The paper investigates quantum control of the proton transfer reaction in a two-dimensional model system using terahertz (THz) laser fields. The model potential, tailored to MP2 data for thioacetylacetone, comprises the proton transfer and the heavy atom coordinates. Two distinct mechanisms of proton transfer are investigated: the resonant versus the tunneling one. The efficiency of laser control in both cases is tested against the instability of pulse characteristics. The study shows that while the resonant scheme allows efficient control for a large range of field parameters, the tunneling scheme is very sensitive to the pulse characteristics, and therefore experimentally hardly realizable
