Problems in DFT with the total spin and degenerate states

The problems arising in the density functional theory when it is applied to the spin- and space-degenerate states are discussed. It is rigorously proved that in the case of orthonormal orbital set, the electron density of an arbitrary N-electron system does not depend upon the total spin S and for all values of S has the same form as it has for a single-determinantal wave function. From this follows that the conventional Kohn-Sham equations cannot distinguish the states with different total spin values. A critical survey of the existing DFT methods of taking into account the total spin is performed. It is shown that all these methods, including state- and orbital-dependent functional method, modify only the expression for the exchange energy and use the correlation functionals not corresponding to the total spin of the state. It is also proved that the diagonal element of the density matrix is invariant with respect to the symmetry of the state, hence in this respect there is no difference between degenerate and nondegenerate states. On the other hand, for the degenerate states, the Born-Oppenheimer approximation fails, so that makes it impossible to apply the density functional formalism. (c) 2007 Wiley Periodicals, Inc.