  The electrostatic gating effects on molecular transistors are investigated
using the density functional theory (DFT) combined with the nonequilibrium
Green's function (NEGF) method. When molecular energy levels are away from the
Fermi energy they can be linearly shifted by the gate voltage, which is
consistent with recent experimental observations [Nature 462, 1039 (2009)].
However, when they move near to the Fermi energy (turn-on process), the shifts
become extremely small and almost independent of the gate voltage. The fact
that the conductance may be beyond the gate control in the "ON" state will
challenge the implementation of molecular transistors.
