Evolution of the electronic structure of cyclic polythiophene upon bipolaron doping

Electronic structures of undoped and doped cyclic polythiophene (PT) are studied using modified $\sigma$-bond compressibility model. Cyclic PT doped with odd number of bipolarons creates an aromatic polyene backbone containing (4$n$+2) $\pi$-electrons and the system is driven towards the quinoid form. Consequently, we find an insulator-metal transition for dopant concentration $\geq$ 14 mol $\%$ and a $\sim$ 0.8 eV redshift in Fermi energy at 30 mol$\%$. For even number of bipolarons, we propose here that the form having two singly occupied degenerate orbitals will be stable in a sufficiently large cyclic PT.