Excitable structure

To solve this we first neglect entirely the second and third excited structures. We then solve the secular equation, which is now only a cubic, and evaluate the ratio of the coefficients, a b c. Finally, we assume that this same ratio holds in... 

It will be noticed that the singly excited structures contribute somewhat over 30 percent to the total resonance energy instead of only about 20 percent as in benzene. The doubly and triply excited structures, however, make only a very small contribution. 

The principal source of inaccuracy in the treatment given the free radicals is the neglect of all excited structures. In the case of benzene the three excited structures contribute 0.2055a to the resonance energy, which is about 20 percent... 

It is probable that the errors introduced by the neglect of all except unexcited and first-excited structures and by equating /3 and /S to a cancel each other to a considerable extent, especially for more complicated molecules than the dihydro-... 

The secular equation for 1,2-dihydroanthracene resulting from the consideration of (I) the symmetrical unexcited structure, (II) the two unsymmetrical unexcited structures, (III) the sixteen first-excited structures not involving conjugation of the double bond and the naphthalene nucleus, and (IV) the six first-excited structures involving this conjugation, is... 

In Table III are given calculated values of the resonance energy for straight conjugated chains containing two, three, and four double bonds and a branched chain with three double bonds (the list could be easily extended). In each case the secular equation was solved as a quadratic, all first-excited structures being given the same... 

System Number of first-excited structures Resonance energy... 

Conjugated Benzene Rings For biphenyl we consider four unexcited structures, twelve first-excited structures not involving conjugation, and nine involving conjugation, as shown in Fig. 4. These lead to the secular equation... 

For ortho, meta, and para diphenylbenzene we consider eight unexcited structures of the type indicated by the letter A in Fig. 5, thirty-six first-excited structures of type B, and thirty-six of type C, in which there is conjugation with the central ring. This includes all first-excited structures for m-diphenylbenzene. For ortho and para diphenylbenzene, however, there are in addition nine first-excited structures of type D, in which the two end rings are conjugated together. The secular equation for the ortho compound is... 

For 1,3,5-triphenylbenzene, with 16 unexcited, 96 unconjugated first-excited, and 108 conjugated first-excited structures, the secular equation is... 

Similar prediction can be made for larger molecules. It must be pointed out that the contributions of excited structures become important for bonds with small double bond character, inasmuch as in conjugated systems excited structures alone may lead to as much as 20% double bond character it is probable that the maximum carbon-carbon bond distance in aromatic hydrocarbons is about 1.46 A., the minimum being the double bond distance 1.38 A. 

Furan, Pyrrole, and Thiophene.-—The carbon-heteroatom distances found in furan, pyrrole, and thiophene correspond to 5 = = 5%, 12 = = 6%, and 17 = = 10% double-bond character, respectively. Resonance of the normal structure I with structures of the types II and III (X = O, NH, S) is assumed to be responsible for this double-bond character, while excited structures characteristic... 

Zhuravskii, S. G., Aleksandrova, L. A., Ivanov, S. A., Sirot, V. S., Lopotko, A. I., and Zhloba, A. A. (2004b). Protective effect of carnosine on excitable structures of the auditory apparatus in albino rats with acute acoustic trauma. Bull. Exp. Biol. Med. 137, 98-102. 

The versatile and rich chemistry that is exhibited by these P-N ring systems and their exciting structural features suggest that cyclophosphazenes will continue to attract a lot of attention in the coming years. 

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