  We propose a self-consistent generalized quantum master equation (GQME) to
describe electron transport through molecular junctions. In a previous study
[M.Esposito and M.Galperin. Phys. Rev. B 79, 205303 (2009)], we derived a
time-nonlocal GQME to cure the lack of broadening effects in Redfield theory.
To do so, the free evolution used in the Born-Markov approximation to close the
Redfield equation was replaced by a standard Redfield evolution. In the present
paper, we propose a backward Redfield evolution leading to a time-local GQME
which allows for a self-consistent procedure of the GQME generator. This
approach is approximate but properly reproduces the nonequilibrium steady state
density matrix and the currents of an exactly solvable model. The approach is
less accurate for higher moments such as the noise.
