  A quantum circuit rule for combining quantum interference (QI) effects in the
conductive properties of oligo(phenyleneethynylene) (OPE)-type molecules
possessing three aromatic rings was investigated both experimentally and
theoretically. Molecules were of the type X-Y-X, where X represents pyridyl
anchors with para (p), meta (m) or ortho (o) connectivities and Y represents a
phenyl ring with p and m connectivities. The conductances GXmX (GXpX) of
molecules of the form X-m-X (X-p-X), with meta (para) connections in the
central ring were predominantly lower (higher), irrespective of the meta, para,
or ortho nature of the anchor groups X, demonstrating that conductance is
dominated by the nature of QI in the central ring Y. The single-molecule
conductances were found to satisfy the quantum circuit rule Gppp/Gpmp =
Gmpm/Gmmm. This demonstrates that the contribution to the conductance from the
central ring is independent of the para versus meta nature of the anchor
groups.
