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Drawing the structure of polymer chains

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  1. Electronic structure of conjugated polymers This chapter is based on notes prepared by Jean-Luc Brédas, Professor at the University of Georgia. 1. From molecules to conjugated polymers: Evolution of the electronic structure 2. Electronic structure of systems with a degenerate ground state: Trans-polyacetylene Drawing the structure of polymer chains polyacetylene shorthand notation

  2. Example of a 1-dimensional system The Born interpretation of the wavefunction  Physical meaning of the wavefunction: If the wavefunction of a particle has the value (r) at some point r of the space, the probability of finding the particle in an infinitesimal volume d=dxdydz at that point is proportional to |(r)|2d  |(r)|2 = (r)*(r) is a probability density. It is always positive! Hence, if the wavefunction has a negative or complex value, it does not mean that it has no physical meaning… because what is important is the value of |(r)|2 ≥0; for all r. But, the change in sign of (r) in space (presence of a node) is interesting to observe in chemistry: antibonding orbital overlap. Node

  3. 1. From molecules to conjugated polymers: Evolution of the electronic structure 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. 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