The role of neutral and charged hydrogenic molecules in detached regimes of tokamak plasmas is investigated using simplified 1D parallel numerical models. Using MAST-Upgrade like conditions, simulations are implemented to study the rollover of target flux in upstream density scan and target temperature scan. It is found that if H2 and H2+ are considered in simulations a lower target temperature and a larger upstream density will be required to trigger the diverter detachment under the same input power and particle flux, and the critical detachment threshold is found to be P_up/P_recl~0.8 N/MW at rollover. Molecule-plasma interactions are found to be as crucial as atom-plasma interactions during divertor detachment, both of which account for the main plasma momentum loss. Further analysis of the momentum loss decomposition shows molecule-plasma elastic collision dominates molecule-plasma interactions, while molecular charge exchange cannot effectively reduce plasma momentum. In terms of H_alpha emission, a strong rise of H_alpha signal could be found due to molecular excitation channels when the upstream density further increases after rollover.