  We achieve, at room temperature, conductance enhancements over two orders of
magnitude in single molecule circuits formed with polycyclic benzoquinoidal
(BQn) diradicals upon increasing molecular length by ~0.5 nm. We find that this
extreme and atypical anti-ohmic conductance enhancement at longer molecular
lengths is due to the diradical character of the molecules, which can be
described as a topologically non-trivial electronic state. We adapt the 1D-SSH
model originally developed to examine electronic topological order in linear
carbon chains to the polycyclic systems studied here and find that it captures
the anti-ohmic trends in this molecular series. The mechanism of conductance
enhancement with length is revealed to be constructive quantum interference
(CQI) between the frontier orbitals with non-trivial topology, which is present
in acene-like, but not in linear, molecular systems. Importantly, we predict
computationally and measure experimentally that anti-ohmic trends can be
engineered through synthetic adjustments of the diradical character of the
acene-like molecules. Overall, we achieve an experimentally unprecedented
anti-ohmic enhancement and mechanistic insight into electronic transport in a
class of materials that we identify here as promising candidates for creating
highly conductive and tunable nanoscale wires.
