The use of explicit orientation-dependent functions, to represent the effects of non-spherical features in the molecular charge distribution, in model intermolecular pair potentials is developed in order to produce more accurate transferable anisotropic sitesite potentials for organic molecules. An isotropic atom-atom intermolecular potential-energy surface for methane is analysed using the orientation-dependent expansion functions appropriate to a pair of tetrahedral molecules, to determine the ability of a wide variety of one-centred anisotropic model potentials to reproduce the surface. The analysis is used to develop a simple anisotropic carbon potential scheme for CH3 and CH2 groups, which can predict the crystal structures of pentane, hexane and octane as accurately as the widely used isotropic atom-atom potential, and has the advantage of being more computationally efficient and more flexible for future development. The derivation of the appropriate orientationdependent functions for tetrahedral molecules, using angular momentum theory, in a form which is very convenient for crystal structure analysis is given. These functions are also used to examine the use of van der Waals radii to predict molecular packing.