Planar geometry

FIGURE 7.1 Three different isotropic regions 1-3 separated by planar boundaries at z = 0 and z = d, where the z-axis is taken to be perpendicular to the boundaries. There are M, discrete point charges e i = 1, 2, 3 1= 1, 2,. . . , in region i of dielectric permittivity Si 1, 2, 3). The position of each charge is given by cylindrical coordinates 

We give below the explicit expressions for V for various cases. 

FIGURE 7.2 A charge ei located at position (pi, zi) in region 1 of relative permittivity Si. 

FIGURE 7.4 A charge ej at position pi, (f i, zi) in region 1 of relative permittivity Si and a charge 2 located at position (p2, Z2) in region 2 of relative permittivity 2- 

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Figure 8. Three-dimensional mean-potential surface for the X IT state of HCCS, (Pi, Pa, y), presented in form of its ID sections. Curves represent the function given by Eq. (75). (with Ati — 0.0414, k2 — 0.952, tt 2 — 0.0184) for fixed values of coordinates p, and P2 (attached at each curve) and variable y — 4 2 4t Here y — 0 corresponds to cis-planar geometry and Y = ft to trans-planar geometry. Symbols results of explicit ab initio computations.

Interestingly, the rate constants for Diels-Alder reaction of the ternary complexes with 3.9 are remarkably similar. Only with 2,2 -bipyridine and 1,10-phenanthroline as ligands, a significant change in reactivity is observed. It might well be that the inability of these complexes to adopt a planar geometry hampers the interaction between the copper ion and the dienophile, resulting in a decrease of the rate of the catalysed Diels-Alder reaction. 

Cyclobutane has less angle strain than cyclopropane and can reduce the torsional strain that goes with a planar geometry by adopting the nonplanar puckered confer matron shown m Figure 3 11... 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

Planar geometry required for aromaticity destabilized by van der Waals repulsions between indicated hydrogens... 

Valence shell electron pair repulsion (VSEPR) model (Section 110) Method for predicting the shape of a molecule based on the notion that electron pairs surrounding a central atom repel one another Four electron pairs will arrange them selves in a tetrahedral geometry three will assume a trigo nal planar geometry and two electron pairs will adopt a linear arrangement... 

The chemistry of propylene is characterized both by the double bond and by the aHyUc hydrogen atoms. Propylene is the smallest stable unsaturated hydrocarbon molecule that exhibits low order symmetry, ie, only reflection along the main plane. This loss of symmetry, which implies the possibiUty of different types of chemical reactions, is also responsible for the existence of the propylene dipole moment of 0.35 D. Carbon atoms 1 and 2 have trigonal planar geometry identical to that of ethylene. Generally, these carbons are not free to rotate, because of the double bond. Carbon atom 3 is tetrahedral, like methane, and is free to rotate. The hydrogen atoms attached to this carbon are aUyflc. 

Another important factor affecting the electronic properties is the steric barrier to planarity along the polymer chain. Since polyheterocycles and polyarylenes must adopt a planar geometry in the ionized state to form quinoid-like segments, steric factors that limit the ability of the polymer to adopt geometries which are planar with respect to adjacent rings have a detrimental effect on the electronic properties (181). 

The reaction occurs within 10 s of excitation. It is believed that the first step after excitation is attainment of a planar geometry, which occurs within 10 s. The planar geometry optimizes the orientation of the orbitals for the pericyclic ring opening. ... 

Integral equations have been developed for inhomogeneous fluids. One such integral equation is that of Henderson, Abraham and Barker (HAB) [88] who assumed the OZ equation for a mixture and regarded the surface as a giant particle. For planar geometry they obtained... 

For a flash fire, the flame can be represented as a plane surface. Appendix A contains equations and tables of view factors for a variety of configurations, including spherical, cylindrical, and planar geometries. 

Penta-atomic polyhalide anions [XY4] favour the square-planar geometry (D4h) as expected for species with 12 valence-shell electrons on the central atom. Examples are the Rb+ and Cs+ salts of [C1F4], and KBrp4 (in which Br-F is 189 pm and adjacent angles F-Br-F are 90 ( 2°). The symmetry of the anion is slightly... 

Since X-ray determinations of structure were too time-consuming to be widely used in the l9-2()s and 1940s and. in addition, square-planar geometry was a comparative rarity, any paramagnetic compound, which on the basis of stoichiometry appeared to be 4-coordinate, was presumed to be tetrahedral. 

Their existence led Werner to infer a square-planar geometry for Pt. ... 

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