Out-of-plane displacements

It is quite apparent (Figures 3,4) that the hyperfine constants of the central and terminal atoms in the two radicals are strongly influenced by the out-of-plane displacement. For the central atom, the coupling increases with 161 and tms is clearly related to a strong change in hybridization. 

FIGURE 30.1 The internal coordinates in five representative molecular systems and the Mulliken net charges of bonded atoms (from HF calculations). The last diagram defines the dihedral angles in formamide, relative to the NCO plane, determining the out-of-plane displacements of the cis (Hc), trans-(Ht) and formyl (Hf) hydrogens, respectively. 

Fig. 1 Geometry of approach of the amine nitrogen to the carbonyl carbon in the eight-membered ring of clivorine [partial structure, left drawn using the published coordinates (Birnbaum, 1972)]. The full formula is also shown. Note the out-of-plane displacement of the carbonyl carbon towards the nitrogen atom.

Fig. 10 Relationship between pyramidalization (out-of-plane displacement AZ of cadmium) and shortening and lengthening, respectively, of the C-X and C-Y bonds in XCdLjY (AY values are negative). Data from Biirgi (1973).

There is disorder in the crystal structure of [CrO(salen)]PF6> but the average out-of-plane displacement (which takes place on oxygen transfer to the metal) of the Cr atom is 0.52 A, and the average Cr=0 distance 1.56 A. 

For the planar ground state, the vibrational representation decompose as rv = 3Ai Bi 2B2, where the Ai modes transform as a translation along the z (C—S) axis and the mode as the single out-of-plane displacement along the x-direction. The last two modes lie in the molecular cr (y,z) plane and are antisymmetric to the a (x,z) plane. Figure 2.6 gives a schematic view of the... 

Figure 2.20. Potential energy functions and vibrational levels for the out-of-plane displacements for the first three singlet states of thiophosgene. (Reprinted with permission from Ref. [15].)...

For PtR, the large out-of-plane distortion of the 5 -G N(7)-Pt bond is the most noteworthy shortcoming of Model 4bi, compared to the other models (Models 3 and 4) that account well for the 1H-NMR data. The PtL X-ray structure also had substantial out-of-plane displacement ( 1 A) of the Pt from the 5 -G base plane [124] [125]. However, in Models 3 and 4 of PtR, there is much less out-of-plane distortion of the Pt (0.6-0.7 A). As mentioned earlier, 195Pt-NMR data indicate no substantial distortions around Pt when coordinated to a duplex DNA [97]. Thus, we believe the out-of-plane distortion of the Pt-N(7) bond is probably much smaller in solution than that found in the PtL X-ray study. The distortion in the models may arise from the limitations of the force field. 

Here the + sign denotes the out-of-plane displacement in the +x direction. 

Detailed comparison of puckered forms should consider not only the mode of puckering, but also the amplitude. A general expression that combines mode and amplitude for any ring, derives from the formula for out-of-plane displacements of a continuous ring [209], at the regular positions, 9 ... 

X—Sit-N fragment. Use of the Fouling relationship between bond distance increment and bond number Ad = — C x log n and the Burgi assumption between the bond number and the out-of-plane displacement of the Si atom or valent angles about silicon in penta-coordinate species including silatranes, a... 

The pseudo JT effect was then invoked independently by Mizuhashi and Ber-suker et al. to explain the large out-of-plane displacement of the iron(II) ion in Hb and also the oxy-deoxy reaction mechanism. 

Figure 9.1.13 Views of the Single Crystal X-Ray Diffraction Structures of Lanthanum(III) Texaphyrin 9.73 (top), Gadolinium(III) Texaphyrin 9.78 (middle), and Lutetium(III) Texaphyrin 9.75 (bottom) Showing the Out-of-plane Displacement of the Metal Ions.

In order to reduce the computational effort, without losing correspondence with the experimental counterparts, a slice of the specimen, 1.6 mm thick (1/4 of the real specimen thickness), is modelled. The out of plane displacements along the surfaces of the plate are constrained to avoid buckling. The computational mesh comprises 65365 nodes and 32482 10-node quadratic tetrahedrons. Fig. 5. The core is modeled using a uniform minimum mesh size of 0.8 mm the mesh coarsens in the steel layer, with one tetrahedral element aeross the thickness. The cohesive elements are adaptively inserted along previously eoherent interfaces when the local effective stress attains a eritieal value [6]. 

Preparation. - The diphosphines (223) can be oxidised to the related dioxides on treatment with oxygen or hydrogen peroxide. Treatment of the diphosphine (223, R = Ph) with an excess of sulfur in hot toluene affords the corresponding bis(sulfide). X-ray studies of representative dioxides and the above disulfide reveal considerable steric strain in the molecule, resulting in out of plane displacement of phosphorus atoms. " The reaction of (223, R = Ph) with an... 

To give a flavor of the types of results that can be obtained using this method, fig. 12.12 shows results on nanoindentation. The nanoindentation calculations were carried out using a pseudo-two-dimensional geometry which allows for out-of-plane displacements but not out-of-plane displacement gradients. As the... 

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