Poly cycle

TABLE 12. Poly cycles through benzocyclobutene ring opening... 

If an (r, ) poly cycle P is finite, then it has a single boundary and Aut(P) is a dihedral group consisting only of rotations and mirrors around this boundary. So its order divides 2r, 4, or 2q, depending on what Aut(P) fixes the center of an r-gon, the center of an edge, or a vertex. 

We have seen in Section 4.5 a full classification of (3, 3)gen, (3,4)gen-, and (4, 3)gen-polycycles. We have also seen that, for all other (r, q), there is a continuum of (r, )-poly cycles. The purpose of this chapter is to introduce a decomposition of polycycles into elementary components in an analogous way to decompose the molecules into atoms. This method will prove to be very effective but only in the elliptic case, since, for all other cases, we will show that there is a continuum of such elementary components (see Theorem 7.2.1). The first occurrence of the method is in [DeSt02b], followed by [DDS05b] and [DDS05c]. 

A (5, 3)-polycycle is called O-elementary if it is elementary and if its boundary sequence is of the form 22391... 223 . By inspection of the list of finite elementaiy (5, 3)-poly cycles (see Figure 7.2), we obtain that there are exactly three O-elementary polycycles Ei, Cu and C3. 

If G is a ( 5, b, 3)-map that is bR, then we remove all its b-gonal feces and obtain a (5,3)ge -polycycle. This (5,3)ge -polycycle is decomposed into elementaiy (5,3)ge,r poly cycles along bridges (see Chapter 7 for definition of those notions). In this chapter a bridge is an edge, which is not contained in any b-gonal face but whose two vertices are contained into different b-gonal faces. 

All the reactions may involve attack of a phenylsilyl radical formed upon irradiation on C6o to give the radical intermediate as shown in Scheme 53. There is probably a rapid equilibrium between this radical and the cyclohexadienyl radical. The product ratio depends on the relative rates of recombination with the other silicon radical produced initially. Bulky phenylalkylsilyl radicals react preferentially at the 16-position of the C6o poly cycle in the initially formed radical. In contrast, trimethylsilyl and silylsilyl radicals prefer the cyclohexadienyl ring. 

For, example, joining azo groups into are rigid carbon poly cycle, such as in bis (diazenes) N1 and N2. These proximate, parallel in-plane preoriented bis(diazenes) were synthesized by the Prinzbach group are candidates for lacking N=N/N=N photocycloadditions. Thett-tt distances (d) are equal to approximately 280 pm and the nitrogen lone pairs are unable to interact because of steric reasons. On the other hand, an efficient overlap of the p orbitals is enforced. 

Abu-Shanab, F. A., Wakefield, B. J., Elnagdi, M. H., Methylpyridines and Other Methylazines as Precursors to Bicycles and Poly cycles, 68, 181. 

The cubane-hke Ge compound [GeN-f-Bu]4 (3) has been obtained as a crystalline sublimable solid by the reaction shown in Scheme I.i5,i6,25 jjjg related cage stmcture of Ge3(N-f-Bu)2(HN-f-Bu)2 consists of a Ge N cube with one comer vacant this open poly cycle can be protonated by HCl to form [Ge3(N-f-Bu)(HN-f-Bu)3]Cl, in which Cl effectively occupies the vacant comer, interacting with the protons on three N atoms of the cube. 

Cryptands are macro-bi- or -poly-cycles able to encapsulate an ion by providing it higher protection because of their cagelike structures, as in (147) and (148). For these ligands the correspondence between cavity size and complex stability is more pronounced than for simple crown ethers. Recent approaches to improve the metal-ion selectivity of cryptands, as for example by replacement of ethylene units between each donor atoms with propylene units, or by insertion of several substituents into the macrocycles, have been reviewed.245 A new, interesting family of cryptands is constituted by borocryptands (149), which are useful receptors for chiral substrates, where enantiomeric differentiation can be achieved by using NMR spectroscopy.246... 

The photophysical properties of polyacene molecules depend markedly on the number of rings and the fluorescence behaviour of hexacene has now been compared with that of earlier members of the series. A similar comparison has been made of the photophysical properties of catacondensed aromatic poly-cycles. Fluorescence from an upper-excited singlet state has been described for benz[a]azulene derivatives while the fluorescence properties of some antiaromatic molecules have been described in detail. Several thiopyrylium and pyrylium salts have been studied and the effects of various substituents attached to the heterocycle have been examined in terms of the triplet yield. A full evaluation of the photophysical properties of 4-aminonaphthalimide, and its... 

Figure 8 An example ofKasteleyn s odd orientation of a planar poly cycle...

Before dreaming up improved ways to synthesize graphene nanoribbons and their precursors, another synthetic cmicept must be introduced, and that is cyclodehydrogenation of non-planar ohgo- and polyphenylenes towards graphene-like benzenoid poly cycles. This reaction has played an important role in our search for graphenes and, like the above transformations, has served as a key tool in fabricating 2D polymers. 

Recently, Wang and Lee developed a series of reactions involving the ethylenediamine diacetate-catalyzed reactions for the highly efficient synthesis of the biologically interesting poly cycles bearing citran [118], They successfiiUy applied these cyclization reactions to the synthesis of three... 

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