  Nanoscale optoelectronics and molecular-electronics systems operate with
current injection and nonequilibrium tunneling, phenomena that challenge
consistent descriptions of the steady-state transport. The current affects the
electron-density variation and hence the inter- and intra-molecular bonding
which in turn determines the transport magnitude. The standard approach for
efficient characterization of steady-state tunneling combines ground-state
density functional theory (DFT) calculations (of an effective scattering
potential) with a Landauer-type formalism and ignores all actual many-body
scattering. The standard method also lacks a formal variational basis. This
paper formulates a Lippmann-Schwinger collision density functional theory
(LSC-DFT) for tunneling transport with full electron-electron interactions.
Quantum-kinetic (Dyson) equations are used for an exact reformulation that
expresses the variational noninteracting and interacting many-body scattering
T-matrices in terms of universal density functionals. The many-body
Lippmann-Schwinger (LS) variational principle defines an implicit equation for
the exact nonequilibrium density.
