There are a number of flora and fauna (so to speak) that emerge when discussing charges in materials. I came from the solid state and semiconductor physics side, where Pankove's excellent book Optical Processes in Semiconductors was quite helpful (and as a Dover reprint quite inexpensive).
In semiconductors, one of the first that is brought up is the exciton, where a free electron in the conduction band and a free hole in the valence band can become a bound, hydrogen-like state. This only happens at low temperatures because room temperature has more than enough thermal energy to make it fall apart. These states do not appear in a ground state calculation of the energy bands because, well, they are not in the ground state - they are an excited state, but an excited state at a lower energy than you would have expected from the ground state calculations.
Another is phonons (broadly) as elastic waves, but more specifically the optical phonon branches. These are called 'optical' because they can couple to light - the elastic wave of the phonon results in relative movement of adjacent atoms in the material so as to mechanically set up a dielectric polarization which interacts with the E&M of the photons.
Now, polymers are not bulk semiconductors like silicon. Nonetheless, the general principles apply. So lets look at what interactions there might be in polymers. As a fairly recent paper, you might start with Joel H. Bombile et al., Physical Chemistry Chemical Physics 2018 https://doi.org/10.1039/C7CP04355D. In the abstract one finds
Polarons can form when charges induce deformations of the surrounding medium, including local vibrational modes or dielectric polarization.
Conceptually this is no different from the related animals in the bulk semiconductor zoos, its just that the details of how the polymer chain deforms is a bit different. You excite an electron into an excited state from the ground state. This can deform the chain/ring/whatnot a bit. Now when you calculate the electronic structure of the deformed material you find a different energy for that excited state - that is the polaron state. It is not to be found in a ground state calculation because the ground state is not deformed in the 'right' way.
Such interactions of charge and atomic configuration are quite broad and can be found in many other situations. One example is the Bourgoin-Corbett mechanism for diffusion - changing the charge state on an atom in the lattice changes the local configuration which can enable athermal (no activation energy required) diffusion. Again, this would not be captured in a ground state calculation.
