A quantum circuit rule for combining quantum interference 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 G XmX (G XpX ) 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 quantum interference in the central ring Y. The single-molecule conductances were found to satisfy the quantum circuit rule G ppp /G pmp ¼ G mpm /G mmm . This demonstrates that the contribution to the conductance from the central ring is independent of the para versus meta nature of the anchor groups. S tudies of the electrical conductance of single molecules attached to metallic electrodes not only probe the fundamentals of quantum transport but also provide the knowledge needed to develop future molecular-scale devices and functioning circuits [1][2][3][4][5][6][7][8][9] . Owing to their small size (on the scale of Angstroms) and the large energy gaps (on the scale of eV), transport through single molecules can remain phase coherent even at room temperature, and constructive or destructive quantum interference (QI) can be utilized to manipulate their room temperature electrical 10-13 and thermoelectrical 14,15 properties. In previous studies, it was reported theoretically and experimentally that the conductance of a phenyl ring with meta (m) connectivity is lower than the isomer with para (p) connectivity by several orders of magnitude [16][17][18][19][20][21][22][23][24][25] . This arises because partial de Broglie waves traversing different paths through the ring are perfectly out of phase leading to destructive QI in the case of meta coupling, while for para or ortho coupling they are perfectly in phase and exhibit constructive QI. (See, for example, equation 8 of ref. 26.) It is therefore natural to investigate how QI in molecules with multiple aromatic rings can be utilized in the design of more complicated networks of interference-controlled molecular units.The basic unit for studying QI in single molecules is the phenyl ring, with thiol 17,21 , methyl thioether 27 , amine 17 or cyanide 19 anchors directly connecting the aromatic ring to gold electrodes. Recently, Arroyo et al. 28,29 studied the effect of QI in a central phenyl ring by varying the coupling to various anchor groups, including two variants of thienyl anchors. However, the relative importance of QI in central rings compared with QI in anchor groups has not been studied systematically because the thienyl anchors of Arroyo et al. 28,29 were five-membered rings, which exhibit only constructive interference. To study the relative effect of QI in anchors,...

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The compounds and complexes 1,4‐C6H4(C≡C‐cyclo‐3‐C4H3S)2 (2), trans‐[Pt(C≡C‐cyclo‐3‐C4H3S)2(PEt3)2] (3), trans‐[Ru(C≡C‐cyclo‐3‐C4H3S)2(dppe)2] (4; dppe=1,2‐bis(diphenylphosphino)ethane) and trans‐[Ru(C≡C‐cyclo‐3‐C4H3S)2{P(OEt)3}4] (5) featuring the 3‐thienyl moiety as a surface contacting group for gold electrodes have been prepared, crystallographically characterised in the case of 3–5 and studied in metal|molecule|metal junctions by using both scanning tunnelling microscope break‐junction (STM‐BJ) and STM‐I(s) methods (measuring the tunnelling current (I) as a function of distance (s)). The compounds exhibit similar conductance profiles, with a low conductance feature being more readily identified by STM‐I(s) methods, and a higher feature by the STM‐BJ method. The lower conductance feature was further characterised by analysis using an unsupervised, automated multi‐parameter vector classification (MPVC) of the conductance traces. The combination of similarly structured HOMOs and non‐resonant tunnelling mechanism accounts for the remarkably similar conductance values across the chemically distinct members of the family 2–5.

The most probable single-molecule conductance of each member of a series of 12 conjugated molecular wires, 6 of which contain either a ruthenium or platinum center centrally placed within the backbone, has been determined. The measurement of a small, positive Seebeck coefficient has established that transmission through these molecules takes place by tunneling through the tail of the HOMO resonance near the middle of the HOMO−LUMO gap in each case. Despite the general similarities in the molecular lengths and frontier-orbital compositions, experimental and computationally determined trends in molecular conductance values across this series cannot be satisfactorily explained in terms of commonly discussed "single-parameter" models of junction conductance. Rather, the trends in molecular conductance are better rationalized from consideration of the complete molecular junction, with conductance values well described by transport calculations carried out at the DFT level of theory, on the basis of the Landauer−Buẗtiker model.

The single-molecule conductance of metal complexes of the general forms trans-Ru(CCArC CY) 2 (dppe) 2 and trans-Pt(CCArCCY) 2 (PPh 3 ) 2 (Ar = 1,4-C 6 H 2 -2,5-(OC 6 H 13 ) 2 ; Y = 4-C 5 H 4 N, 4-C 6 H 4 SMe) have been determined using the STM I(s) technique. The complexes display high conductance (Y = 4-C 5 H 4 N, M = Ru (0.4 ± 0.18 nS), Pt (0.8 ± 0.5 nS); Y = 4-C 6 H 5 SMe, M = Ru (1.4 ± 0.4 nS), Pt (1.8 ± 0.6 nS)) for molecular structures of ca. 3 nm in length, which has been attributed to transport processes arising from tunneling through the tails of LUMO states.

and break-off distance data, we demonstrate that a PPh 3 supporting ligand in the platinum complexes can provide an alternative contact point for the STM tip in the molecular junctions, orthogonal to the terminal CuCSiMe 3 group. The attachment of hexyloxy side chains to the diethynylbenzene ligands, e.g. trans-Pt{CuCC 6 H 2 (Ohex) 2 CuCSiMe 3 } 2 (PPh 3 ) 2 (Ohex = OC 6 H 13 ), hinders contact of the STM tip to the PPh 3 groups and effectively insulates the molecule, allowing the conductance through the full length of the backbone to be reliably measured. The use of trialkylphosphine (PEt 3 ), rather than triarylphosphine (PPh 3 ), ancillary ligands at platinum also eliminates these orthogonal contacts. These results have significant implications for the future design of organometallic complexes for studies in molecular junctions.

The single molecule conductances of a series of bis-2,2':6',2″-terpyridine complexes featuring Ru(II), Fe(II), and Co(II) metal ions and trimethylsilylethynyl (Me3SiC≡C-) or thiomethyl (MeS-) surface contact groups have been determined. In the absence of electrochemical gating, these complexes behave as tunneling barriers, with conductance properties determined more by the strength of the electrode-molecule contact and the structure of the "linker" than the nature of the metal-ion or redox properties of the complex.

The ancillary ligands 4'-(4-pyridyl)-2,2':6',2''-terpyridine and 4'-(2,3-dihydrobenzo[b]thiophene)-2,2'-6',2"-terpyridine were used to synthesize two series of mono- and dinuclear ruthenium complexes differing in their lengths and anchoring groups. The electrochemical and single-molecular conductance properties of these two series of ruthenium complexes were studied experimentally by means of cyclic voltammetry and the scanning tunneling microscopy-break junction technique (STM-BJ) and theoretically by means of density functional theory (DFT). Cyclic voltammetry data showed clear redox peaks corresponding to both the metal- and ligand-related redox reactions. Single-molecular conductance demonstrated an exponential decay of the molecular conductance with the increase in molecular length for both the series of ruthenium complexes, with decay constants of βPY =2.07±0.1 nm(-1) and βBT =2.16±0.1 nm(-1) , respectively. The contact resistance of complexes with 2,3-dihydrobenzo[b]thiophene (BT) anchoring groups is found to be smaller than the contact resistance of ruthenium complexes with pyridine (PY) anchors. DFT calculations support the experimental results and provided additional information on the electronic structure and charge transport properties in those metal|ruthenium complex|metal junctions.