The effect of using a realistic model for the electrostatic forces on the calculated structures of molecular crystals is explored by using atomic multipoles derived from an SCF 6-31G** wave function. This was tested on a wide ranging database of 40 rigid organic molecules containing C, H, N, and O atoms, including nucleic acid bases, nonlinear optic materials, azabenzenes, nitrobenzenes, and simpler molecules. The distributed multipole electrostatic model, plus an empirical repulsion-dispersion potential, was able to successfully reproduce the lattice vectors and available heats of sublimation of the experimental room temperature structure in almost all cases. Scaling the electrostatic energy to allow for the effect of electron correlation on the molecular charge density generally improved the lattice energies and the calculated structures to a lesser extent. However, omitting the anisotropic multipole moments usually gave very poor, sometimes qualitatively wrong structures, emphasizing the sensitivity of these crystal structures to the electrostatic forces. We also investigated the sensitivity of the structures to the empirical repulsion-dispersion potential parameters by attempting to optimize these. Since the experimental structures are mainly reproduced to within the errors that could be attributed to the use of static minimization and rigid molecules, it appears that going beyond the atomic charge model to a realistic electrostatic model is a key development in the modeling of the crystal structures of polar and hydrogen-bonded molecules.