Symmetry dependence and universality of practical algebraic functionals in density-matrix-functional theory

When dealing with a fully symmetrical ground state, the symmetry dependence of the universal Hohenberg-Kohn energy functional F[γ] of the first-order reduced density matrix (RDM) γ can be conveniently neglected. The situation changes drastically in the case of the dissociation of a symmetrical molecule with the state crossing, in the course of which the potential energy curve of the initial non-fully symmetrical ground state is eventually crossed with that of the fully symmetrical state. In this case, as is demonstrated in the present paper, the second-order RDM Γij,kl in the representation of the natural orbitals (NOs) is symmetry dependent. Since Γij,kl is the goal in the design of Γij,kl(n) as a functional of NO occupations {n}, which is part of a practical density matrix functional F[γ],Γij,kl(n) must also depend on the symmetry, especially the irreducible representation of the symmetry group. The result has immediate implications for study of structural (or phase) transitions based on a single symmetry-independent functional. The demonstration is given in the minimal-base model of the dissociation of the prototype H4 molecule in the rhombic structure.