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Fig. 3.22 Conformations
of polyacetylene
from general considerations—the symmetrical arrangement of the neighboring
hydrogen atoms with respect to carbon atoms in the trans-(CH) n and the asymmet-
rical arrangement in cis-(CH) n , which, due to steric interactions, H
H leads to a
series of shortened and elongated distances between the CH groups. A similar
conclusion may be reached on the basis of ab initio quantum-mechanical
calculations.
Soliton solutions (more precisely, topological defects) arise upon detailed con-
sideration of the electronic structure of such a system of conjugated bonds of
sufficient length. First of all, based on obvious geometric considerations, it is
easy to see that the chain of conjugated bonds of the trans-(CH) n type can exist in
two degenerate energy forms. Their interaction leads to the possibility of occur-
rence of a topological defect in the electronic structure (Fig. 3.17 ), which is one of
the elementary excitations of this conjugated system.
In 1962 Pople and Walmsley investigated this type of a defect making the simple
assumptions that the defect is localized on one CH group and that only two single
bonds surround this defect (as shown in Fig. 3.23 ) and that there are only two types
of bonds: single and double. As a result they showed that in addition to the valence
band formed by bonding orbitals and to the conduction band, formed by the
antibonding orbitals, two localized nonbonding orbitals arise that correspond to
the two defects being considered. They are situated in the middle of the gap
between the valence and the conduction band (Fig. 3.23 ).
A soliton in trans-polyacetylene is a topological defect which connects two
geometrically inequivalent configurations (A and B, Fig. 3.23 ) of the degenerate
ground state and is entirely due to this degeneration. In the long conjugated chains
different mechanisms may be responsible for the formation of defects of the soliton
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