In order to asses performance of the LDA in describing physisorption on graphene, adsorptions of TCNE, TCNQ, TNF, TTF, and DMPD as well as four benzene derivatives on C 54 H 18 and C 110 H 30 were explored with a variety of DFTs such as MPWB1K, M06-2X, PBE-D and LSDA. Although it is well known that the LDA considerably overestimate non-covalent interaction, the LSDA predicted adsorption energies except for TCNE on C 110 H 30 are systematically lower than those from the M06-2X by 0.4–3.2kcal/mol, and they are more significantly lower than those from the PBE-D for all the molecules by 3–6kcal/mol. However, the LSDA adsorption energy sequence is consistent with that from the PBE-D, TNF∼TCNQ>TCNE∼DMPD>TTF. Moreover, the domain interaction between the electron donor and acceptor molecules with graphene through cooperative π⋯π, C–H⋯π and N–H⋯π were visualized with sign(λ 2 )×ρ, and the relationships between the binding energy with London force, molecular electronegativity, and frontier orbital level were extensively discussed.