Spin dependence of density functionals that respect spin-rotational invariance

Abstract The interaction energy functional W [ γ ij , S ] of the Hubbard model is investigated as a function of total spin S. Exact numerical results are obtained for W [ γ ij , S ] on rings, where γ ij = γ 12 for all nearest neighbors. The functional dependence of W [ γ ij , S ] is analyzed for different S. The properties of W [ γ ij , S ] are discussed in the limits of weak ( γ 12 0 ) and strong ( γ 12 ∞ ) electronic correlations, and in the crossover region γ 12 ∞ γ 12 γ 12 0 . Scaling of W [ γ ij , S ] in units of the uncorrelated energy W 0 [ γ ij 0 , S ] shows a pseudo-universal behavior as a function of g 12 = ( γ 12 - γ 12 ∞ ) / ( γ 12 0 - γ 12 ∞ ) .