  {Analytical equations like Richardson-Dushman's or Shockley's provided a
general, if simplified conceptual background, which was widely accepted in
conventional electronics and made a fundamental contribution to advances in the
field. In the attempt to develop a (highly desirable, but so far missing)
counterpart for molecular electronics, in this work, we deduce a general
analytical formula for the tunneling current through molecular junctions
mediated by a single level that is valid for any bias voltage and temperature.
Starting from this expression, which is exact and obviates cumbersome numerical
integration, in the low and high temperature limits we also provide analytical
formulas expressing the current in terms of elementary functions. They are
accurate for broad model parameter ranges relevant for real molecular
junctions. Within this theoretical framework we show that: (i) by varying the
temperature, the tunneling current can vary by several orders of magnitude,
thus debunking the myth that a strong temperature dependence of the current is
evidence for a hopping mechanism, (ii) real molecular junctions can undergo a
gradual (Sommerfeld-Arrhenius) transition from a weakly temperature dependent
to a strongly (``exponential'') temperature dependent current that can be tuned
by the applied bias, and (iii) important insight into large area molecular
junctions with eutectic gallium indium alloy (EGaIn) top electrodes can be
gained. E.g., merely based on transport data, we estimate that the current
carrying molecules represent only a fraction of f \approx 4 \times 10^{-4} out
of the total number of molecules in a large area \ce{Au-S-(CH2)13-CH_3 / EGaIn}
junction.
