Polarizabilities permanent moment measurement

Another important class of forces, induction or polarization forces, involves permanent moments that induces multipoles in a polarizable species. Polarizability, a, measures the ability of an atomic or molecular species to develop an induced dipole moment, as a response to an applied electric field E. Within the limits of linear response theory, the induced dipole moment is given by the product of polarizability tensor times the electric field E. 

Thus, it is natural to expect a polarizability or a permanent moment to be subject to vibrational influence. Likewise, a laboratory measurement of a particular electrical property may not compare directly with a value calculated for a fixed structure. 

The two papers cited above also give explicit expressions for the polarization (induction) energies between polar molecules. They are expressed in terms of permanent moments and static polarizabilities of the interacting molecules. Both are observable quantities that can be measured by experiment. 

If a gas, a solution or a pure liquid is introduced between the plates of a charged condenser, the molecules strive, as already pointed out, to orientate themselves with the axis of their maximum polarizability or, if a permanent moment exists, with the axis of this moment, parallel to the direction of the field. Should the thermal agitation be such, however, that this orientation is effected only to a very small extent, the previously isotropic medium exhibits anisotropy which can be detected as double refraction on the passage of polarized light. This electric double refraction imposed by the presence of the external field is called the Kerr effect. The phenomenon is measured by the path difference AX, between the beam polarized in the direction of the field and that polarized perpendicular to the field. It is given by the equation... 

The 7t value is a measure of solvent dipolaiity and polarizability. For nonha-loaliphatic solvents and nonaromatic ones, the 7t parameter is correlated with the permanent dipole moment of the solvent molecule. 

Methods for determining permanent dipole moments and polarizabilities can be arbitrarily divided into two groups. The first is based on measuring bulk phase electrical properties of vapors, liquids, or solutions as functions of field strength, temperature, concentration, etc. following methods proposed by Debye and elaborated by Onsager. In the older Debye approach the isotope effects on the dielectric constant and thence the bulk polarization, AP, are plotted vs. reciprocal temperature and the isotope effect on the polarizability and permanent dipole moment recovered from the intercept and slope, respectively, using Equation 12.5. 

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. 

Fro. IX-1.—Values of the ratio of polarisation P to field strength E for hydrogen chloride gas, as a function of the reciprocal of the absolute temperature. The slope of the line is a measure of the permanent electric dipole moment of the molecules, and the intercept of the line is a measure of the temperature-independent polarizability of the molecules. 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

The dipole polarizability of DBT has been measured experimentally by refractometry techniques, and evaluated theoretically with ab initio and DFT methods in the A electronic ground state. The molecular dipole polarizability a is the linear response of a molecular electronic distribution to the action of an external electric field Such an external field causes charge rearrangements in the molecular structure that are reflected in changes in the permanent molecular dipole moment <2001JP0709>. 

Concentration-dependent measurements of this quantity yield the permanent dipole moment in the electronic ground state. The static first-order polarizability a(0 0) in (105) can be estimated from refractive index measurements of a(-w w), (103). 

In the expressions (184) and (184b) the second, temperature-dependent term defines the Born effect due to superposition of the two non-linear processes of second-order distortion and reorientation of permanent dipole moments in the electric field. Buckingham et al. determined nonlinear polarizabflities If and c for numerous molecules by Kerr effect measurements in gases as a function of temperature and pressure. It is here convenient to use the virial expansion of the molar Kerr constant, when the first and second virial coefficients Ak and Bk result immediately from equations (177), (178), and (184). Meeten et al. determined nonlinear molecular polarizabilities by measuring K in liquids as a function of temperature. 

Intermolecularforces The strength of these forces can affect the vapor pressure and solubihty in certain solvents. One property is the dipole moment, which is a measure of the permanent charge separation within a molecule (polarity). Another property is the polarizability which is a measure of a second molecule s abihty to induce a dipole in the molecule of interest The dielectric constant is a physical property that can be used as a measure of both the dipole moment and the polarizabihty. 

To fulfill the need for understanding what structures will allow enhancement of optical nonlinearity, we have coupled ab-initio theoretical calculations of optical nonlinearity with synthesis of sequentially built and systematically derivatized model compounds, and the measurement of their optical nonlinearities. Now I would like to discuss very briefly our efforts to compare microscopic optical nonlinearities. An expression, similar to the expansion of the bulk polarization as a function of the applied field, can be written for the induced dipole moment. Naturally, the nonlinear term Y, for example, is the third derivative of the induced dipole moment with respect to the applied field. Also, using the Stark energy analysis, one can write the nonlinear terms 3 (and Y) as a sum over all excited states terms involving transition-dipoles and permanent dipoles, similar to what one does for polarizability. Consequently, the two theoretical approaches are (i) the derivative method and (ii) the sum-over-s1j tes method. We have used the derivative method at the ab-initio level. We correlate the predictions of these calculations with measurements on systematically derivatized and sequentially built model compounds. Some conclusions of our theoretical computations are as follows ... 

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