Crystal structure predictions for glycol and glycerol are reported. A series of increasingly accurate energy calculations is applied. and the final predictions are based solely on ab initio derived energies. A recently developed transferable ab initio potential is used for intermolecular interactions, augmented with ab initio derived conformational energies. The experimental structure of glycol was predicted with a low energy, 1.1 kJ/mol above the global minimum. For glycerol the experimental structure corresponded to the global minimum. This latter result provides a proposal for the positions of the hydrogen atoms in the crystal structure of glycerol. A three-dimensional hydrogen-bonded network is formed which consists only of intermolecular hydrogen bonds. Together with previous work, the ab initio intermolecular potential has now been applied to predict the crystal structures of six different compounds. The energy difference between the observed crystal structure and the global energy minimum varied from 0 to 2 kJ/mol. Standard Force fields fail to consistently produce such low values. This demonstrates the importance of highly accurate force fields in crystal structure prediction.