Abstract
IN a recent communication Davies1 has made an interesting extension of Longuet-Higgins and Salem's treatment2 of bond alternation to the case of mono-cyclic ring compounds of the type (AB)n such as the phosphonitrilic halides. The total energy is separated into ζ- and π-parts: E = Eζ + Eπ. He shows that:
for ‘homomorphic’ systems3, where the combining orbitals on A and B have the same site symmetry, and that: 
for ‘heteromorphic’ systems, where the site symmetries are different4. 
The following symbols have been used in equations (1) to (4) : alternate bonds are of length r1 = r0 + x, r2 = r0 − x; the resonance integral is5: 
(note that we write a where ref. 2 has 1/a); δ is the difference between the Coulomb integrals for atoms A and B; and l takes the values 0, ±1, … ± (m − 1),m, where m = ½n for n even, and m = ± ½ (n − 1) for n odd. Furthermore6: 
where f(r) is the energy of one ζ-bond. Davies stated1 that Eπxx is finite whatever n, and he concluded that : (a) for the infinite heterocyclic polyene, the stable configuration always has equal bonds, whatever the value of δ (other than zero); (b) for the finite polyene, and for sufficiently small δ, there may be a critical value of n below which bond alternation should occur.
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References
Davies, D. W., Nature, 194, 82 (1962).
Longuet-Higgins, H. C., and Salem, L., Proc. Roy. Soc., A, 251, 172 (1959).
a, Craig, D. P., Proc. and Disc. Kekulé Symposium, 21 (Butterworths, 1959); b, J. Chem. Soc., 997 (1959).
See also Dewar, M. J. S., Lucken, E. A. C., and Whitehead, M. A., J. Chem. Soc., 2423 (1960).
Functional forms for β(r) and P(r) different from those chosen in ref. 2 do not affect the main conclusions of the theory (Haigh, C. W., to be published).
Davies, quoting Coulson, ref. 7, wrote ∂2Eσ/∂x2 = nf″; but the latter wrote ∂2Eσ/∂r12 = nfn″, without assuming r1 + r2 = 2r0.
Coulson, C. A., Tetrahedron, 12, 393 (1961).
Salem, L., and Longuet-Higgins, H. C., Proc. Roy. Soc., A, 255, 435 (1960).
Lennard-Jones, J. E., and Turkevich, J., Proc. Roy. Soc., A, 158, 301 (1937).
See Gouterman, M., and Wagnière, G., J. Chem. Phys., 36, 1192 (1962) for C24H24 and particularly Fig. 5.
Longuet-Higgins, H. C., Proc., and Disc. Kekulé Symposium, 17 (Butterworths, 1959).
Shaw, R. A., Fitzsimmons, B. W., and Smith, B. C., Chem. Revs., 62, 275 (1962). For (PNCl2)3 we place greater reliance on Wilson, A., and Carroll, D. F., J. Chem. Soc., 2548 (1960), than on Giglio, E., Ricerca Sci., 30, 721 (1960).
Chapman, A. C., and Paddock, N. L., J. Chem. Soc., 635 (1962). Chapman, A. C., quoted in ref. 16c.
The use of more recent bond-lengths [see, for example, Coulson, C. A., and Golebiewski, A., Proc. Phys. Soc., A, 78, 1315 (1961) does not affect these figures.
Longuet-Higgins, H. C., and Salem, L., Proc. Roy. Soc., A, 257, 445 (1960).
a, Craig, D. P., Heffernan, M. L., Mann, R., and Paddock, N. L., J. Chem. Soc., 1376 (1961), especially Table 1, and Fig. 1. b, Cruickshank, D. W. J., J. Chem. Soc., 5501 (1961). c, Craig, D. P., and Paddock, N. L., J. Chem. Soc, 4118 (1962).
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HAIGH, C., SALEM, L. Bond Alternation in Heterocyclic Ring Systems. Nature 196, 1307–1309 (1962). https://doi.org/10.1038/1961307a0
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DOI: https://doi.org/10.1038/1961307a0
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