Bipolarons in quinolinium di-tetracyanoquinodimethanide [Qn(TCNQ${)}_2$] and (N-methylphenazinium${)}_{\mathrm{x}}$(phenazine${)}_{1\mathrm{-}\mathrm{x}}$ tetracyanoquinodimethanide [(NMP${)}_{\mathrm{x}}$(Phen${)}_{1\mathrm{-}\mathrm{x}}$(TCNQ)]

Optical-absorption data have shown that Qn(TCNQ${)}_2$ and (NMP${)}_{\mathrm{x}}$(Phen${)}_{1\mathrm{-}\mathrm{x}}$(TCNQ) are semiconductors up to T=300 K, with gaps due mainly to Peierls distortion on the TCNQ chains. To explain the observed slow falloff of the Peierls gaps with temperature, there must be a small additional contribution to the gap due to the cation potential and perhaps Coulomb effects. As a result of the interchain potential, the stable soliton defects arising from electrons in excess of 0.5/TCNQ molecule are polarons rather than kinks. The stable polarons are found to consist of pairs of -(1/2)e,-(1/2)e kinks or +(1/2)e,+(1/2)e kinks, thus being bipolarons. The energy levels, creation energy, and length of the bipolarons are calculated in terms of the interchain potential ${\Delta }_e$. To obtain an approximate value for ${\Delta }_e$ the Peierls portion of the gap ${\Delta }_0$ is calculated as a function of temperature T for different ${\Delta }_e$ values and compared with the temperature variation of ${\Delta }_0$ obtained from optical absorption. To carry this out it is necessary to determine the numbers of positive and negative bipolarons as functions of T. This is done by calculating their chemical potentials and relating these to the Fermi energy. It is found that the theoretical ${\Delta }_0$(T) agrees best with experiment for a ${\Delta }_e$/$k_B$ value of ∼25 K. The energy levels of the electrons bound in a bipolaron may then be calculated. Unambiguous evidence for the presence of bipolarons is not found in the optical absorption. Consideration shows that the bipolaron absorption may be quite broad, due to structural imperfections as well as to overlap, and therefore difficult to detect.