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. (C) 2003 American Institute of Physics.