  Designing molecular nanowires with high electrical conductance that
facilitate efficient charge transport over long distances are highly desirable
for future molecular-scale circuitry. However most of the molecular wires act
as tunnel barriers and their electrical conductance is decaying exponentially
with increasing the length. Just recently a few studies have shown increasing
conductance with length. In this study, for the first time, we have identified
new class of molecular wires that exhibit both increase and decrease of room
temperature conductance with length (dual attenuation factor) depend on their
connection points to electrodes. We show that this dual attenuation factor is
an inherent property of these graphene-like nanowires and its demonstration
depends on the constructive quantum interference pattern for different
connectivities to electrode. This is significant because a given nanographene
molecular wire can show both negative and positive attenuation factor. This
enables a systematic design of connectivity dependent high/low-conductance
molecular wires for future molecular-scale circuitry.
