In this paper we further develop the formalism of tunneling currents for the description of the tunneling transition in long-distance bridge-mediated electron transfer reactions introduced in our previous work [A. A. Stuchebrukhov, Adv. Chem. Phys. 118, 1 (2001)]. Here we consider the Hartree-Fock picture of electron tunneling in a many-electron system and, based on the corresponding orbitals analysis of the tunneling process, we introduce an effective one-electron approximation. In this picture, the (electron or hole) tunneling is described by a single pair of orbitals, as in a true one-electron theory, yet all the polarization and exchange effects characteristic for many-electron treatment are retained in it. The pair of tunneling orbitals, which is different from the usual HOMO's of the donor and acceptor complexes, is found in a self-consistent way in a special orthogonalization procedure. This picture results in much simplified formulas for current density and for interatomic currents, as well as for the tunneling matrix element, and provides a simplified way of thinking about electron tunneling in many-electron systems. (C) 2003 American Institute of Physics.