The interactions of molecular hydrogen with Li containing benzene molecules were studied by means of density functional theory (DFT), second-order Møller-Plesset perturbation theory (MP2), and coupled-cluster theory including all single and double excitations in conjunction with a perturbative estimate of triple excitations [CCSD(T)]. At the DFT and MP2 levels the resolution of the identity (RI) approximation was invoked in the framework of the approaches RI-DFT and RI-MP2. The benzene derivatives studied in this work are lithium benzide (C6H5Li), lithium phenoxide (C 6H5OLi) and lithium benzoate (C6H 5COOLi). By extrapolating the MP2 and CCSD(T) energies to the complete basis set limit, the interaction energy of dihydrogen with these benzene species is found to be 2.54, 2.66 and 2.57 kcal/mol respectively. In all cases, the H2 molecule takes a side-on position on the Li atom. The interactions are larger than typical van der Waals (vdW) forces and can be attributed to dipole⋯induced dipole electrostatic forces. Therefore, the organolithium structures studied can perhaps be used as building units for potential hydrogen storage materials.