The nonretarded van der Waals coefficients C6 and C8 are determined for all pairs of neutral sodium and potassium microclusters with 1, 2, 8 and 20 atoms. The spherical jellium approximation is used to replace their ionic cores, and the valence electrons are treated in the local density approximation of density functional theory. The dynamical polarizabilities of these systems are computed making use of three different methods, two microscopic and quantum mechanical linear response formulations and one classical. It is found that quantum size effects, in particular Landau fragmentation, play a crucial role in the determination of these coefficients. Furthermore, we find that self-interaction errors present in standard microscopic approximations lead to sizeable effects in the strength of the van der Waals coefficients. On the other hand, we find that the vibrational temperature of these clusters has a very small effect in the van der Waals interaction which can be disregarded within the range of temperatures presently reachable experimentally.
