The convergence of the density functional energy of H 2 is shown to be exponential with respect to basis set size from results obtained with fully optimized basis sets. The convergence is slightly slower than for the Hartree-Fock energy, but the basis set requirements are very similar. The variation in optimal exponents between different density functional methods is similar to that between different molecules for the Hartree-Fock method. The results indicate that hierarchical basis sets for systematically approaching the Hartree-Fock limit are likely also to be suitable for estimating the basis set limit for density functional methods.