  The Hubbard model is investigated in the framework of lattice density
functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with
respect the lattice sites is considered as the basic variable of the many-body
problem. A new approximation to the interaction-energy functional $W[\gamma]$
is proposed which is based on its scaling properties and which recovers exactly
the limit of strong electron correlations at half-band filling. In this way, a
more accurate description of $W$ is obtained throughout the domain of
representability of $\gamma_{ij}$, including the crossover from weak to strong
correlations. As examples of applications results are given for the
ground-state energy, charge-excitation gap, and charge susceptibility of the
Hubbard model in one-, two-, and three-dimensional lattices. The performance of
the method is demonstrated by comparison with available exact solutions, with
numerical calculations, and with LDFT using a simpler dimer ansatz for $W$.
Goals and limitations of the different approximations are discussed.
