  Using classical density functional theory, we study the behavior of dimers,
i.e. hard rods of length $L=2$, on a two-dimensional cubic lattice. For
deriving a free energy functional, we employ Levy's prescription which is based
on the minimization of a microscopic free energy with respect to the many-body
probability under the constraint of a fixed density profile. Using that, we
recover the functional originally found by Lafuente and Cuesta and derive an
extension. With this extension, the free energy functional is exact on cavities
that can hold at most two particles simultaneously. The new functional improves
the prediction of the free energy in bulk as well as in highly confined
systems, especially for high packing fractions, in comparison to that of
Lafuente and Cuesta.
