The optimization of the parameters of the Lennard-Jones (LJ) 12-6 potential of the sulfur atom in thiophene has allowed the AUA 4 potential to be successfully extended to alkyl and polythiophenes. Monte Carlo Gibbs ensemble and grand canonical simulations combined with histogram reweighting techniques have been performed to investigate the resulting phase equilibrium and the critical region of different molecules of this family in order to test the proposed potential. Excellent agreement with experimental densities, enthalpies of vaporization, and saturation pressures has been obtained in most of the cases. In particular, the critical point of our model for thiophene has been located with a statistical precision of less than 0.1% and is within 1% of the experimental value. The calculation of the critical points has been made through a recently implemented methodology based on the calculation of a fourth order cumulant (Binder parameter) combined with the use of finite size scaling methods, allowing the critical points to be located in a straightforward and accurate way.