Electronic susceptibility, second-order

The contribution of the electron to the diamagnetic susceptibility of the system can be calculated by the methods of quantum-mechanical perturbation theory, a second-order perturbation treatment being needed for the term in 3C and a first-order treatment for that in 3C". In case that the potential function in 3C° is cylindrical symmetrical about the s axis, the effect of 3C vanishes, and the contribution of the electron to the susceptibility (per mole) is given... 

The n-electron excitations are viewed as occuring on molecular sites weakly coupled to their neigbors and providing sources of nonlinear optical response through the on-site microscopic second order nonlinear electronic susceptibility... 

An applied electric field can also change a material s linear susceptibility, and thus its refractive index. This effect is known as the linear electro-optic (LEO) or Pocket s effect, and it can be used to modulate light by changing the voltage applied to a second-order NLO material. The applied voltage anisotropically distorts the electron... 

Materials that have a nonzero second-order susceptibility will produce light at twice the incident frequency. The magnitude of this effect is small, and has been a practical consideration only since the advent of lasers. If the symmetry of a crystal or other medium is such that it has a center of inversion, no SHG effect will be observed. However, surfaces by their very nature break this inversion symmetry. Hence, an SHG signal may arise at the electrode-solution interface even though both bulk phases may be considered centrosymmetric [66], The magnitude of the SHG signal is sensitive to surface conditions (e.g., electrode potential, ionic or molecular adsorption, etc.). Surface spectroscopy is also feasible since the SHG signal will be enhanced if either the incident frequency (to) or SHG (2co) corresponds to an electronic absorption of a surface species [66]. 

The susceptibility tensors measure the macroscopic compliance of the electrons. Since the second order polarization is a second rank tensor, SHG is zero in a centrosymmetric or randomly oriented system. To make the material capable of SHG, the NLO dopants must be oriented noncentrosymmetricaly in the polymer matrix (2-3). When modeling the poled, doped films using a free gas approximation, the poled second order susceptibilities are given by (2.19)... 

In other words, the electrons confined to their ground state are only slightly disturbed by the incident photons Hence the NLO effects should be classified into the second category where short-range forces play a decisive role We therefore make the assumption that, in the NLO effects, the electron motion may be regarded as confined to small regions In other words, any NLO susceptibility (or second-order susceptibility) in crystals is a localized effect arising from the action of incident photons on the electrons in certain orbitals of atomic clusters ... 

Based upon the method of calculation adopted, a complete computer programme consisting of three main parts can easily be written for support of such calculations. The three parts are as follows (a) the CNDO part or EHMO part with Madelung correction for calculation of the localized electron orbitals in the anionic group (b) the transition matrix element calculation part and (c) the second-order susceptibility part for the calculation of the microscopic susceptibility of the anionic group followed by the calculation of the macroscopic SHG coefficients of the crystal. 

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

A second-order dependence on both the reductant and acidity was observed in the oxidation of alcohols with butyltriphenylphosphonium dichromate study of MeCD2OH and Me2CDOH indicated the presence of a substantial kinetic isotope effect. The reaction was studied in 19 organic solvents and the rates were correlated with mul-tiparametric equations. The reaction is susceptible to both electronic and steric effects of the substituents. A mechanism involving the formation of a dichromate ester and an a-C-H cleavage has been proposed.4... 

Bis(trifluoromethyl) A3-iodane 6a undergoes degenerate ligand exchange with added alkoxide PhC(CF3)2OK more rapidly (second-order rate constant = 49 M 1s 1 at 56 °C) than that of dimethyl A3-iodane 6b (second-order rate constant =61 M 1s 1 at 93 °C), in which an associative mechanism involving the formation of [12-1-4] species was proposed [16]. The CF3 substituents, which lower the electron density on iodine(III) relative to the CH3 substituents, make the iodine of 6a more susceptible to attack by alkoxide ion. Dynamic 19F NMR of A3-iodane 7 showed an intramolecular ligand exchange via intermediacy of bicyclic tetracoordinated iodate with a AG of ca. 12 kcal/mol at - 80 °C [17]. 

Extended pyridine derivatives have also been considered in the development of new materials as they present rigid systems with different electronic character than benzene. Self-assembled multilayers (SAMs) of stilbazolium derivatives, such as those based on compound 63, have been investigated <1996JA8034> and shown to have very high structural regularity and subsequently be very smooth. These show promise for nonlinear optical materials, as they have very high second-order susceptibility. 

The fact that the susceptibility is proportional to the second order of the number of unpaired electrons explains the steep slope of the NO curves in Figure 8. This shows again that the surface has quite a different electron structure from that of the bulk. The NO is sorbed only on the surface, since there is no evidence that it is able to enter the crystal lattice of palladium. As we have indicated, the... 

Figure 2 (a) Linearized electron dispersion in the Luttinger approximation (A) and diagrammatic representation of elementary interactions g, g4 (B). Solid and dashed lines represent electrons near kF and - kF, respectively. The g3 interaction exists only in case of a half-filled band (b) Diagrammatic representation of the Cooper pair susceptibility A(q, to) and the density wave susceptibility II (2kF + q, second order (D) which shows the mixture between Cooper and Peierls channels. 

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