Electronic Energy Gaps for π-Conjugated Oligomers and Polymers Calculated with Density Functional Theory

In varying contexts, the terms "energy gap" (energy difference) or "band gap" may refer to different experimentally observable quantities or to calculated values that may or may not represent observable quantities. This work discusses various issues related to calculations of electronic energy gaps for organic π-conjugated oligomers and linear polymers by density functional theory (DFT). Numerical examples are provided, juxtaposing systematic versus fortuitous agreement of orbital energy gaps with observable fundamental (ionization vs electron attachment) or optical (electronic excitation) energy gaps. Successful applications of DFT using nonempirically tuned hybrid density functionals with range-separated exchange (RSE) for calculations of optical gaps, fundamental gaps, and electron attachment/detachment energies are demonstrated. The extent of "charge-transfer like" character in the longest-wavelength singlet electronic excitations is investigated.