  We decompose the energy error of any variational DFT calculation into a
contribution due to the approximate functional and that due to the approximate
density. Typically, the functional error dominates, but in many interesting
situations, the density-driven error dominates. Examples range from
calculations of electron affinities to preferred geometries of ions and
radicals in solution. In these abnormal cases, the DFT error can be greatly
reduced by using a more accurate density. A small orbital gap often indicates a
substantial density-driven error.
