Four-membered cycles

In the synthesis of the boron-containing four-membered cycle 26 the reaction is started by a salt elimination of type (a) followed by an intramolecular condensation... 

Each of these tin atoms acts as a Lewis acid, with two neighboring nitrogen atoms functioning as electron donors. The ten-membered ring folds up to generate a four-membered cycle bridged at the 1,3- and 2,4-positions. The structure, which can easily be deduced from high-resolution NMR spectra, is displayed in Fig. 14. 

The introduction of more bulky groups to the silicon atom and, by contrast, a decrease in steric strains at the carbon atom in betaines of the silicon series decreases the dihedral P-C-Si-S angle and shortens the + P- S nonvalent contact and S-Si bond length. A comparison of the geometric parameters for betaines 20o and 20a, q indicates explicitly a tendency for four-membered cycle closure when such changes are introduced. 

The energies of the covalent O-As and N-As bonds are higher than those of the S-As and Se-As bonds by about 25kcal/mol. This favors the closure of the strained four-membered cycles in arsonium betaines at X = O, NMe because the energy gain due to the formation of the O-As and N-As bonds overcomes the destabilization effect of formation of small cycles. The structural parameters of cycles for the compounds of the second group and cyclic isomers of the third group are presented in Table XII. 

The convergent synthesis of a range of aryl ester dendrimers with peripheral tetrathiafulvalene units was also reported (Devonport et al. 1998). The dendrimers acquire some amount of the cation-radical tetrathiafulvalene tips on reacting with iodine in solutions. Another promising material is polyphenylene dendrimers functionalized with benzophenone units. On being transformed into the potassium ketyl derivatives, the dendrimers bring forth intermolecular biradicals. These technically attractive species contain four-membered cycles that coordinatively combine two potassium cations... 

Fig. 3. The escalator structure of the three fused four-membered cycle in [Me2Si(Nt Bu)2In— Me]2(41).

Fig. 12. Five fused four-membered cycles with magnesium atoms as spiro centers and methyl bridges in the dimeric [(MeSi)(NrBu)3(AlMe2)(H)MgMe]2 (75).

In the crystal structure of guanosine 5 -phosphate 3H20 [GUANPH01] (Fig. 17.56) the free acid of the nucleotide is in the zwitterion form with N(7) pro-tonated. There is a four-membered cycle formed by two water molecules and two phosphate groups which is part of an infinite, homodromic chain. The N(l)-H and amino N(2)-H form a chelated bifurcated hydrogen bond with a phosphate oxygen, and N(2)-H is further involved in a three-center bond with another phosphate oxygen atom. 

As an example, consider a four-member cycle with a co-reactant B in the second step ... 

Example 8.6. Rate for a hypothetical cycle with quasi-equilibrium steps. Assume that the second and third steps in the four-membered cycle 8.34 are in quasi-equilibrium and the fourth step is irreversible (k = 0) ... 

Assume the second step in the four-membered cycle 8.34 is irreversible, so that X21 = 0. The Christiansen matrix then reduces to... 

Four-membered cycles with two nitrogen atoms, general review 83HC(42,2)443. 

One Nitrogen and One Oxygen Atom Four-membered cycles with one nitrogen and one oxygen atom 85S1083. 

As seen in Fig. 8, free ions are less active than ion pairs, and the higher the size of the counterion, the higher the rate constant. A similar effect is produced by the size of the cation itself the ratio between the constants of propagation rate of the ion pair and the free ion is higher for a four-membered cycle than for a three-mem-bered one with the same counterion. The counterion seems to take an active part in the transition complex whose structure is the more favorable the larger the size of participating particles becomes. 

The dimeric cyclophosphazene molecule (F3PNMe)2 contains distorted trigonal bipyramids around each of the phosphorus atoms, with an axial-equatorial orientation of the planar four-membered cycle with respect to the bipyramids. Thus, in this case the rule does not hold that fluorine atoms ould be in axial positions in trigonal bipyramids of substituted fluorophosphoranes In such a structure the PN bonds are not equivalent, with axial bond distances approximating the Schomaker-Stevenson estimate of 1.75 A. The equatorial bond distances, 1.595 A, are considerably smaller than all the other PN bond distances we are aware of. 

For the anchimeric assistance of the four-member cycle on solvolysis of a-cyclo-butylcarbinyl compounds see and for the inclusion of the cyclobutane ring... 

The experimental data could best be explained by a C2v model with a planar four-membered cycle see figure. The stmcture of this molecule can be characterized by a dynamic model in which the T1 atom moves with fairly large amplitude about its equilibrium position along trajectories lying on the surface of a sphere described by the comers of the Re04 tetrahedron. A substantial difference between the equilibrium stmcture and the effective average stmcture given in the table is expected. 

If a graph contains a single cycle, then the number of spanning trees is simply eqnal to the size of the cycle. Thus, since the graph Gj contains a four-membered cycle (see Figure 1.1), it possesses four spanning trees, denoted by ST (n = 1,2, 3,4). They are depicted in Figure 2.22, and will be ntilized later on in Section 4.17. 

Indeed, in the case of cyclopropane derivatives (a three-membered cycle) the calculations [64] using the extended Hiickel method point to the preferability of the reaction path providing for retention of configuration. In actual practice, the SN2-type reactions for the series of cyclopropane derivatives proceed at very low rates and no reliable confirmation of the retention of configuration at the carbon being attacked at the stage of kinetical control has so far been produced [60]. For the cyclobutane derivatives (a four-membered cycle), ab initio (STO-3G) calculations [65] of alternative reaction paths bear witness to the preferability of a rear-side approach with inversion of configuration. 

Organocatalytic Asymmetric Synthesis of Four-Membered Cycles 11113... 

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