Six-Electron Systems

A. Sherman and H. Eyring (J. Am. Chem. Soc. 54, 2661 (1932)) have published matrix elements for this six-electron system, giving the Coulomb and single exchange integrals. Their coefficients do not show the regularities which our treatment leads to, since their five functions do not form a canonical set. 

During the reaction, the diene ring loses an H atom or an R radical and is now to be considered as a neutral five-electron donor or an anionic six-electron system. 

Experimental evidence for the six electron systems has been described in Sect. 2.1.4. Skancke reproduced the relative stabihty of the cross conjugated systems relative to the linear isomers by calculating the trimethylenemethane and buta-l,4-diyl dianions [27] and their dilithio salts [28]. For the four electron systems butadiene is more stable than trimethylenemethane. Experimental examination of the relative stabihties of two electron systems using the trimethylenemethane and buta-14-diyl dications needs to overcome the intrinsic instabihties of dications dissatisfying the octet rule. 

The Mg + dicadon [42] with AN+2 (N= 1) valence electrons has a stable structure in agreanent with the rule, but this is a local energy minimum. The linear structure is more stable because it minimizes the Coulomb repulsion. This is in contrast to the tetrahedral stmcture of the Li dication with two electrons (N= 0). The six electron systems caimot form closed-shell structures in the tetrahedron, but the two electron systems can do. 

Also the a-n interaction in Diels-Alder additions, which occurs with sy -fashion with regard to both diene and dienophile, is explained (Fig. 7.38). For the first place, the p-a type interaction is allowed, by the selection rule already mentioned, between the jr-part of butadiene and the ji-part of ethylene. Once this weak p-a type interaction starts, the p AO part forms a six-electron system. The HO of this -part will come from HO of butadiene jr-part interacting with LU of ethylene jr-part will interact with er-LU s of both butadiene and ethylene. The mode of interaction is as indicated in Fig. 7.38. 

Bivalent tin compounds can easily be transformed to fourvalent tin compounds by oxidizing agents. Mechanistically, this reaction can be understood as an insertion of a six-electron system into a two-electron bond, resulting in a tetrahedrally tetra-coordinated tin atom. This process is often also regarded as an oxidative addition, a distinction being made between additions to a-bonds and to it-bonds. 

Quantum mechanical considerations predict that a jr-electron system containing six electrons should be particularly stable.205 Examples of conspicuously stable six electron systems are benzene and the cyclopentadienyl anion. The cycloheptatrienylium cation is also stable, presumably for the same reason.206-207... 

As an example of a six-electron system, trans-trans-octa-2,4,6- triene illustrates the opposite sense of the stereochemical nature of the thermal and photochemical reactions ... 

The real reactions that most resemble these are the production of cyclobutane from two ethylene molecules ((112)2) and the Diels-Alder reaction between butadiene and ethylene ((H2)3). Even these cannot be made to react in the bare forms, but fairly simple activation by substituents will allow the (H2)3 analog to proceed. Apparently, no form of the (1 2)2 analog has ever been observed. Our analysis suggests that there is a fundamental difference between the four-electron and six-electron systems that produces the effect. The book by Woodward and Hoffrnan[58] may be consulted for a rationalization of these results based upon MO theory. 

Since we would assume that for a six-electron system like Bea an MRCI calculation should reproduce the result of a full Cl calculation, we initially reasoned as follows. If CCSD(T) is in excellent agreement with MRCI (and hence presumably with the exact iV-particle space treatment) there are two possibilities. First, it may be that the only thing missing from the CCSD treatment was the connected... 

Electrocyclic closure of both pentadienyl cation and anion have been observed. Cations generated by protonation of dienones close in the predicted conrotatory manner as shown in Equation 12.55.99 The pentadienyl anion, a six-electron system, should close in the disrotatory sense a clear example is the rapid isomerization illustrated in Equation 12.56.100 Photochemical cyclization of pentadienyl cations has been observed Equation 12.57 shows an example in a cyclic system.101 The ready thermal reversion, which should be conrotatory and therefore difficult in the bicyclic system, may possibly occur by a stepwise path.102... 

The example just cited provides a verification of the prediction that the excited-state reactions should be conrotatory for six-electron systems. The prototype octatriene-cyclohexadiene interconversion (Equation 12.64) shows the same pattern.117 The network of photochemical and thermal electrocyclic reactions connected with the formation of vitamin D provide several further examples.118... 

Houk and co-workers calculations16 indicate that in the electrocyclic ring openings of 1,2-dihydroazete, 1,2-dihydropyridine and 1,2-dihydroazocine, there is a marked preference for the outward rotation of the N-H bond for the four- and six-electron systems. No strong preference is observed for the eight-electron system. Suggest an explanation. 

It should be noted that 96 and 97 are six-electron systems and the arrangement is symmetry-allowed. 

C-2 and C-4 in the reacting LUMO, the divinyl ether is a six-electron system with antibonding between C-2 and C-4 in the reacting LUMO of the excited states species. Presumably on account of this, the divinyl ether substrate is di-ir-methane inactive. This rationalization is shown in Scheme 2. 

Comparisons of the solvolysis rates in 80 % aqueous acetone of the secondary dispiro derivatives 45 and 46 with a suitable model compound 47 revealed only small rate differences despite the possibility of cyclic conjugation involving interaction of a jr-system with a biscyclopropylcarbinyl cation Such an ion might have been anticipated to show unusual stability as a cyclic delocalized six-electron system. The product from the benzo... 

Benchmark Studies of Electron Correlation in Six-Electron Systems. 

Colchicine has one benzene ring and one aromatic seven-membered ring with six electrons (c count the electrons in the C=0 bond) as the delocalized structure makes clear. Callistephin h=j benzene ring and a two-ring oxygen-based cation, which is like a naphthalene. You can count it as cei ten-electron system or as two fused six-electron systems sharing one C=C bond, whichever you pre e ... 

Diels-Alder reactions (for example 7.1 and 7.3) are important six-electron systems which can be used synthetically. The six-membered transition state is unstrained, and the probability of both molecules colliding with the correct orientation is reasonably favourable. 

It is most important to recognise that the nitrogen lone pair in pyrrole forms part of the aromatic six-electron system. 

Among other assumptions, one considers only a single set of bonds or electron-pairing scheme when one uses (9). Therefore, it is best applied to frameworks for which a single covalent structure can be written. Under these conditions, it is easy to see why for a four-atom six -electron system, the order of energies is E(linear) < E(trans) < E(skew) < E(cis) ... 

In certain cases, however, it is evident from symmetry or other considerations that more than one valence-bond wave function is important. For example, for six equivalent atoms arranged at the corners of a regular hexagon the two structures I and II of Figure 46-1 are equivalent and must contribute equally to the wave function representing the normal state of the system. It can be shown that, as an approximation, the benzene molecule can be treated as a six-electron system. Of the total of 30 valence electrons of the carbon and hydrogen atoms, 24 can be considered... 

The para position loses density. For the six-electron system, excitation (note arrow A) moves density from a molecular orbital with meta density to an MO with no meta density. However, the para position gains density. 

The stability of six-electron systems of this type is an illustration of the 2 rule. This rule is based on the fact that in a... 

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