The molecular properties of tetrathiapentalene (TTP), a new and promising building block for conducting organic polymers, and of its radical cation have been studied by a hybrid Hartree-Fock/Kohn-Sham method. Parallel computations have been performed for tetrathiafulvalene (TTF), a well-known component of many organic conductors, with the aim of understanding the potentialities of TTP. Our results show that geometrical parameters and vibrational frequencies of radical cations are similar for TTF and TTP, thus suggesting that comparable bulk properties can be expected for both molecules. At the same time, the larger spin delocalization on terminal carbon atoms of TTP+ explains its greater reactivity.