  The study is devoted to elaboration of an alternative image of conjugation in
acyclic polyenes as a weak and essentially local delocalization of
initially-localized pairs of electrons ascribed to individual double bonds
(instead of formation of a completely delocalized electron system as usual). To
this end, polyenes are modelled as sets of weakly interacting formally-double
bonds, where the single bonds represent the interaction between the former and
are treated as a perturbation. Mathematically, the above-formulated goal is
realized by means of a particular version of the non-canonical method of
molecular orbitals (MOs) based on the Brillouin theorem and yielding the
expressions both for total energies and for non-canonical (localized) MOs
(NCMOs) directly without any reference to usual (canonical) MOs. In addition,
total energies and NCMOs are interrelated explicitly in the approach applied,
viz. the former are representable via the so-called delocalization coefficients
of the latter. Adaptation of these general results to the above-specified model
of polyene yields coincidence between the conjugation energy (CE) and the total
delocalization energy of all pairs of electrons contained. Moreover, a local
relation follows between constitution of the nearest environment of a certain
bond, delocalization pattern of the respective pair of electrons and
contribution of just this pair to the total CE of the given polyene. As a
result, different stabilities of distinct polyenes (e.g. of isomers) prove to
be accompanied by variable extents of delocalization of separate pairs of
electrons. Linear and cross-conjugated polyene chains are comparatively
analyzed.
