Trapezoidal distortion

Figure 9.8. A cartoon showing (a) the conical intersection for the [2+2] photocycloaddition of two ethylenes, drawn in the branching space corresponding to the distance between the two ethylenes R (Xj) and a trapezoidal distortion (Xj), and (b) an avoided crossing in a cross-section R (Xi).

The coordination geometry in anhydrous Th(CF3COCHCOMe)4 is a 1111 ( )4-422) antiprism 74 the structure of the monohydrate has been discussed earlier (p. 1144). Th[CF3COCHCO(2-C4H3S)]4 is isostructural with the cerium(IV), uranium(IV) and plutonium(IV) analogues. The coordination polyhedron is a distorted dodecahedron in which the four ligands span the two perpendicular trapezoids of the dodecahedron.75 In the complexes M(n-C3F7COCHCOBut)4, the thorium(IV), uranium(IV) and neptunium(IV) compounds are isomorphous, but the plutonium compound is not. 

Distortion of the trans octahedral structure to the skew-trapezoidal bipyramidal structure 58... 

The most important parameter of the detection system is its response function. We have studied this extensively in Monte Carlo and other calculations. The calculated time-spectrum response to monoenergetic neutrons is composed of a Gaussian timing curve (2.97-ns FWHM), a trapezoidal contribution from detector thickness and non-axial paths, and an exponential tail, calculated by Monte Carlo, from multiple scattering in the neutron scintillator. (Spectrum distortion due to neutrons multiply scattered by structural and other parts of the apparatus and arriving at the neutron... 

Complexes containing two bidentate and two unidentate ligands may be either cis or trans octahedral, but it is important to note that both stractures show very large distortions as the size of the chelate rings is reduced the trans structure turns into the skew-trapezoidal bipyramidal stmcture (Figure 2). 

The cyclobutane radical cation was calculated by several groups, who evaluated Jahn-Teller distorted structures potentially arising upon ionization of cyclobutane [79, 83-87]. Four distorted local minima were considered (Figure 13). A rectangular structure with two weakened C-C bonds (type A) and a rhomboidal structure with four weakened C-C bonds (type B) result from first order Jahn-Teller distortion. Two further structures, a trapezoidal one (one weakened C-C bond type C), and an irregular structure shaped like a kite (two lengthened C-C bonds type D) can be envisaged as a consequence of second-order Jahn-Teller distortion [86]. A detailed recent study also considered puckered equivalents of the planar structure types, A-D... 

The density functional theory calculations mentioned earlier also modeled the ring-opening of cyclobutane radical cation [87]. This reaction proceeded via a distorted trapezoid transition state with two shorter (142.2, 147.1 pm) and two longer bonds (187.7, 208.4 pm), forming the "anti -complex (one long bond 221.6 pm), similar to that calculated earlier [168]. 

Fourier transformation of a FID, which has not decayed to zero intensity causes a distortion ("wiggles") at the base of peaks in the spectrum. By applying a suitable window function WDW the FID will decay smoothly to zero. A variety of window functions options are available, none, exponential EM, gaussian GM, sine SINE, squared sine QSINE and trapezoidal TRAP function. The best type of window function depends on the appearance of the FID and the resulting spectrum. Consequently where possible it is best to fit the window function interactively. 

---