Intermolecular interaction energies of n-butane, n-pentane, and n-hexane dimers were calculated at the MP2 level with a large basis set including multiple polarization functions. The comparison of the calculated interaction energies of five orientations of dimers for each n-alkane molecule, in which the main molecular axes of the two alkane chains are parallel, shows that the interaction between the two n-alkane chains has strong anisotropy. The antiparallel dimers (D-2 dimers of n-butane and n-hexane and C-2h dimer of n-pentane) have the largest interaction. The calculated interaction energies of the most stable n-butane, n-pentane, and n-hexane dimers are -2.80, -3.57, and -4.58 kcal/mol, respectively. The orientations of the most stable dimers are close to those of nearest neighboring n-alkane molecules (n-hexane to n-nonane) in the crystals. The calculated intermolecular interaction energies in the n-hexane crystal show that the intermolecular interaction (-4.23 kcal/mol) along the a-axis is substantially larger than those along the b- and c-axes.