Bond Alternation in Heterocyclic Ring Systems

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.