Poly(3,4-ethylenedioxythiophene) (PEDOT) remains of great research interest, due to its current uses in organic light emitting diodes, solar cells and supercapacitors and future possible uses in batteries and brain-machine interfaces. Debate continues over the electronic properties of PEDOT and other conducting properties. By examining the PEDOT with AlCl₄^- system, which is the charge carrying anion if PEDOT is used as a battery electrode with an aluminium anode and EMIm[Cl]-AlCl₃ ionic liquid electrolyte, the study of the electronic structure of PEDOT with a small and mobile anion as a dopant is combined with insights into the behaviour of PEDOT as a battery electrode. Hybrid DFT is used to examine the atomic partial charge distribution, bond lengths, molecular orbitals and energy gap. The work adds to the modern body of evidence illustrating the shortcomings of early theoretical models based on inorganic semiconductor theory; amongst various other findings, the ends of the chain are shown to be a dominant influence on the electronic structure with no tendency for charges to co-locate by themselves. Meanwhile, the tendency for the anions to locate in particular locations indicates the presence of energy wells with a high energy barrier to anion transport, possibly explaining the voltage hysteresis observed in real life experiments on batteries of this kind.