1 Drawing the structure of polymer chains shorthand notation polyacetylene 6. Electronic structure of conjugated polymers This chapter is based on notes prepared by Jean-Luc Brédas, Professor at the University of Georgia 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

From molecules to conjugated polymers: Evolution of the electronic structure Electronic structure of dihydrogen H 2 When 2 hydrogen atoms approach one another, the ψ 1s wavefunctions start overlapping: the 1s electrons start interacting. To describe the molecular orbitals (MO’s), an easy way is to base the description on the atomic orbitals (AO’s) of the atoms forming the molecule → Linear combination of atomic orbitals: LCAO Note: from N AO’s, one gets N MO’s The zero in energy= e - and p + are ∞ly separated In the H atom, e - is bound to p + with 13.6 eV = 1 Rydberg (unit of energy)

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The polyene series A.Methyl Radical Planar Molecule One unpair electron in a 2p z atomic arbital → π-OA

5 B. Methylene molecule Planar molecule Due to symmetry reason, the π-levels do not mix with the σ levels (requires planarity) First optical transition: ≃ HOMO → LUMO ≃ 7 eV

6 C. Butadiene From the point of view of the π-levels: the situation corresponds to the interaction between two ethylene subunits First optical transition: ≃ 5.4 eV 1 node 0 nodes 2 nodes 3 nodes

7 Frontier molecular orbitals and structure: 1. The bonding-antibonding character of the HOMO wavefunction translates the double-bond/single-bond 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 π-levels and 3 unoccupied π*-levels

8  1 node 0 nodes 2 nodes 3 nodes 4 nodes 5 nodes ** E 4.7 eV Remarks: 1)The energy of the π-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

9 In a bonding situation, the wavefunction evolves in a much smoother fashion than in an antibonding situation 2) Geometry wise: → In the absence of π-electrons (for alkanes): 1.52 ÅAll the C-C bond lengths would be nearly equal → When the π-electrons are throuwn in: the π-electron density distributes unevently over the π-bonds: Apparition of a bond- length alternation ≃ 1.34 Å ≃ 1.47 Å

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Electronic structure of systems with a degenerate ground state: Trans-polyacetylene

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24 b) : The Soliton

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29 III. Electronic structure of systems with a non-degenerate ground state

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33 IV. Doping of conjugated polymers

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37 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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