  A current constrained approach is proposed to calculate negative differential
conductance in molecular nano-junctions. A four-site junction is considered
where a steady-state current is forced by inserting only the two central sites
within the circuit. The two lateral sites (representing e.g. dangling molecular
groups) do not actively participate in transport, but exchange electrons with
the two main sites. These auxiliary sites allow for a variable number of
electrons within the junction, while, as required by the current constrained
approach, the total number of electrons in the system is kept constant. We
discuss the conditions for negative differential conductance in terms of
cooperativity, variability of the number of electrons in the junction, and
electron correlations.
