophore is a point dipole residing in the center of a spherical cavity with radius a in a homogeneous and isotropic dielectric with relative permittivity e,. The so-called Lippert-Mataga equation is as follows ... 

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