The ab initio calculation of intermolecular interactions requires a large basis set to describe systems with dominant dispersion interaction accurately. This paper focuses on calculation of intermolecular bonding energies of weakly bound systems within the supermolecular method and on issues related to the choice of a basis set for these calculations, in particular size of the basis set, efficiency of 2-electron integral codes, basis set superposition error (BSSE), and the linear dependence of basis functions. In an attempt to find more efficient basis sets for calculations of intermolecular interactions, standard basis sets (10s Huzinaga, 6-311G**, cc-pV6Z), or their parts, are extended ( tessellated) by a set of off-centered, s or p functions, symmetrically placed around the nuclei. Standard basis sets ( 10s Huzinaga, 6-311G**, cc-pVXZ, aug-cc-pVXZ, X) D, T, Q, 5, 6) are also augmented by sets of atom-centered, higher angular momentum functions ( p, d, f). The distance from the nucleus of tessellating functions and orbital exponents of tessellating and augmenting functions are optimized with respect to the BSSE-corrected bonding energy at the MP2 or UCCSD level of theory. The two approaches are tested on the model systems with dominant dispersion interactions H-3(2), (CH4)(2), and Ne-2, and their efficiency is compared. Both tessellation and augmentation are successful in describing the intermolecular interactions of these model systems, with augmentation being more efficient. Our results draw attention to the linear dependence problems inevitably present in accurate calculations and confirm the need for underlying standard basis sets that provide good descriptions of core and valence electrons for the tessellation and augmentation approaches to be reliable.