It is argued that the presence of an array of electrostatic quadrupoles in the basal plane of graphite is plausible. Expressions are derived for the interaction of an array of ideal quadrupoles oriented perpendicular to the surface with a charge, a dipole, and a quadrupole. By use of reasonable numerical values for the parameters of the energy functions, numerical calculations are presented for the minimum potential energies of two graphitic sheets, a water molecule over the graphite basal plane, and a nitrogen molecule over the graphite basal plane. Significant changes in these energies are produced when the quadrupolar terms are included. In particular, it is shown that quantities such as the barriers to free translation and the locations of the minimum energy adsorption sites are altered when reasonable estimates of this electrostatic interaction are added to the van der Waals energies.