Symmetry and spin density functional theory

Abstract

It is proposed that density functional theory be made invariant under rotations in the spin space of all of the electrons. Such a constraint requires the fundamental variables of nonrelativistic density functional theory be altered from spin-up and spin-down densities to the total density and the scalar product of the total spin-polarization vector. The assumption that the universal density functional expression for exchange in the absence of spin polarization has all the symmetries of the exact exchange-energy functional is investigated. To possess all symmetries the expression must be linear in the square of the density and the square of the three components of the spin-polarization vector. Partial satisfaction of these symmetry requirements for the Xα expression for exchange leads to dramatically different behavior. The unique 4/3 power of the density and magnitude of the spin-polarization functional has such a strong spin dependence that it is mathematical unstable in the sense of having a multitude of solutions for fixed orbital occupations. A second rotationally invariant expression identical to that of Xα in the diamagnetic and completely ferromagnetic limits has a tendency towards spin polarization that goes to zero cubicly when the spin polarization is small. The latter is investigated for atomic lithium, nickel and the nickel dimer.