A key goal in molecular electronics has been to find molecules that facilitate efficient charge transport over long distances. Normally, molecular wires become less conductive with increasing length. Here, we report a series of fused porphyrin oligomers for which the conductance increases substantially with length by >10-fold at a bias of 0.7 V. This exceptional behavior can be attributed to the rapid decrease of the HOMO-LUMO gap with the length of fused porphyrins. In contrast, for butadiyne-linked porphyrin oligomers with moderate inter-ring coupling, a normal conductance decrease with length is found for all bias voltages explored (±1 V), although the attenuation factor (β) decreases from ca. 2 nm at low bias to <1 nm at 0.9 V, highlighting that β is not an intrinsic molecular property. Further theoretical analysis using density functional theory underlines the role of intersite coupling and indicates that this large increase in conductance with length at increasing voltages can be generalized to other molecular oligomers.

In meta-connected fluorenones, the carbonyl group almost negates the effects of destructive quantum interference, compared with corresponding meta-connected fluorenes.

When a single molecule is connected to external electrodes by linker groups, the connectivity of the linkers to the molecular core can be controlled to atomic precision by appropriate chemical synthesis. Recently, the connectivity dependence of the electrical conductance and Seebeck coefficient of single molecules has been investigated both theoretically and experimentally. Here we study the connectivity dependence of the Wigner delay time of single-molecule junctions and the connectivity dependence of su-perconducting proximity effects, which occur when the external electrodes are replaced by superconductors. Although absolute values of transport properties depend on complex and often uncontrolled details of the coupling between the molecule and electrodes, we demonstrate that ratios of transport properties can be predicted using tables of 'magic numbers,' which capture the connectivity dependence of superconducting proximity effects and Wigner delay times within molecules. These numbers are calculated easily, without the need for large-scale computations. For normal-molecule-superconducting junctions, we find that the electrical conductance is proportional to the fourth power of their magic numbers, whereas for superconducting-molecule-superconducting junctions, the critical current is proportional to the square of their magic numbers. For more conventional normal-molecule-normal junctions, we demonstrate that delay time ratios can be obtained from products of magic number tables.

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