Drawing the structure of polymer chains

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6. Electronic structure of conjugated polymers
This chapter is based on notes prepared by
Jean-Luc Brédas, Professor at the University of
Georgia. 6.1. From molecules to conjugated
polymers Evolution of the electronic
structure 6.2. Electronic structure of systems
with a degenerate ground state
Trans-polyacetylene 6.3. Electronic structure of
systems with a non-degenerate ground state 6.4.
Doping of conjugated polymers
Drawing the structure of polymer chains
polyacetylene
shorthand notation
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6.1. From molecules to conjugated polymers
Evolution of the electronic structure
6.1.1. Electronic structure of dihydrogen H2
The zero in energy e- and p are 8ly
separated In the H atom, e- is bound to p with
13.6 eV 1 Rydberg (unit of energy)

• When 2 hydrogen atoms approach one another, the
  ?1s wavefunctions start overlapping the 1s
  electrons start interacting.
• To describe the molecular orbitals (MOs), an
  easy way is to base the description on the atomic
  orbitals (AOs) of the atoms forming the molecule
• ? Linear combination of atomic orbitals LCAO
• Note from N AOs, one gets N MOs

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6.1.2. The polyene series

• Methyl Radical

• Planar Molecule
• One unpair electron in a 2pz atomic arbital ?
  p-OA

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• B. Methylene molecule
• Planar molecule

• Due to symmetry reason, the p-levels do not mix
  with the s levels (requires planarity)

• First optical transition ? HOMO ? LUMO ? 7 eV

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C. Butadiene

• From the point of view of the p-levels the
  situation corresponds to the interaction between
  two ethylene subunits

• First optical transition ? 5.4 eV

3 nodes
2 nodes
1 node
0 nodes
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Frontier molecular orbitals and structure 1.
The bonding-antibonding character of the HOMO
wavefunction translates the double-bond/single-bon
d character of the geometry in the groundstate
2. The bonding-antibonding character is completly
reversed in the LUMO
The first optical transition (? HOMO to LUMO)
will deeply change the structure of the molecule
D. Hexatriene 3 interacting ethylene
subunits ? 3 occupied p-levels and 3 unoccupied
p-levels
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5 nodes
E
4 nodes
?
3 nodes
4.7 eV
2 nodes
1 node
?
0 nodes

• Remarks
• The energy of the p-molecular orbitals goes up as
  a function of the number of nodes
• ? This is related to the kinetic energy term in
  the Schrödinger equation this is related to the
  curvature of the wavefunction

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In a bonding situation, the wavefunction evolves
in a much smoother fashion than in an antibonding
situation
2) Geometry wise ? In the absence of
p-electrons (for alkanes)
1.52 Å All the C-C bond lengths would be nearly
equal
? When the p-electrons are throuwn in the
p-electron density distributes unevently over the
p-bonds
Apparition of a bond-length alternation
? 1.34 Å ? 1.47 Å
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5.2. Electronic structure of systems with a
degenerate ground state Trans-polyacetylene
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b)
The Soliton
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III. Electronic structure of systems with a
non-degenerate ground state
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IV. Doping of conjugated polymers
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Both the charged soliton and the polaron
participate to the conduction. Based on that,
Sven Stafström will explain the metallic state of
the trans-polyacetylene
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