Skeleton expansion

Numerical calculations of the ionic spectra rely on a systematic skeleton expansion, defined via perturbation theory, with respect to the hybridization based on band states and ionic many-body states. This perturbation technique results in integral equations of the type which are usually solved... 

In most cases, the cleavage of a carbon-carbon bond causes rearrangements of the carbon skeleton Ring contraction, ring expansion, and alkyl group migration are observed under different conditions These transformations proceed in most cases in the presence of catalysts at elevated temperatures Examples where only temperature causes rearrangements will be discussed m the next section... 

Dicyano-substituted triafulvenes react with enamines to produce exclusively the cross-conjugated dicyanomethylene compounds 519, whose formation can be rationalized by a methylene bicyclo(2,l,0)pentane intermediate 51879 296 Since cyclanone enamines 520 and other cyclic enamines 522 react analogously, this C-C-insertion 237) of the triafulvene ring skeleton into the enamine C=C bond represents a versatile ring expansion mode (C + C3), which makes accessible a series of unsaturated medium-ring compounds (521/523) that are otherwise difficult to synthesize. 

This unexpected expansion of the triafulvene skeleton to a four-membered ring system presents further evidence in support of the reaction scheme of triafulvenes toward ylides 427 suggested for cyclopropenones (p. 81). 

Kametani and co-workers used a previously demonstrated ring expansion method to construct the isopavine skeleton (144,145). The method was successfully applied to the synthesis of ( )-reframidine (27) (Scheme 23) (145). Treatment of the 3-aryl-3,4-dihydroisoquinolinium iodide 115 with diazomethane furnished aziridinium iodide 116. On standing in 6 N hydrochloric acid, crude 116 underwent a one-step ring expansion-ring closure to afford ( )-reframidine in 20% yield. The same product could be obtained via benzazepine 118 depending on the reaction conditions. It has been postulated that the aziridinium iodide 116 may have formed a transitory quinonoid intermediate 117 which is attacked... 

Steroids are compounds possessing the tetracyclic skeleton of cyclopenta[a]phenan-threne (1) or a skeleton derived therefrom by one or more bond scissions or ring expansions or contractions. Natural steroids have trivial names. The nomenclature of steroids is not based on these trivial names, but on a few stereoparent hydrides that are common to many compounds. Substitutive nomenclature is used to designate characteristic groups and unsaturation. Structural modifications are expressed by appropriate non-detachable prefixes. 

These authors also showed that the indolizidine skeleton can be prepared from cyclopropyl dipolarophiles (Scheme 1.16). The cycloaddition of alkyhdenecyclo-propanes 67 with various nitrones (e.g., 68) afforded the expected isoxazolidine adducts 69 and 70, commonly forming the C(5) substituted adducts 70 (97,105-108) predominantly but not exclusively (109-111). Thermally induced rearrangement of the spirocyclopropyl isoxazolidine adduct 70 afforded the piperidinones 71 (107,108). These authors propose reaction via initial N—O bond homolysis of 70 to diradical 72 followed by ring expansion through relief of the cyclopropyl ring strain forming the carbonyl of a second diradical intermediate 73, which cyclizes to afford the isolated piperidinone 71. 

Auto-tandem hydroformylation-cyclization, catalyzed by [RhCl(cod)]2, enables expansion of the organic skeleton of unsaturated silyl enol ethers (Scheme 10). Linear aldehydes generated in the hydroformylation step subsequently undergo Rh-catalyzed, intramolecular Mukaiyama aldol addition. Bicyclic ketones are also accessible from cyclic silyl enol ethers. 

The substituted cycloheptane monoterpenes, also called tropones. Eu-carvone 60, nezukone (4-isopropyl-2,4,6-cycloheptatrienone) 61 and y-thujaplicin 62 (Structure 4.14) most probably arise by an unknown ring expansion of the cyclohexane skeleton. 

Technically the lower order contributions to HFS are produced by the constant terms in the low-frequency asymptotic expansion of the electron factor. These lower order contributions are connected with integration over external photon momenta of the characteristic atomic scale mZa and the approximation based on the skeleton integrals in (9.9) is inadequate for their calculation. In the skeleton integral approach these previous order contributions arise as the infrared divergences induced by the low-frequency terms in the electron factors. We subtract leading low-frequency terms in the low-frequency as Tnp-totic expansions of the electron factors, when necessary, and thus get rid of the previous order contributions. 

The crucial property of the integrand in Eq. (10.16), which facilitates calculation, is that the denominator admits expansion in the small parameter /i prior to momentum integration. This is true due to the inequality j 2 2 2 which is valid according to the definitions of the functions a and b. In this way, we may easily reproduce the nonrecoil skeleton integral in (9.9), and obtain once again the nonrecoil corrections induced by the radiative insertions in the electron line [32, 33, 34]. This approach admits also an analytic calculation of the radiative-recoil corrections of the first order in the mass ratio. 

BFRs work by releasing bromine free radicals when they are heated. These free radicals scavenge other free radicals that are part of the flame propagation process and thus reduce the rate of flame expansion and the extent of fire damage. Organobromine compounds are particularly well suited for this function because of the relatively low energy of the C - Br bond. When heated, these bonds break, and the relatively stable bromine free-radical is generated. The BFR s carbon skeleton is more or less irrelevant it is just a convenient way to carry the bromine atoms. Thus, most BFRs have simple carbon skeletons to which several bromine atoms are bonded. 

The microstructural kinematic variable vs for the skeleton is a 2nd order symmetric tensor with positive determinant IJS (G Sym+), that is the left microstretch, which takes into account for contractions or expansions of the large pores in the material (see [5, 6]). Instead the fluid variable /// is the volume fraction (3f, i.e., the proportion of space occupied by the fluid constituent of the body (see [9]). Therefore we have that Af = 0, because a proportion does not change for a rotation, while us (= Us) changes as a 2nd order tensor, thus As has the following components (As)al3l, = Us)aiEll3i - aii Us)1p (see, also, 3 of [3]). 

The cripowellin skeleton has been constructed by ring expansion sodium naphthalenide.98... 

Oxidation reactions on the sulfur atom of penicillins remain the most important reactivity of S-1 encountered in the literature. Penam sulfoxides and sulfones are indeed important compounds as they confer to the skeleton an ease of thiazolidine ring opening by weakening the C(5)-S(l) and S(l)-C(2) bonds (see Section 2.03.5.9) <2004CHE816>. In particular, the former constitute key intermediates in ring-expansion transformations from penams to cephems (see Section 2.03.5.9), while the latter have a special biological interest as /3-lactamase inhibitors (e.g., sulbactam, tazobactam see Sections 2.03.1, 2.03.5.2, and 2.03.12.4). Since CHEC-II(1996) covers all the aspects of these oxidation reactions on the S-1 atom of penicillins, this section focuses on the most relevant recent papers. As there is no particular change in the subject, only a few articles have been released since 1995. 

Lange, G.L., Decicco, C.P., Willson, J., and Strickland, L.A. (1989) Ring expansions of [2 + 2] photoadducts. Potential applications in the synthesis of triquinane and taxane skeletons. Journal of Organic Chemistry, 54, 1805—1810. 

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