On the Constrained Search-Coordinate Scaling Formulations in DFT

First, a review of the early history of DFT is given, including anecdotes, and the constrained-search formulation is presented within the context of this history. Then it is shown how this formulation leads to the derivation of key constraints for approximating density functionals. These constraints include those that involve the coordinate scaling of the total density, and of the individual up and down spin densities, where the use of spin-free wavefunctions for the derivations has very recently proven to be effective.

The utility of expressing the total energies of ground-states and excited states as simple sums of augmented orbital energies shall also be discussed. Then several open problems in DFT shall be presented.