Exchange Functionals for Particles of Arbitrary Spin

The Hartree−Fock exchange energy formula for electrons is generalized to fermions of arbitrary spin quantum number s. The explicit s-dependence of the exchange energy reveals that the spin-scaling relation for exchange functionals can be viewed as conversion between spin-unpolarized forms for the same functional appropriate for particles with s = 0 and s > 0. This implies that any exchange functional of the electron density can be easily adapted to fermions of arbitrary spin by a simple change of certain constant factors. Implications of this finding for the self-interaction error problem and for multicomponent density-functional theory are pointed out.