Kohn-Sham formulation of density-functional theory

We rederive the Kohn-Sham formulation of density-functional theory by considering it as a special case of the mapping of the physical density to that of a Slater determinant with an arbitrarily chosen density. It follows that the application of the variational principle requires an additional constraint, with a Lagrange multiplier function that modifies the effective local potential. The Kohn-Sham theory is then regained in the limit of the vanishing Lagrange multiplier. We then study the possibility of applying a similar idea to a formulation, proposed recently by the authors, in terms of the density matrix rather than the density; it follows from well-known relations that this cannot be done. [S1050-2947(98)01008-7].