Average molecular polarizability

TABLE 8. Estimated average molecular polarizabilities, based ou empirical hybrid atom aud group values (Table 7) ... 

In the work of Famini and Wilson,a molecular volume, Vmc, (units of 100 A ) is used to model the cavity term that measures the energy required to create a solute-molecule sized cavity in the solvent. The dipolarity/polarizability term, which attempts to account for dispersion-type interactions, is modeled by the polarizability index, tij, (unitless). This index is defined as the average molecular polarizability divided by the molecular volume, a/Vmc, and helps account for the correlation between polarizability and molecular volume. 

The negative signs are physically reasonable because these additional parameters would be expected to be associated with increased intramolecular attractions. The authors provided no measure of intercorrelation indeed, one might expect some correlation of a, the average molecular polarizability, with the presence of C=0, COOH, NO2, and CN groups. The counting descriptors are not QM quantities their inclusion is not philosophically satisfying, but they do improve the fit. 

Liquid Phase Calculations of the Linear Response. The data in Table 5 for the isotropic polarizability, derived formally via the Lorentz-Lorenz equation (1) from the measured refractive index, shows that the assumption that individual molecular properties are largely retained at high frequency in the liquid is very reasonable. While the specific susceptibilities for the gas and liquid phases differ, once the correction for the polarization of the surface of a spherical cavity, which is the essential feature of the Lorentz-Lorenz equation, has been applied, it is clear that the average molecular polarizabilities in the gas and liquid have values which always agree within 5 or 10%. 

Here y is average molecular polarizability (generally, yij is a tensor), Eioc is a local electric field acting on each molecule and Pe is a field induced electric dipole in a molecule. So, if we find Eioc we could calculate P and then the value of s, using Eq. 7.12, and known macroscopic field E in the sample, see Fig. 7.4a. 

Miller KJ, Savchik JA (1979) New empirical-method to calculate average molecular polarizabilities. J Am Chem Soc 101 7206-7213... 

Mkadmh et have proposed an atom additive model to compute the static average molecular polarizabilities. First, the molecular polarizabilities of a learning set of molecules was calculated by means of the modified Thole dipole field tensor, an evolution of the point induced dipole due to Silber-stein. Values of linear screening factors were optimized to achieve minimum deviation from experimental polarizabilities and thus isotropic polarizabilities of C, H, O, N, and S were estimated in order to be applied in a simple additive model to calculate the average molecular polarizabilities of a vast number of molecules. Excellent correlations between the computed polarizability values and the experimental ones in all of the investigated groups have been achieved. 

A recent quantum-chemical ab initio ACPF (averaged coupled-pair functional) calculation gave the parallel and perpendicular components of the polarizability of NH(X Z"), 0C = 11.770 ao ( = 1.744 A ) and a = 9.016 ao ( = 1.336 A ) the average molecular polarizability thus is a= (oC + 2a )/3 = 9.934 Sq ( = 1.472 A ). Slightly higher values were obtained for the two lowest excited states, a and b of NH [1]. Using the time-dependent coupled Hartree-Fock method, the frequency-dependent polarizability a(co) was calculated for the isotropic static polarizability, a value of 9.3655 a was obtained [2]. 

As shown by Gelbart and Gelbart [16], the predominant orientational interaction in nematics must be the isotropic dispersion attraction modulated by the anisotropic molecular hard core. The isotropic part of the dispersion interaction is generally larger than the anisotropic part because it is proportional to the average molecular polarizability a. And the anisotropy of this effective potential comes from that of the asymmetric molecular shape. Thus this effective potential is a combination of intermolecular attraction and repulsion. It can be written as... 

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