  We present a self-consistent method for the evaluation of the electronic
current flowing through a multi-terminal molecular wire. The method is based on
Buttiker- Landauer theory which relates the current to one-electron scattering
probabilities. The scattering problem is solved using a tight-binding form for
Schroedinger's equation that incorporates a self-consistent evaluation of the
electro-static potential in the region of the molecular wire. We apply the
method to a three-terminal molecular wire connected to metallic leads. The
molecular wire is a pi-conjugated carbon chain with thiol end groups,
self-assembled on the cleaved edge of a multilayer of alternating thin metal
and insulating films. The ends of the chain bond to two outer metal layers that
act as source and drain, and the chain bridges a third (inner) metal layer that
acts as a gate. We show that transistor action should occur in this device if
on the surface of the metal gate there are absorbed atoms that acquire charge
as the gate voltage is increased, thereby enhancing the interaction between the
gate and molecule and creating a strong potential barrier that hinders electron
flow along the molecular wire. We find that electronic solitons play an
important role in the response of this system to applied voltages.
