Kohn–Sham equations for nanowires with direct current

The paper describes the derivation of the Kohn–Sham equations for a nanowire with direct current. A value of the electron current enters the problem as an input via a subsidiary condition imposed by pointwise Lagrange multiplier. Using the constrained minimization of the Hohenberg–Kohn energy functional, we derive a set of self-consistent equations for current carrying orbitals of the molecular wire.