Polarizability electronic-vibrational

Meanwhile, in the London dispersive force Eq. (7), the characteristic electronic vibrational frequency, v, is directly related to the deformation polarizability, ao, of the molecule by [61,63,64]... 

The ellipsoid described by the above equation conforms to the shape of the electron clouds surrounding the entire molecule. The ellipsoid may be further regarded as representing the polarizability because vibrational modes which induce a change in the size or shape of the polarizability ellipsoid are considered to be Raman active modes. 

In the electronic-vibrational polarizability on the other hand, the nuclear part of the electric dipole moment operator Eq. (4.32), cannot contribute because the... 

For all the magnetic linear response properties derived in Chapters 5 and 6 one would obtain expressions similar to the electronic-vibrational polarizability, Eq. (8.7). On the other hand, the diamagnetic contributions to the magnetic properties as well as all first-order properties, i.e. properties defined as first derivatives of the energy, will take the following simple expectation value form... 

In order to evaluate the vibrational polarizability, Eq. (8.8), one needs the energies of all vibrational states of the electronic ground state and the corresponding vibrational dipole transition moments, which requires knowledge of the potential energy and electric dipole moment surface of this single electronic state. For the electronic-vibrational polarizability, Eq. (8.7), however, one would need to know not only all excited electronic states, and the electronic dipole transition moments to them but also all the vibrational states, of these excited states, which makes this... 

The stretching or compression of a bond changes the electronic wave function and therefore changes the polarizability. The vibration of a diatomic molecule is Raman active, whether the molecule is homonuclear or heteronuclear. A vibrational normal... 

Infrared and Raman spectroscopy each probe vibrational motion, but respond to a different manifestation of it. Infrared spectroscopy is sensitive to a change in the dipole moment as a function of the vibrational motion, whereas Raman spectroscopy probes the change in polarizability as the molecule undergoes vibrations. Resonance Raman spectroscopy also couples to excited electronic states, and can yield fiirtlier infomiation regarding the identity of the vibration. Raman and IR spectroscopy are often complementary, both in the type of systems tliat can be studied, as well as the infomiation obtained. 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

FIGURE 2.1 Energy of the 0-0 vibrational transition in the principal electronic absorption spectrum of violaxanthin (l Ag-—>1 BU+), recorded in different organic solvents, versus the polarizability term, dependent on the refraction index of the solvent (n). The dashed line corresponds to the position of the absorption band for violaxanthin embedded into the liposomes formed with DMPC (Gruszecki and Sielewiesiuk, 1990) and the arrow corresponds to the polarizability term of the hydrophobic core of the membrane (n = 1.44). 

Further work on long polyenes, including vibrational distortion, frequency dispersion effects and electron correlation, would be important for evaluating more accurate asymptotic longitudinal polarizabilities and hyperpolarizabilities. 

An electric dipole operator, of importance in electronic (visible and uv) and in vibrational spectroscopy (infrared) has the same symmetry properties as Ta. Magnetic dipoles, of importance in rotational (microwave), nmr (radio frequency) and epr (microwave) spectroscopies, have an operator with symmetry properties of Ra. Raman (visible) spectra relate to polarizability and the operator has the same symmetry properties as terms such as x2, xy, etc. In the study of optically active species, that cause helical movement of charge density, the important symmetry property of a helix to note, is that it corresponds to simultaneous translation and rotation. Optically active molecules must therefore have a symmetry such that Ta and Ra (a = x, y, z) transform as the same i.r. It only occurs for molecules with an alternating or improper rotation axis, Sn. 

Raman (R) and resonance Raman (RR) spectroscopy detects vibrational modes involving a change in polarizability. For RR, enhancement of modes is coupled with electronic transition excited by a laser light source. This technique is complementary to IR and is used for detection of v(O-O) and v(M-0), especially in metalloproteins. In porphyrins, one may identify oxidation and spin states. 

One of the main aims of such computations is the prediction and rationalization of the optoelectronic spectra in various steric and electronic environments by either semiempirical or ab initio methods or a combination of these, considering equilibrium structures, rotation barriers, vibrational frequencies, and polarizabilities. The accuracy of the results from these calculations can be evaluated by comparison of the predicted ionization potentials (which are related to the orbital energies by Koopman s theorem) with experimental values. 

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. 

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