Keeping in view the possible applications of singlet open-shell molecules as semiconductors, non-classical derivatives of the heterocyclic rings benzobis(thiadiazole) (BBT) and its positional isomer thiadiazolothienopyrazine (TTP) are characterized using DFT methodologies. M06-2X, B3LYP and BHandHLYP functionals were used to optimize the geometries and estimate the vertical transition energies. It is observed that unlike the BHandHLYP functional (50% exchange), which gives rise to spin-contaminated solutions for all molecules in the series, M06-2X (54% exchange) affords a wavefunction either with no instability or negligible instability for most of the molecules. The results are compared with the earlier reported experimental data and those obtained herein using the spin-flip (SF)-5050 method. It is found that B3LYP does not fare well while on the other hand the M06-2X and SF-50-50 are in good agreement with the experimental results. It is seen that M06-2X TD-DFT for the molecules can be carried out without major spin contamination and also that the more time-consuming CI can be avoided for the calculation of transition energies. The biradical nature of the molecules is estimated by the singlet-triplet gap. Intramolecular charge transfer is calculated. It is found that the ring substituents donate charge in the ground state, creating a zwitterionic structure. Thus the substituents play an interesting dual role, decreasing the stability of the molecule by increasing the biradical character (small HOMO-LUMO gap), and stabilization of this ground state by intramolecular charge transfer.