  By using a well established 'ab initio' theoretical approach developed in the
past to quantitatively study the superconductivity of condensed matter systems,
which is based on the Kohn-Sham Density Functional theory, I study the
superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional
layers of fermionic dipolar molecules, where the pairing mechanism leading to
superfluidity is provided by the inter-layer coupling between dipoles. The
finite temperature superfluid properties of both the homogeneous system and one
were the fermions in each layer are confined by a square optical lattice are
studied at half filling conditions, and for different values of the strength of
the confining optical potential. The T=0 results for the homogeneous system are
found to be in excellent agreement with Diffusion Monte Carlo results. The
superfluid transition temperature in the BCS region is found to increase, for a
given inter-layer coupling, with the strength of the confining optical
potential. A transition occurs at sufficiently small interlayer distances,
where the fermions becomes localized within the optical lattice sites in a
square geometry with an increased effective lattice constant, forming a system
of localized composite bosons. This transition should be signalled by a sudden
drop in the superfluid fraction of the system.
