Drawing the structure of polymer chains

1. 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

2. 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 ∞ly 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 ψ1s 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

4. 6.1.2. The polyene series • Methyl Radical • Planar Molecule • One unpair electron in a 2pz 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 3 nodes 2 nodes 1 node 0 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. 5 nodes E 4 nodes * 3 nodes 4.7 eV 2 nodes 1 node  0 nodes • Remarks: • 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 Å All 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

18. 5.2. Electronic structure of systems with a degenerate ground state: Trans-polyacetylene

21. a)

24. b) : The Soliton

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

33. IV. Doping of conjugated polymers

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