Tetrahedron, inverted

In certain small-ring systems, including small propellanes, the geometry of one or more carbon atoms is so constrained that all four of their valences are directed to the same side of a plane (inverted tetrahedron), as in 98. An example is 1,3-... 

SiLLt has C2v symmetry and it exhibits an inverted tetrahedron 60 (Figure 11) the equatorial and axial lithium atoms exchange easily via a C4v symmetrical transition state, which is only 3.2 kcalmol-1 higher in energy than 60 (bond lengths in pm)118. 

The structure of a [4.2.1]propellane derivative prepared in 35-45 % yield similarly to the [4.1.1]homolog from 1-chloroquadricyclane in the presence of anthracene was also determined, again exhibiting the inverted tetrahedron phenomenon ... 

KSiHs, RbSiH3 and CsSiHs form a NaCl-type lattice KSiH3 is reported to crystallize also in an orthorhombic modification at low temperature. Ab initio calculations at the MP4/6-31G //3-21G level predict a molecular tetrahedral structure 1 for NaSiHs. An analogous structure was found for LiSiHs. However, an inverted tetrahedron 2 was calculated at the MP4SDTQ/6-31G //6-31G level of theory to be by 2.4 kcalmol more stable than 1, because of more favourable electrostatic interactions. ... 

The NMR spectral changes in fluorohectorite also indicate that a cross-linking reaction has occurred (34). In both beidelite and fluorohectorite it is suggested (33,34) that the cross-linking operates through inversion of some clay lattice tetrahedra as shown in Figure 6. hi beidelite the center of the inverted tetrahedron... 

Other strained structures include propellanes - molecules with two vicinal carbons independently connected by three separate bridges. These compounds exhibit an inverted tetrahedron at the bridge carbons, and are so reachve [21, 131] that they polymerize spontaneously or in the presence of trace impurihes (see Table 13.7). 

Figure 4. The H3 and H4 loops. Ac the center, the conical intersections are shown schematically an equilateral triangle for H3 and a perfect tetrahedron for Kt, <2p> Jid Q, are the phase-preserving and phase-inverting coordinates, respectively.

Fujita et al., [37] Stang et al., [38] and Steel et al. [39] have recently described the synthesis of MSL4 cages which are topologically analogous to a truncated tetrahedron (Fig. 9-14). These systems, which may be regarded as inverted M4L6 frame-... 

Roberge, C., Fleitz, F., Pollard, D. and Devine, P., Synthesis of optically active cyanohydrins from aromatic ketones evidence of an increased substrate range and inverted stereoselectivity for the hydroxynitrile lyase from Linum usitatissimum. Tetrahedron Asymm., 2007,18, 208. 

Back-side attack in the SN2 reaction. The S 2 reaction takes place through nucleophilic attack on the back lobe of carbon s sp3 hybrid orbital. This back-side attack inverts the carbon atom s tetrahedron, like a strong wind inverts an umbrella. 

The shape of simple carbanions as determined on the basis of a number of experiments is found to be pyramidal, similar to that of amines. The central carbon atom is sp hybridized with the unshared pair occupying one apex of the tetrahedron (if the electron pair is viewed as a substituent). These species invert rapidly at room temperature, passing through a higher energy planar form in which the electron pair occupies a p-orbital. However, when the carbanion is stabilized by delocalization, it assumes sp hybridization for effective resonance. 

Ionic surfactants with only one alkyl chain are generally extremely hydrophilic so that strongly curved and thus almost empty micelles are formed in ternary water-oil-ionic surfactant mixtures. The addition of an electrolyte to these mixtures results in a decrease of the mean curvature of the amphiphilic film. However, this electrolyte addition does not suffice to drive the system through the phase inversion. Thus, a rather hydrophobic cosurfactant has to be added to invert the structure from oil-in-water to water-in-oil [7, 66]. In order to study these complex quinary mixtures of water/electrolyte (brine)-oil-ionic surfactant-non-ionic co-surfactant, brine is considered as one component. As was the case for the quaternary sugar surfactant microemulsions (see Fig. 1.9(a)) the phase behaviour of the pseudo-quaternary ionic system can now be represented in a phase tetrahedron if one keeps temperature and pressure constant. 

This sequence of operations is actually difficult to understand without the use of a mechanical model. Follow the position of apex 1 as you first rotate 90° clockwise around the axis and then invert the new position of 1 through the center of the tetrahedron. As you can see, an equivalent and indistinguishable (if the marker 1 were not present) orientation is produced by this set of operations. 

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