Spin dependence of density functionals that respect spin-rotational invariance

The interaction energy functional W[γij,S] of the Hubbard model is investigated as a function of total spin S. Exact numerical results are obtained for W[γij,S] on rings, where γij=γ12 for all nearest neighbors. The functional dependence of W[γij,S] is analyzed for different S. The properties of W[γij,S] are discussed in the limits of weak (γ120) and strong (γ12∞) electronic correlations, and in the crossover region γ12∞<γ12<γ120. Scaling of W[γij,S] in units of the uncorrelated energy W0[γij0,S] shows a pseudo-universal behavior as a function of g12=(γ12-γ12∞)/(γ120-γ12∞).