Polarization distortion-induced

In the last few years, several workers have analyzed charge density distribution in molecular crystals with non-linear optical (NLO) properties [71-74]. The NLO response can, in principle, be explained by an anharmonic distortion of the electron density distribution due to the electric field of an applied optical pulse. The polarization P induced in a molecule is... 

For a vibration to be allowed in the Raman spectrum there must be a change of polarizability accompanying the vibration. An atom or molecule in an electric field will be distorted and therefore be polarized. This induced dipole moment is proportional to the applied field ... 

The microscopic origin of the nonlinear response is the distortion induced in the molecular charge distribution due to the electrical field. The presence of a microscopic dipole produces a macroscopic polarization in the unit volume P = N r) where N is the number density of polarizable units and (er) the expectation value of the dipole moment induced in each unit. In order to evaluate (sr) we will use the density matrix formalism, because it is the easiest way to relate microscopic properties to macroscopic ones and to cope with macroscopic coherence effects. In the absence of fields, the medium is supposed to be described by an unperturbed Hamiltonian Hq and to be at equilibrium. When the fields are applied, the field-matter interaction contributes a time-dependent term V(t) =-E(t)P(t) to the global energy. The evolution of the system under this perturbation can be described through the equation of motion of the density operator ... 

Fig. 27,7 Calculated iso-density lines of highest electron density (cut in b-c plane) at equilibrium nuclear geometry R q of NbaAl (a) and at the distorted geometry R cr of Nb atoms in Fn phonon mode when nonadiabatic e-p interactions trigger transition into antiadiabatic state and inter-sites polarization is induced. Figures (b-f) represents different geometrical fxjsitions of Nb atoms on the circumferences of the flux circles...

At 321 mn there is a vibronic origin marked This has one quantum of v, the antisynnnetric C-H stretching mode, in the upper state. Its intensity is induced by a distortion along This state has B2 vibrational symmetry. The direct product of B2 and A2 is B, so it has B vibronic syimnetry and absorbs x-polarized light. One can also see a 4 6,, vibronic origin which has the same syimnetry and intensity induced by... 

Now let us examine the molecular origin of Molecular polarity may be the result of either a permanent dipole moment p or an induced dipole moment ind here the latter arises from the distortion of the charge distribution in a molecule due to an electric field. We saw in Chap. 8 that each of these types of polarity are sources of intermolecular attraction. In the present discussion we assume that no permanent dipoles are present and note that the induced dipole moment is proportional to the net field strength at the molecule ... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

Carbon atoms in free space have spherical symmetry, but a carbon atom in a molecule is a quite different entity because its charge density may well distort from spherical symmetry. To take account of the finer points of this distortion, we very often need to include d, f,. .. atomic orbitals in the basis set. Such atomic orbitals are referred to as polarization functions because their inclusion would allow a free atom to take account of the polarization induced by an external electric field or by molecule formation. 1 mentioned polarization functions briefly in Section 9.3.1. 

The concerns we have expressed are bound to get even more acute if the problem under study demands that we are able to adequately describe distortion effects induced in the electron distribution by external fields. The evaluation of linear (and, still more, non linear) response funetions [1] by perturbation theory then forces one to take care also of the nonoccupied portion of the complete orbital spectrum, which is entrusted with the role of representing the polarization caused by the external fields in the unperturbed electron distribution [4], ... 

When the iterative maximum localization extended Hiickel (IML-EH) method is applied to the drug molsidomine 12 (Section 5.03.12), the angle widening at N2-N3-C4 observed by X-ray analysis, 115° instead of the typical 108°, is due to induced polarization <1998JMT291>. The N3 position is the most electron deficient, followed by C-5. The N+-N bond connecting N3 to the morpholine ring has no 71 character despite the electron deficiency at N3 and the distortion toward planarity. 

The relative changes in intensity of the vibronic bands in the pyrene fluorescence spectrum has its origin in the extent of vibronic coupling between the weakly allowed first excited state and the strongly allowed second excited state. Dipole-induced dipole interactions between the solvent and pyrene play a major role. The polarity of the solvent determines the extent to which an induced dipole moment is formed by vibrational distortions of the nuclear coordinates of pyrene (Karpovich and Blanchard, 1995). 

An ion-induced dipole force results when an ion in close proximity to a non-polar molecule distorts the electron density of the non-polar molecule. The molecule then becomes momentarily polarized, and the two species are attracted to each other. This force is active during every moment of your life, in the bonding between non-polar O2 molecules and the Fe " ion in hemoglobin. Ion-induced dipole forces, therefore, are part of the process that transports vital oxygen throughout your body. 

Simultaneously, as though I was having a yet deeper thought, I somehow intuitively "understood" that the distortion or polarizing of the light of the flame was an effect caused by the distortion of psychic space-time induced by our experiment and the nearby, ubiquitous presence of the lapis. This thought was followed by another Perhaps the... 

---