We have obtained the ground state and the equilibrium geometries of Au(n) (-) and Au(n-1)Cu(-) in the size range of n=13-19. We have used first principles density functional theory within plane wave and Gaussian basis set methods. For each of the cluster we have obtained at least 100 distinct isomers. The anions of gold clusters undergo two structural transformations, the first one from flat cage to hollow cage and the second one from hollow cage to pyramidal structure. The Cu doped clusters do not show any flat cage structures as the ground state. The copper doped systems evolve from a general 3D structure to hollow cage with Cu trapped inside the cage at n=16 and then to pyramidal structure at n=19. The introduction of copper atom enhances the binding energy per atom as compared to gold cluster anions.