Second-order structural effects

We assume that the double bonds in 1,3-butadiene would be the same as in ethylene if they did not interact with one another. Introduction of the known geometry of 1,3-butadiene in the s-trans conformation and the monopole charge of 0.49 e on each carbon yields an interaction energy <5 — 0.48 ev between the two double bonds. Simpson found the empirical value <5 = 1.91 ev from his assumption that only a London interaction was present. Hence it appears that only a small part of the interaction between double bonds in 1,3-butadiene is a London type of second-order electrical effect and the larger part is a conjugation or resonance associated with the structure with a double bond in the central position. 

In general, as the variation of the temporal profile of the non-stationary light beam due to the SS effect or the second-order GVD effect is continuous, emission of radiation field from the guiding region is also continuous upon propagation of the pulse. This emission prevents formation of a spatiotemporal soliton in the step-index guiding structures. 

However, commonly due to a spread of quadrupole parameters caused by structural variation, with the extreme case being glassy or amorphous materials, the distinct features of fhe lineshape can be lost. This is particularly true if Cq is small. Then an approach which records spectra at several magnetic fields will allow bofh fhe second-order quadrupole effect parameter Pq, defined as... 

Fig. 10. Extrapolation of the half maximum center (o) and of the line position corrected for the light-shift, second order Doppler effect and 8D hyperfine structure ( ) versus the light power P in the case of the 2 >i/2 (F = 1) — 8D5/0 transition of deuterium...

The principal structural requirement for second order nonlinear effects in assemblies of molecules is the lack of a centre of symmetry, and considerable efforts have been expended in trying to induce potentially useful molecular entities to crystallize in non-centrosymmetric or polar crystals (Curtin and Paul 1981 Liter et al. 1991). As demonstrated below, this is a necessary, but not sufficient condition for obtaining nonlinear effects. True to form, the variety of crystallization experiments has led to a number of polymorphic structures, and to information about the relationship between the properties of these materials and their structures, as well as useful guidelines for attempting to obtain the desired non-centrosymmetric crystal structures. 

Overtone spectroscopy developed for irradiates the sample at approximately twice the Larmor frequency (Tycko and Opella 1987). If the quadrupole interaction is sufficiently large that second-order quadrupole effects are significant, the (— 1 1) transition becomes weakly allowed. In powders the spectmm is still structured, allowing the interactions to be deduced, but is narrowed by a factor of 8vq/xq. 

Continuing the theme of comprehensive studies, Woessner [23] recently carried out another major investigation of clay structure. The main improvement here is the use of high-speed MAS. Some of the spectra were collected at 9 kHz, which was significantly faster than for most spectra of clays published to that point. Several of the conclusions reached are in agreement with previous structural studies. One additional parameter that was extracted was the SOQE (second-order quadrupole effect), which is simply the isotropic part of the second-order quadrupolar interaction. The QCC (quadrupolar coupling constant) and T] (asymmetry parameter) are defined in this paper as follows... 

Mossbauer Spectroscopy. Mdssbauer spectroscopy has been used as a powerful technique to probe the electronic structure of the five- and six-coordinate ferrous nitrosyl porphyrins. The isomer shifts of both types of complexes (5 0.35 mm s ) are similar and show temperature dependences that are consistent with a second-order Doppler effect, but are slightly smaller than those of most other iron(II) porphyrin complexes (5 0.45 mm Unlike the isomer... 

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