The alternation of bond lengths in long conjugated chain molecules

Abstract

Ooshika (1957) has recently found, using the self-consistent molecular orbital theory, that a cyclic polyene C$_{2n}$H$_{2n}$ exhibits marked bond alternation if n is very large. Here we show that, provided $\sigma $ bond compression is taken into account, this result follows inevitably from even the simple l.c.a.o. theory, and is independent of the analytic form of either $\beta $(r), the resonance integral, or f(r), the $\sigma $ bond energy. An investigation of the linear polyenes C$_{2n}$H$_{2n+2}$ and C$_{2n+1}$H$_{2n+3}$ leads to the same conclusions, which contradict those of Lennard-Jones (1937) and Coulson (1938) but agree with those of Ooshika (1957) and Labhart (1957). A simple calculation, based on an exponential form for $\beta $(r), leads to a value of about 0$\cdot $04 angstrom for the difference in length between adjacent bonds in the infinite chain.