In this work, we investigate the ion pair tetramethylphosphonium cation, [P1,1,1,1]+, and bis(oxalato)borate anion, [BOB]−, as a model system for the study of ionic liquids interacting with both hydroxylated and oxygen terminated α-SiO2 (001) surfaces, using first-principles electronic structure theory. We use a single ionic pair and clusters of ion pairs, in order to have exclusively neutral supercell slab models. We use dispersion-corrected density functional theory (DFT) to ascertain that both the strong physical binding between the ions, dominated by ionic binding, and the weaker physical binding of ions to the different surfaces are correctly described. We have found that the binding of ion pairs is stronger to the hydroxylated α-SiO2 (001) surface compared to the oxygen terminated surface, which is attributed to the formation of H-binding with the oxygen atom(s) of the [BOB]− anion. Through rotation of ionic pair(s), we estimate the surface-ions energy barrier for translational movement and, thus, the strength of H-binding of the ions. At the surface of hydroxylated α-SiO2 (001), we have studied how water molecules form a network of H-binding with the OH groups of the surface and the [BOB]− anion, which offers an explanation for the reduction in the friction of ionic liquids on the inclusion of water. We suggest modeling protocols for simulation of ion pairs on surfaces, which can open up the possibility to use DFT to aid in designing and understanding the physicochemical mechanism of interactions of ionic materials (including ionic liquids) in various technological applications.