  We present a model of the molecular transistor, operation of which is based
on the interplay between two physical mechanisms, peculiar to open quantum
systems that act in concert: PT-symmetry breaking corresponding to coalescence
of resonances at the exceptional point of the molecule, connected to the leads,
and Fano-Feshbach antiresonance. This switching mechanism can be realized in
particular in a special class of molecules with degenerate energy levels, i.e.
diradicals, which possess mirror symmetry. At zero gate voltage infinitesimally
small interaction of the molecule with the leads breaks the PT-symmetry of the
system that, however, can be restored by application of the gate voltage
preserving the mirror symmetry. PT-symmetry broken state at zero gate voltage
with minimal transmission corresponds to the 'off' state while the PT-symmetric
state at non-zero gate voltage with maximum transmission - to the 'on' state.
At zero gate voltage energy of the antiresonance coincides with exceptional
point but the transmission variation mainly takes place due to the coalescence
of resonances at the exceptional point. We construct a model of an
all-electrical molecular switch based on such transistors acting as a
conventional CMOS inverter and show that essentially lower power consumption
and switching energy can be achieved, compared to the CMOS analogues.
