Molar polarizability,effect

CMR represents the overall calculated molar refractivity. Its negative sign bring out a steric effect. It is interesting to note here that there is a high mutual correlation between ClogF and CMR (r= 0.966). Thus, it is very hard to predict for this data set if it is a negative hydrophobic or a polarizability effect. 

Dielectric polarization is the polarized condition in a dielectric resulting from an applied AC or DC field. The polarizability is the electric dipole moment per unit volume induced by an applied field or unit effective intensity. The molar polarizability is a measure of the polarizability per molar volume thus it is related to the polarizability of the individual molecules or polymer repeat unit. 

As the molar polarizabilities represent an easily available experimental set of data, the expressions above become important for the theoretical evaluation of molecular response properties in fact they represent the most direct quantities to compare with the computed results obtained applying a given model for the solvent effects. 

In this section, we investigate the relations between the macroscopic susceptibilities and the molecular polarizabilities. Consistent microscopic interpretations of many of the non-linear susceptibilities introduced in Section 2 will be given. Molar polarizabilities will be defined in analogy to the partial molar quantities (PMQ) known from chemical thermodynamics of multicomponent systems. The molar polarizabilities can be used as a consistent and general concept to describe virtually all linear and non-linear optical experiments on molecular media. First, these quantities will be explicitly derived for a number of NLO susceptibilities. Physical effects arising from will then be discussed very briefly, followed by a survey of experimental methods to determine second-order polarizabilities. 

The quadratic effect of an externally applied field on the refractive index n is described by the third-order susceptibility (- ) w,0,0) (Kerr susceptibility). The two independent components Yilzz and x ixx can be interpreted in terms of molar polarizabilities. The results for 2 symmetric molecules with only one significant component of the second-order polarizability are expressed in (113) and (114),... 

Van der Waals interactions are the most difficult ones with respect to both theoretical and experimental evaluations. Computational descriptions need to include polarization functions and solvent effects [114, 115]. Experimentally determined stability constants also may be due to electrostatic effects, in particular with stacking between aromatic units, and to solvents effects. The latter may dominate in water, which at the same time is the most suitable medium for dispersive interactions due to its low molar polarizability. The problems are most evident with recent in-... 

MRx is the calculated molar refractivity of X-substituents and its negative coefficient suggests steric hindrance. 7 is an indicator variable, which acquired a value of 1 for amides and 0 for the esters. The negative coefficient of the indicator variable suggests an unfavorable cytotoxic effect for the amide derivatives against this cancer cell line. It is interesting to note here that there is a high mutual correlation between nx and MRx (r = 0.877). Thus, it is very hard to predict for this data set if it is a positive hydrophobic or polarizability effect of the X-substituents. We derived Eq. 17a with MRx and finally preferred Eq. 17 on the basis of their statistics, which are better than those of Eq. 17a ... 

P = An empirical constant, called an affinity constant, whose value is defined as unity for benzene. P values are in effect scaling divisors between benzene and some other solvent Affinity in the D/R equation means similarity of the ability of the solvent to be polarized (Box A2.3) to the same level as is benzene. The reference of Footnote 15 (pages 344 and 354) reports a correlation of P with molar polarizibility (Pe). 

The Kerr effect may be described as follows. Let b, b2, and b-j be the three imaginary principal axes at right angles. The mean molar polarizability of the molecule ot is defined as... 

Isotope Effects on Dipole Moments, Polarizability, NMR Shielding, and Molar Volume... 

Abstract Although the electronic structure and the electrical properties of molecules in first approximation are independent of isotope substitution, small differences do exist. These are usually due to the isotopic differences which occur on vibrational averaging. Vibrational amplitude effects are important when considering isotope effects on dipole moments, polarizability, NMR chemical shifts, molar volumes, and fine structure in electron spin resonance, all properties which must be averaged over vibrational motion. 

In the equation s is the measured dielectric constant and e0 the permittivity of the vacuum, M is the molar mass and p the molecular density, while Aa and A (po2) are the isotope effects on the polarizability and the square of the permanent dipole moment respectively. Unfortunately, because the isotope effects under discussion are small, and high precision in measurements of bulk phase polarization is difficult to achieve, this approach has fallen into disfavor and now is only rarely used. Polarizability isotope effects, Aa, are better determined by measuring the frequency dependence of the refractive index (see below), and isotope effects on permanent dipole moments with spectroscopic experiments. 

Using Equation 12.12 one obtains (AA/A — Av /v 2) = (Aao/ao). We see that precise refractive index differences measured over a reasonable range of wavelengths allow the recovery of the polarizability isotope effect (i.e. the isotope effect on the electric field induced dipole moment), provided the molar volume and its isotope effect are available. 

Van Hook, W. A. and Wolfsberg, M., Comments on H/D isotope effects on polarizabilities. Correlation with virial coefficient, molar volume and electronic second moment isotope effects. Z Naturforsch. 49A, 563 (1994)... 

MR, the molar refractivity, which parameterizes polarizability and steric effects and Verloop s parameters, which are steric substituent values calculated from bond angles and distances. 

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