title: Quantum interference in polyenes.
abstract: The explicit form of the zeroth Green's function in the Hückel model, approximated by the negative of the inverse of the Hückel matrix, has direct quantum interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of quantum interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Green's function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments - if coherence in probe connections can be arranged - in some cases new destructive interference results, while in others one may have constructive interference. One such case may already exist in the literature.
authors.affiliation: Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, New York 14853, USA.
authors.forename: Yuta
authors.initials: Y
authors.lastname: Tsuji
authors.affiliation: Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, New York 14853, USA.
authors.forename: Roald
authors.initials: R
authors.lastname: Hoffmann
authors.affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115, USA and Department of Mathematics, Massachusetts Institute of Technology, Building E18, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA.
authors.forename: Ramis
authors.initials: R
authors.lastname: Movassagh
authors.affiliation: School of Electrical and Computer Engineering, Purdue University, Electrical Engineering Building, 465 Northwestern Ave., West Lafayette, Indiana 47907-2035, USA.
authors.forename: Supriyo
authors.initials: S
authors.lastname: Datta