Symmetry in density-functional theory

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Abstract
The formal structure of density-functional theory in the constrained-search formulation is analyzed and a theory is derived which is symmetrized with respect to the symmetry group of the Hamiltonian operator. This theory is valid for an arbitrary given electronic system and takes into account symmetries in spin as well as in ordinary space. The symmetrized theory is based on the totally symmetric part of the density instead of the density or spin density itself. In the corresponding symmetrized Kohn-Sham formalism no symmetry dilemma can occur. The concepts of symmetrized N-representability and symmetrized v-representability are defined. Known examples of non-v-representable densities are shown to be symmetrized v-representable. The related question of the convexity of the universal functionals involved is discussed. The computational demands of this symmetrized formalism are on the level of non-spin-polarized calculations for all systems, independent of their actual spin structure. The usual treatment of symmetry within density-functional theory is investigated. The widespread usage of non-symmetry-dependent density functionals in cases when it is formally not justified is identified as a possible source of errors.