Molecular polarizability, influence

In Section 7.1.2 a method for the calculation of mean molecular polarizability was presented. Mean molecular polarizability can be calculated from additive contributions of the atoms in their various hybridization states in a molecule (see Eq. (6)). Mean molecular polarizability, a, expresses the magnitude of the dipole moment, fi, induced into a molecule imder the influence of an external field, E (Eq. (15))... 

Because P depends on the molecular polarizability a, the activation energy may change under the influence of the introduced charge-transfer dipoles between dye and acceptor. 

The model employed for the hydration force implies a continuum, even for low separation distances between particles. It was also assumed that the hydration, doublelayer, and van der Waals interactions are additive. The double layer affects the hydration force mainly because of the decrease of the molecular polarizability by large electric fields. However, in the present case, in the vicinity of the surface the electric field due to the double layer is smaller than E by an order of magnitude and hence its influence on the hydration force can be neglected at small separation distances. 

The molecular polarizabilities can be interpreted quantum mechanically by using the methods of time-dependent perturbation theory. Under the influence of the electric fleld, the molecular ground state ( g)) is changed by admixture of excited states ( /), m). ..). Collections of such expressions are available in the literature (Ward, 1965 Orr and Ward, 1971 Bishop, 1994b). A comprehensive treatment has also been given by Flytzanis (1975). Here, we only quote the results for the linear optical polarizability a(-a) a)) and the second-order polarizability /3(-2a) o), co). The linear optical polarizability may be represented by the sum of two-level contributions (45). 

Sung and Lazar [173], and Birks [82] depend on a parabolic rather than a linear fit of the data (as mentioned in Section 3.2) and may still apply for restricted systems indeed, some such limitation applies to theories on most aspects of carcinogenesis. Thus Cammerata, Yau and Rogers [175] presented relations between ionization potentials—molecular polarizabilities and partition coefficients. The inference of a link between solubility theories and MO indices is not unexpected in view of the influence of molecular polarizability on dispersion-attraction interaction energies in solution. An approximate, though rather less relevant, inverse dependence of ionization potential on polarizability has been noted [176]. 

It is, therefore, obvious that the enormous enhancement in scattering observed in SERS can arise from an increase in either the electromagnetic field or molecular polarizability, or both. The theory of electromagnetic enhancement in SERS assumes that molecules of an adsorbate at a metallic surface are under the influence of an electromagnetic field... 

The electric polarization from internal continuum (EPIC) model has been developed to accurately predict the polarizability tensor of molecules ". The EPIC approach uses an intramolecular effective dielectric constant, together with associated atomic radii, to represent the detailed molecular polarizability. For a single atom of radius R in vacuum under the influence of a uniform electric field (E), the polarizability is given by the electric fleld prefactor of the induced dipole moment (Sin is the inner dielectric) ... 

The first term in Eqs. [28]-[31] is related to hydrophobicity, whereas hydrophilicity is encoded by the others terms. The third term in Eqs. [30] and [31] is introduced to incorporate effects of molecular polarizability. Calculations of partition coefficients for 90 model compounds indicate that Eq. [30] is the best one and that a fast and cheap method to calculate atomic charges (e.g., the Gasteiger-Marsili approach>26) is perfectly adequate. The accuracy obtained with Eq. [30] is comparable to that reported by Bodor et al. 29,i3o addition, this method yields distinct values for geometric isomers or different conformers of flexible compounds, indicating that it is able to determine the influence of 3D arrangements of atoms on the overall lipophilic character of a structure. 

The purpose of this Chapter is to describe the dielectric properties of liquid crystals, and relate them to the relevant molecular properties. In order to do this, account must be taken of the orientational order of liquid crystal molecules, their number density and any interactions between molecules which influence molecular properties. Dielectric properties measure the response of a charge-free system to an applied electric field, and are a probe of molecular polarizability and dipole moment. Interactions between dipoles are of long range, and cannot be discounted in the molecular interpretation of the dielectric properties of condensed fluids, and so the theories for these properties are more complicated than for magnetic or optical properties. The dielectric behavior of liquid crystals reflects the collective response of mesogens as well as their molecular properties, and there is a coupling between the macroscopic polarization and the molecular response through the internal electric field. Consequently, the molecular description of the dielectric properties of liquid crystals phases requires the specification of the internal electric field in anisotropic media which is difficult. 

Here we discuss a joint theoretical and experimental study of the influence of solvent polarity on the second-order molecular polarizability p of p-nitroaniline and the push-pull polyene l,l-dicyano-6-dibutylamine-hexa-triene [144]. The calculations are carried out at the Har-tree-Fock ab initio level on the basis of an expanded self-consistent reaction field approach and are compared to hyper-Rayleigh scattering measurements performed in solvents with a wide range of dielectric constants. 

Eq. (8.45) shows that for an ordinary Raman experiment the absolute differential Raman scattering cross sections can be expressed in terms of derivatives of the molecular polarizability invariants a and y with respect to normal coordinates. These derivatives contain valuable information about the variation of molecular polarizability with vibrational motion. Gas-phase Raman scattering cross sections are most suited for intensity analysis since at low partial pressure of the sampling gas these quantities are not influenced by effects of intermolecular interactions, thus reflecting properties of individual molecules. 

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

Epoi also relies on a local picture as it uses polarizabilities distributed at the Boys LMOs centroids [44] on bonds and lone pairs using a method due to Garmer et al. [35], In this framework, polarizabilities are distributed within a molecular fragment an therefore, the induced dipoles do not need to interact together (like in the Appleq-uist model) within a molecule as their value is only influenced by the electric fields from the others interacting molecules. 

Our objective has been to develop methods that allow the calculation of various electronic parameters such as partial atomic charge, q, electronegativity, polarizability, a, for each atom of a molecule. In this way, the values assigned to an atom not only reflect the type of the atom, but also the particular molecular environment into which this atom is embedded (Fig. 18). The electronic parameters assigned to the atoms of a bond will then be used to arrive at a quantitative value for this bond which reflects its reactivity. A detailed description of a reaction will also have to include parameters characteristic of the reagent in order to account for its influences on bond breakage and formation. 

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