  Standard approximations for the exchange-correlation (XC) functional in
Kohn-Sham density functional theory (KS-DFT) typically lead to unacceptably
large errors when applied to strongly-correlated electronic systems.
Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the
ground-state density and energy of a system are obtained through
self-consistent calculations on isolated fragments, with a partition energy
representing the \textit{inter}-fragment interactions. Here we show how typical
errors of the local density approximation (LDA) in KS-DFT can be largely
suppressed through a simple approximation, the generalized overlap
approximation (GOA), for the partition energy in PDFT. Our method is
illustrated on simple models of one-dimensional strongly-correlated linear
hydrogen chains. The GOA, when used in combination with the LDA for the
fragments, improves the LDA dissociation curves of hydrogen chains and produces
results that are comparable to those of spin-unrestricted LDA, but without
breaking the spin symmetry. GOA also induces a correction to the LDA electron
density that partially captures the correct density dimerization in
strongly-correlated hydrogen chains. Moreover, with an additional correction to
the partition energy, the approximation is shown to produce dissociation
energies in quantitative agreement to calculations based on the Density Matrix
Renormalization Group method.
