Understanding and reducing errors in density functional calculations.

We decompose the energy error of any variational density functional theory 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 error in density functional theory can be greatly reduced by using a more accurate density. A small orbital gap often indicates a substantial density-driven error.