Anisotropic electronic polarizability

Molar Kerr constants have been reported for BH3 and BX3 (X = all halogens) adducts of NMeg in dioxan and benzene solutions. The anisotropic electron polarizabilities of the adduct molecules were derived from the measurements in dioxan solution and these were found to indicate an overall reduction in polarizability on adduct formation. 

The b s quoted (from Mortensen and Smith, 1960) represent the two bonds as being more anisotropic than they appear in Table 22, but Ziircher comments that the Mortensen-Smith polarizabilities should be taken with caution. He stresses that his own calculations have an approximate character and involve quantities and equations of varying precision. Nevertheless their interest lies in the indication that the directions of greatest diamagnetic susceptibility in bonds should be perpendicular to those of greatest electronic polarizability and vice-versa. Such an inverse relationship is in accord with empirical (Bothner-By and Naar-Colin, 1958) and theoretical (Pople, 1957) deductions to date rough predictions of the shielding of a proton by a remote bond... 

However, anisotropic electron density distributions around nuclei have consequences for other intermolecular interactions. Atom-atom repulsions (both Coulombic and Pauli repulsion) depend on the electron density and are thus anisotropic [53]. Dispersion interactions depend on the polarizability tensor [54], which in turn depends on the electron density [55, 56], so that dispersion is also anisotropic [57]. 

Because the electric vector of the light has components normal to the beam, in anisotropic materials they feel different electronic polarizabilities, i.e., different refractive indices. For this reason, the speed of the light of different polarization directions will be different Vo = c/n describes the speed of the "ordinary" wave, and Ve = c/n relates to the "extraordinary" beam, which exists only in anisotropic materials. Due to the differences of the speeds, there will be a phase difference between the ordinary and extraordinary vvaves. Since the wavevector k of the light relates to the wavelength, X as k =k = n = n-, the difference between the phases (the so called retardation) of the ordinary and extraordinary waved can be expressed as ... 

The combination of molecular order and fluidity in a single phase results in several remarkable properties unique to liquid crystals. By now, it is quite evident that the constituent molecules of liquid crystal mesophases are structurally very anisotropic. Because of this shape anisotropy, all the molecular response functions, such as the electronic polarizability, are anisotropic. The long range order in the liquid-crystal phases prevents this molecular anisotropy from being completely averaged to zero, so that all the macroscopic response functions of the bulk material, such as the dielectric constant, are anisotropic as well. We have, therefore, a flexible fluid medium whose response to external perturbations is anisotropic. 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

The polarizability tensor, a, introduced in section 4.1.2, is a measure of the facility of the electron distribution to distortion by an imposed electric field. The structure of the electron distribution will generally be anisotropic, giving rise to intrinsic birefringence. This optical anisotropy reflects the average electron distribution whereas vibrational and rotational modes of the molecules making up a sample will cause the polarizability to fluctuate in time. These modes are discrete, and considering a particular vibrational frequency, vk, the oscillating polarizability can be modeled as... 

It follows from the preceding results that the electro-optical properties of molecules in degenerate electronic states should have unusual temperature dependence, which is absent in the case of nondegenerate states. Even for nondipolar degenerate electronic states (e.g., for states in which the reduced matrix elements of the dipole moment are zero) for certain relationships between the vibronic constant and the temperature, there may be a quadratic dependence of the Kerr effect on p, similar to that observed in the case of molecules that are simultaneously anisotropic polarizable and possess a proper dipole moment. The nonlinear dependence on p under consideration is due exclusively to the vibronic interaction that redetermines the vibronic spectrum and leads to different polarizability in different vibronic states. This dependence on p has to be distinguished from that which arises due to the nonzero value of the dipole moment in the initial ground electronic state (e.g., as in the case of the E term in molecules with D3h symmetry). The two sources of the... 

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