A note on tunable transconductance of a branching molecular wire

It is shown that the Griffith boundary conditions on the wavefunction of an electron moving coherently on a molecular network of one-dimensional conductors (delocalized bonds) lead to a branching resistance at the node that can be tuned resonantly. The latter provides mechanism for regulating the transfer of an extraneous electron over a 'molecular wire' connecting two cormponents of a supramolecular device.