Polarization propagator symmetry

Up to this point, our main concern was to reformulate the results of the LD ligand influence theory in the DMM form. Its main content was the symmetry-based analysis of the possible interplay between two types of perturbation substitution and deformation, controlled by the selection rules incorporated in the polarization propagator of the CLS. The mechanism of this interplay can be simply formulated as follows substitution produces perturbations of different symmetries which are supposed to induce transition densities of the same symmetries. In the frontier orbital approximation, only those densities among all possible ones can actually appear, which have the symmetry which enters into decomposition of the tensor product TH TL to the irreducible representations. These survived transition densities then induce the geometry deformations of the same symmetry. 

From the spectral representation, Eq. (3.110), we can easily verify the general symmetry property of the polarization propagator... 

Polarization effects are another feature of Raman spectroscopy that improves the assignment of bands and enables the determination of molecular orientation. Analysis of the polarized and non-polarized bands of isotropic phases enables determination of the symmetry of the respective vibrations. For aligned molecules in crystals or at surfaces it is possible to measure the dependence of up to six independent Raman spectra on the polarization and direction of propagation of incident and scattered light relative to the molecular or crystal axes. 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

For molecules that do not possess a plane of symmetry, the mirror images are not superimposable. It is a property of such molecules that they rotate a beam of polarized light. If the beam is rotated to the right (when looking along the beam in the direction of propagation) the substance is said to be dextrorotatory (or simply dextro). Those substances... 

For high-symmetry media like gases, liquids, cubic crystals, or uniaxial crystals with their optical axis parallel to B, and with the propagation direction of the light parallel to B, the optical eigenmodes are right- and left-handed circularly polarized waves, denoted by + and —. For such media, Eq. (1) can be simplified to [8,9]... 

In Example 2.2, Equation 2.11 reduced to equations for three uncoupled modes capable of propagating along the x axis of a cubic crystal. Undm- such conditions, the propagation direction is referred to as a pure-mode direction. In general, pure modes result when waves are propagating along a symmetry plane of a crystal and have polarization perpendicular to or parallel to this plane. Also, propaga-... 

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