Binding or potential energy curves have been calculated for the ground-state diatomics H(2)(+), He(2)(+), LiH(+), H(2), N(2), and C(2), for the transition state H(3), and for the triplet first excited state of H(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) gene...