  We present a method which uses density functional theory (DFT) to treat
transport through a single molecule connected to two conducting leads for the
weak and intermediate coupling. This case is not accessible to standard
non-equilibrium Green's function (NEGF) calculations. Our method is based on a
mapping of the Hamiltonian on the molecule to a limited set of many-body
eigenstates. This generates a many-body Hamiltonian with parameters obtained
from ground state L(S)DA-DFT calculations. We then calculate the transport
using many-body Green's function theory. We compare our results with existing
density matrix renormalization group (DMRG) calculations for spinless and for
spin-1/2 fermion chains and find good agreement.
