The basis set convergence of density functional calculations is analyzed by comparing nuclear centred polarization functions with bond functions placed at the bond midpoints, and combinations of these two. The H₂, N₂ and N₄ systems are analyzed by explicit optimization of the exponents of the polarization and bond functions. While addition of bond functions can reduce the requirements for high angular momentum functions at the nuclei, there do not appear to be any computational advantages to using bond functions instead of nuclear centred polarization function for energetic purposes.