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As the barriers between the minima corresponding to individual conformations
are sufficiently large, these conformations correspond to long lifetimes. Therefore
in recent years, electron-conformational transitions are widely used to create
molecular switching devices.
At least two types of nonlinear systems in which solitons can propagate are
known. The first one is constituted by molecular chains built from interacting
fragments, which are additionally linked by weak interactions (e.g., hydrogen
bonds), i.e., electronic and vibrational properties of the fragments in the chain do
not substantially differ from the properties of individual molecules. An example of
such a system is a chain of peptide groups connected by hydrogen bonds in a helical
protein fragment. In the peptide group intramolecular vibrational excitation with
relatively large dipole moment of transition is possible. It provides a strong
interaction between neighboring molecules, which leads to collective, rather
quickly decaying, excitation, called exciton. Another collective excitation occurs
in these molecular chains as a result of the interaction of intramolecular excitations
(vibrations) and the nonlinearity, caused by the coupling of these vibrations with
the local displacements of equilibrium positions of the molecules. Solitons are
stable entities that propagate over large distances along the chain without energy
dissipation. The second type of systems that manifest collective effects is conju-
gated polymers, such as trans-polyacetylene, in which the possibility of soliton
excitation is caused by the degeneration of the ground electronic state.
Polyacetylene (Fig.
3.22
) is a conjugated hydrocarbon (CH)
n
with the simplest
structure. It is well known that the carbon atom has four valence electrons. In
accordance with the generally accepted semiempirical notions in molecular frag-
ments such as ethylene (the main structural fragment of the polyacetylene chain),
three of them are located on four hybrid
sp
2
orbitals and form single bonds with the
neighboring hydrogen and carbon atoms situated in the same plane. These connec-
tions correspond to completely filled zones deep in the atom. The fourth valence
electron of the carbon atom (
-electron) corresponds to the wave function 2
pz
which is perpendicular to the plane of the molecule. The functions of neighboring
atoms of this type overlap, which leads to the formation of
ˀ
-orbitals. It is precisely
these delocalized electrons that determine the characteristic properties of conju-
gated molecules, while
ˀ
˃
-electrons form a rigid skeleton of the molecule and the
field in which the mobile
-electrons move. Therefore, the usual approximation for
conjugated systems is the splitting of energy into two parts:
ˀ
E
¼
E
˃
þ E
ˀ
,
where
E
˃
is the energy of the “
˃
-skeleton” of the molecule in the absence of
interaction with
ˀ
-electrons and
E
ˀ
is the energy of
ˀ
-electrons in the effective field
of the
-skeleton.
Polyacetylene exists as two isomers: trans-(CH)
n
and cis-(CH)
n
(Fig.
3.22
).
While performing quantum-mechanical calculations it is usually assumed that
equal distances between CH groups correspond to the trans-(CH)
n
skeleton,
whereas alternation of
˃
˃
-
bonds takes place in the cis-(CH)
n
. This follows primarily