We need clean drinking water, but current water purification methods are not always sufficient. This study examines the binding and binding mechanisms when graphene oxide is used as a filter material for removing perfluorinated substances and trihalomethanes. We use density functional theory calculations to examine the binding of the harmful molecules on graphene oxide. Our results indicate that the binding energies between graphene oxide and the investigated molecules are in the range of 370-1450 meV per molecule, similar to the binding energies obtained in other studies, where adsorption of similar size molecules onto graphene oxide has been investigated. This indicates that graphene oxide has the potential to separate the molecules of interest from the water. Significant contribution to the binding energies comes from the van der Waals (dispersion) interaction between the molecule and graphene oxide, while the hydrogen bonding between the functional groups of graphene oxide and the hydrogen atoms in functional groups on the molecules also plays a role in the binding.