Elegant expressions are derived for the computation of dipole and quadrupole moments of molecules using the electrostatic potential and electric field evaluated on an oriented molecular surface. These expressions are implemented for Hirshfeld surfaces, applied to various molecular crystals, and compared with the results from the quantum theory of atoms in molecules. The effect of intermolecular interactions is also explored by examining the differences between electrostatic moments derived from a periodic Hartree-Fock electron density and an electron density resulting from a superposition of noninteracting molecules. The enhancement of the dipole moment for hydrogen bonded molecular crystals is typically 30%-40% and shown to be largely independent of the partitioning scheme. Dipole moments calculated from Hirshfeld surfaces systematically underestimate those from zero-flux surfaces, a result attributed to the translation of the Hirshfeld surface relative to the zero-flux surfaces for these molecules. For acetylene and benzene, the differences between a crystal calculation and the sum of noninteracting molecules are small, and both partitioning schemes yield quadrupole and second moment results in close agreement. (c) 2006 American Institute of Physics.