Implementing the Keldysh formalism into the ab initio Gaussian Embedded Cluster Method for the calculation of quantum transport

We discuss the key steps that have to be followed to calculate quantum transport out of equilibrium by means of the {\it ab initio} Gaussian Embedded Cluster Method recently developed by the authors. Our main aim is to emphasize through several examples that, if a sufficiently large portion of the electrodes is included in the {\it ab initio} calculation, which does also incorporate an electrochemical potential difference $\mu_L-\mu_R=eV$, there is no need to impose an electrostatic potential $V$ drop accross the system.