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 "0D cavity" functional originally found by Lafuente and Cuesta and derive an extension by applying a more general "cluster density functional theory" method introduced by Lafuente and Cuesta as well. Moreover, we introduce a new free energy functional, which is based on approximated configurational probabilities. Both derived free energy functionals are exact on cavities that can hold at most two particles simultaneously. The first functional allows to improve the prediction of the free energy in bulk and both of them improve the prediction in highly confined systems, especially for high packing fractions, in comparison to the "0D cavity" functional.
