Cyclic chains

In the case of (HCN), Kofranek et al. found the threshold of conversion of linear to cyclic, on energetic grounds, to occur at approximately n = 4. The linear trimer is favored over the cyclic by 2.1 kcal/mol, but the latter tetramer is more stable than the linear by 0.1 kcal/mol, again at the SCF/[53/3] level. 

Kurnig et al. reexamined the relative stabilities of the linear and cyclic trimers, motivated by experimental indications that two conformers coexist . They included correlation via the ACPF method which they consider equivalent in this case to CPF, along with a basis set of [321/31] quality. Their results in Table 5.6 show that the linear trimer is more stable than the cyclic by 2 kcal/mol, with respect to binding energy at the SCF level, but this difference is reduced to 0.7 with correlation included. Including zero-point vibrations and other corrections yields the AH° data in the last row which nearly mirror the trends in AE. Given the errors which remain at this level of calculation, the calculated preference for the linear trimer by 0.5 kcal/mol in AH° was not considered by the authors as definitive, and the smallness of this quantity accounted for the presence of both geometries in the experiments. 

For periodic boundary conditions eqn (3.1) with J = 0 is diagonalized by the Bloch transforms, 

Since = Nk, namely the number operator, we see that H is diago- 

Equation (3.11) is the one-dimensional tight-binding band structure, shown in Fig. 3.1.  

We may construct the Bloch functions by recalling from Section 2.4 that the creation operator creates an electron with spin a in the 7r-orbital localized on the nth site. Thus, projecting the Bloch state, A ), onto the coordinate representation, r), we have the Bloch function. 

For readers not familiar with the second quantization approach. Appendix A describes a first quantization representation and solution of the eqn (3.1). 

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The cyclic conjugation is continuous if the donors are on one side of the cyclic chain and the acceptors are on the other side (Scheme 14a). Electrons delocalize from a donor Dj to Aj. The electron accepted by Aj can readily delocalize to the neighbor on the other side because it is an acceptor (A ). An electron can delocalize from D, to A. The delocalization can take place along the other path. donates an electron to A. The resulting electron hole in can be supplied with an electron by the neighbor Dj. This is equivalent to the delocalization from Dj to A. Electrons can delocalize in a cyclic manner. Thermodynamic stability of continuously conjugated molecules is under control of the orbital phase property or determined by the number of n electrons. 

Cyclic conjugation is continuous in o-benzoquinone and discontinuous in p-benzoquinone (Scheme 15, cf. Scheme 4). The donors (the C=C bonds) are on one side of the cyclic chain and the acceptors (the C=0 bonds) are on the other side in o-benzoquinone. In p-benzoquinone the donors and the acceptors are alternatively disposed along the chain. The thermodynamic stability of o-benzo-quinone is under control of the orbital phase property. The continuity conditions are not satisfied. o-Benzoquinone is antiaromatic. The thermodynamic stability of p-benzoquinone is free of the orbital phase (neither aromatic nor antiaromatic) and comes from the delocalization between the four pairs of the neighboring donors and acceptors. In fact, p-benzoquinone, which melts at 116 °C, is more stable than o-benzoquinone, which decomposes at 60-70 °C. 

According to the theory of cyclic conjugation, the Hueckel rule is applicable only to a continuous cyclic conjugation, but not to a discontinuous one (Schemes 14 and 15). In the discontinuously conjugated molecules, electron donors and acceptors are alternately disposed along the cyclic chain [25].The thermodynamic stability depends neither on the number of n electrons nor the orbital phase properties, but on the number of neighboring donor-acceptor pairs. Chemical consequences of the continuity-discontinuity of cyclic conjugation are reviewed briefly here. 

Almost all known inorganic heterocychc molecules, where N, O and S atoms with lone pair orbitals are donors while B atoms with vacant p orbitals are acceptors, are classified into discontinuous conjugation. The donors and the acceptors are alternately disposed along the cyclic chain. The thermodynamic stabilities are controlled by the non-cycUc electron delocalization or by the number of neighboring donor-acceptor pairs, but not by the number of % electrons [83]. In fact, both 4n % and 4n + 2% electron heterocycles are similarly known [84,85] (Scheme 33), contradicting the Hueckel rule. 

With one more N-B bond, the cyclic conjugation is discontinuous in 1,3,2,4-diaza-diborine. The donors and acceptors are alternately disposed along the cyclic chain. Electrons cannot effectively delocalize in a cyclic manner, but between the adjacent donor-acceptor pairs in a non-cyclic manner. The diazadiborine is not predicted to be aromatic. 

The cohesive energy per carbon atom in a poly-yne ring is only 99.1 kcal/mol, clearly lower than the value in Cc. Anticipating a long and complicated route of formation when starting from graphite, in does not seem likely that any of the larger clusters observed experimentally would have a linear or cyclic chain structure. 

Cyclic Chain Termination in Oxidation of Organic Compounds... 

Cyclic Chain Termination by Aromatic Amines and Aminyl Radicals... 

Transition Metal Ions as Catalysts for Cyclic Chain Termination References... 

The a-aminoalkylperoxyl radicals RCH(00 )NHR possess a dual reactivity oxidative (due to the peroxyl group) and reducing (due to the amino group) [5]. As a result, many antioxidants terminate the chains of oxidized amines by the mechanisms of cyclic chain termination (see Chapter 16). 

Cyclic chain termination by antioxidants. Oxidation of some substances, such as alcohols or aliphatic amines, gives rise to peroxyl radicals of multiple (oxidative and reductive) activity (see Chapters 7 and 9). In the systems containing such substances, antioxidants are regenerated in the reactions of chain termination. In other words, chain termination occurs as a catalytic cyclic process. The number of chain termination events depends on the proportion between the rates of inhibitor consumption and regeneration reactions. Multiple chain termination may take place, for instance, in polymers. Inhibitors of multiple chain termination are aromatic amines, nitroxyl radicals, and variable-valence metal compounds. 

CYCLIC CHAIN TERMINATION BY AROMATIC AMINES AND AMINYL RADICALS... 

On the basis of these results, the following general mechanism was suggested for the cyclic chain termination by inhibitor InH in oxidized alcohol [3] ... 

The oxidation of primary and secondary alcohols in the presence of 1-naphthylamine, 2-naphthylamine, or phenyl-1-naphthylamine is characterized by the high values of the inhibition coefficient / > 10 [1-7], Alkylperoxyl, a-ketoperoxyl radicals, and (3-hydroxyperoxyl radicals, like the peroxyl radicals derived from tertiary alcohols, appeared to be incapable of reducing the aminyl radicals formed from aromatic amines. For example, when the oxidation of tert-butanol is inhibited by 1-naphthylamine, the coefficient /is equal to 2, which coincides with the value found in the inhibited oxidation of alkanes [3], However, the addition of hydrogen peroxide to the tert-butanol getting oxidized helps to perform the cyclic chain termination mechanism (1-naphthylamine as the inhibitor, T = 393 K, cumyl peroxide as initiator, p02 = 98 kPa [8]). This is due to the participation of the formed hydroperoxyl radical in the chain termination ... 

Organic acids retard the formation of nitroxyl radicals via the reaction of the peroxyl radical with the aminyl radical [10], Apparently, the formation of a hydrogen bond of the >N H0C(0)R type leads to the shielding of nitrogen, which precludes the addition of dioxygen to it, yielding the nitroxyl radical. Thus, the products of the oxidation of alcohols, namely, acids have an influence on the mechanism of the cyclic chain termination. 

As noted above, the duration of the retarding action of an inhibitor is directly proportional to the / value. In systems with a cyclic chain termination mechanism, the / coefficient depends on the ratio of the rate constants for two reactions, in which the inhibitor is regenerated and irreversibly consumed. In the oxidation of alcohols, aminyl radicals are consumed irreversibly via the reaction with nitroxyl radical formation (see earlier) and via the following reaction [11] ... 

Table 16.1 presents the inhibition coefficients / and the termination rate constants kn in systems with the cyclic chain termination mechanism with aromatic amines. Naturally, these are apparent rate constants, which characterize primarily the rate-limiting step of the chain termination process. 

The question why the aminyl radicals ensure cyclic chain termination in those systems in which the hydroperoxyl and hydroxyalkylperoxyl radicals are formed, but not in the oxidation of hydrocarbons where alkylperoxyl radicals are the chain-propagating species deserves special attention [22 24]. Indeed, the disproportionation of the aminyl and peroxyl radicals... 

Cyclic chain termination with aromatic amines also occurs in the oxidation of tertiary aliphatic amines (see Table 16.1). To explain this fact, a mechanism of the conversion of the aminyl radical into AmH involving the (3-C—H bonds was suggested [30]. However, its realization is hampered because this reaction due to high triplet repulsion should have high activation energy and low rate constant. Since tertiary amines have low ionization potentials and readily participate in electron transfer reactions, the cyclic mechanism in systems of this type is realized apparently as a sequence of such reactions, similar to that occurring in the systems containing transition metal complexes (see below). 

At the same time, quinones do not practically retard oxidation of hydrocarbons, since alkyl radicals react very rapidly with dioxygen (see Chapter 4) to give alkylperoxyl radicals, which scarcely react with quinones. Quinones exhibit their inhibiting properties as alkyl radical acceptors only in the oxidation of polymers (see Chapter 19). However, quinones were found to decelerate the oxidation of alcohols very efficiently and for long periods by ensuring cyclic chain termination via the following reactions [31-34] ... 

The cross-disproportionation of nitroxyl and hydroperoxyl radicals is an exothermic reaction. For example, the enthalpies of disproportionation of TEMPO radical with H02, Me2C(0H)02, and cydo-C(,Y 10(OH)O2 radicals are equal to 109, —92, and 82 kJ mol-1, respectively. The Ee0 value for the abstraction of an H atom from the O—H bond in ROOH by a nitroxyl radical is 45.6 kJ mol 1 and AHe min = —58 kJ mol-1. Since AHe < AHe min, (see Chapter 6), the activation energy of such exothermic reactions for these reactions is low (E 0.5RT), and the rate constant correspondingly is high [31 34]. Therefore, in the systems in which hydroperoxyl, hydroxyperoxyl, and aminoperoxyl radicals participate in chain propagation, the cyclic chain termination mechanism should be realized. 

The reaction of AmO with H02 occurs with AH < A//c min and, subsequently, with a low activation energy (E=0.5RT) and a high rate constant. The latter is higher than 2kt for peroxyl radicals (see Chapter 6), which is important for cyclic chain termination. The inverse situation takes place in reactions of nitroxyl radical disproportionation with alkylperoxyl radicals. For these reactions we observe inequality AH > A//c min and, subsequently, relatively a high activation energy (E> 0.5RT) and a low rate constant. The latter are lower than 2kt for... 

Why are the activation energies of the reactions of nitroxyl radicals with O—H bonds lower than those in their reactions with C—H bonds As in the case of the reaction of R02 with quinones, the difference in E values occurs as a result of the different triplet repulsions in TS [23]. When a TS of the O H O type is formed (the AmO + H02 reaction), the triplet repulsion is close to zero because the O—O bond in the labile compound AmOOH is very weak. Conversely, the triplet repulsion in the reaction of AmO with the C—H bond is fairly great, due to the high dissociation energy of the AmO—R bond. This accounts for the difference between the activation energies and between the rate constants for the reactions considered above. Thus, the possibility of the realization of a cyclic chain termination mechanism in the reactions of nitroxyl radicals with peroxyl radicals, incorporating O—H groups, is caused by the weak triplet repulsion in the TS of such disproportionation reactions... 

Thus, nitroxyl radicals can participate in various cyclic mechanisms of chain termination. Additional information about cyclic chain termination is described in Chapter 19. 

If the hydrogen peroxide concentration is large, the exchange reaction between R02 and H202 occurs rapidly, and this reaction becomes the rate-limiting stage of cyclic chain termination. 

Recently an analogous mechanism for cyclic chain termination has been established for quinones [47], Quinones, which can act as acceptors of alkyl radicals, do not practically retard the oxidation of hydrocarbons at concentrations of up to 5 x 10 3 mol L 1, because the alkyl radicals react very rapidly with dioxygen. However, the ternary system, /V-phenylquinonc imine (Q) + H202 + acid (HA), efficiently retards the initiated oxidation of methyl oleate and ethylbenzene [47]. This is indicated by the following results obtained for the oxidation of ethylbenzene (343 K, p02 = 98 kPa, Vi = 5.21 x 10-7 mol L 1 s 1). 

TRANSITION METAL IONS AS CATALYSTS FOR CYCLIC CHAIN TERMINATION... 

The superoxide ion is a very weak hydrogen atom abstractor, which cannot continue the chain, and is destroyed via disproportionation with any peroxyl radical. So, the studies of the mechanisms of cyclic chain termination in oxidation processes demonstrate that they, on the one hand, are extremely diverse and, on the other, that they are highly structurally selective. The 20 currently known mechanisms are presented in Table 16.6. 

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