Geometric distortions

During the calibration the geometric distortions in the images are reduced from a maximum of more than 11 pixels to less than 0.3 pixels (pixel size about 0.28mm 0.28mm). The whole calibration results in a maximum deviation of the projected calibration marks from the measured calibration marks in the image of less than 0.4 pixel (2D-error). 

The broad conclusion of all these studies is that alkyl radicals are shallow pyramids and that the barrier to inversion of the pyramidal structures is low. Radicals also are able to tolerate some geometric distortion associated with strained ring systems. 

Note that the magnitude of the imaginary frequency is not very large (-226), indicating that the geometric distortion desired by the molecule is modest. The... 

Compare energies for equatorial and axial chair conformers for methylcyclohexane, R = Me, and tert-butylcyclohexane, R = CMe3. Which is more stable in each molecule Use equation (1) to calculate the ratio of major to minor conformers for each system at 298 K. Which molecule shows a larger preference Why (Hint Compare nonbonded interactions and/or geometrical distortions in the higher-energy conformers that are absent in the lower-energy conformers.)... 

Fig. 9. Sketch of potential energy curves of a segment of conducting polymers in the ground state and in the ionized state Eip, is the vertical ionization energy, E ] the relaxation energy gained in the ionized state, Eip d the ionization energy of the distorted molecule, and Ej, the geometrical distortion energy in the ground state...

Fig. 10. Formation of the bipolaron (= diion) state in poly-p-phenylene upon reduction In the model it is assumed that the ionized states are stabilized by a local geometric distortion from a benzoid-like to a chinoid-Iike structure. Hereby one bipolaron should thermodynamically become more stable than two polarons despite the coulomb repulsion between two similar charges...

The cyclopentyl cation (39) undergoes a rapid degenerate rearrangement which can be frozen out at cryogenic temperatures as shown by solid state CPMAS 13C NMR spectra.57 MP2/6-31G(d,p) calculations show that cyclopentyl cation has a twisted conformation 4058 in which the axial hydrogens are bend toward the carbocation center. This is due to the pronounced geometrical distortion caused by the hyper-conjugative interaction of the /i-cr-C-H-bond with the formally vacant 2pz-orbital at the C+ carbon of this secondary carbocation. 

The puzzle may be explained by the operation of electrostatically induced geometric distortion in both ground and giant CS states of syn,syn-24. Gas phase ab initio MO calculations indicate that there is an electrostatic attraction between the zinc porphyrin and the viologen dication in the ground state of... 

Gas phase calculations on the CS state of 22 also predict a large change in the cavity size, from 10 A in the ground state, to only about 6 A in the CS state, and that this change is mainly caused by out-of-plane bending of both DC V and DMAn groups.1381 Similar geometric distortions are predicted for other U-shaped dyads in their CS states. 

Pyramidalization is a common indication of increased reactivity at sp2 hybridized centres. These centres often become tetrahedral when they react, so the geometrical distortion is in the direction of the transition state for the reactions concerned. The way the rest of the structure responds to the distortion is therefore relevant to the structure of the transition state for such reactions. 

In order to examine the nature of the unusual geometric distortions observed in the X-ray structures of complexes 3 and 4, we have performed a series of density functional theory (DFT) and combined quantum mechanics and molecular mechanics (QM/MM) calculations [22-27], Although the computational resources to wholly treat both 3 and 4 at the DFT level are available, we have employed the combined QM/MM method to unravel the... 

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