When an electron is removed from the π system of a p-type conjugated polymer such as poly(3-hexylthiophene-2,5-diyl) (P3HT), the backbone locally changes structure from aromatic to quinoidal.  The unpaired electron that remains, along with the accompanying distorted backbone structure, are together referred to as a polaron.  In the traditional band picture borrowed from inorganic semiconductors, the creation of a polaron causes two electronic energy levels that are associated with the half-filled state to move into the band gap, creating two new allowed optical transitions, P1 and P2.  If the oxidative driving force to remove electrons is strong enough, an already-oxidized polymer segment can be oxidized again, removing the unpaired electron from the half-occupied level in the band gap.  This doubly-charged species is referred to as a bipolaron.  In the traditional band picture, this removal of a second electron causes the two intra-gap states to move further into the gap, and the resulting allowed bipolaronic optical transition, BP1, is bluer than the P1 transition of the single polaron.  Several groups, however, who looked at the Kohn-Sham orbitals and energy levels from DFT calculations, have recently argued that the traditional picture is incorrect.  Instead, the DFT calculations suggest that polaron creation causes only one unoccupied state to move into the band gap near the valence band edge while states in the conduction and valence bands bend downward in energy.  We show that the results of ultrafast transient absorption experiments are not consistent with this DFT-based picture, but instead agree well with the traditional picture.  To understand the discrepancy, we performed TD-DFT calculations with long-range corrected functionals.  Not only does  the TD-DFT calculated absorption spectrum matches with the experimental absorption spectrum, but we were also able to reproduce the traditional band picture using natural transition orbitals (NTOs).  We are also able to explain the electronic structure of bipolarons with TD-DFT, something that was not possible with traditional DFT calculations.

Electronic structure of doped conjugated polymers: TD-DFT vs. DFT

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