We have investigated a large set of symmetric and asymmetric molecules to demonstrate a general rule for molecular-scale quantum transport, which provides a new route to materials design and discovery. The rule states "the conductance GXBY of an asymmetric molecule is the geometric mean of the conductance of the two symmetric molecules derived from it and the thermopower SXBY of the asymmetric molecule is the algebraic mean of their thermopowers". The studied molecules have a structure X-B-Y, where B is the backbone of the molecule, while X and Y are anchor groups, which bind the molecule to metallic electrodes. When applied to experimentally measured histograms of conductance and thermopower, the rules apply to the statistically most probable values. We investigated molecules with anchors chosen from the following family: cyano, pyridl, dihydrobenzothiol, amine and thiol. For the backbones B, we tested 14 different structures. We found that the formulas (GXBY)(2) = GXBX*GYBY and SXBY = (SXBX + SYBY)/2 were satisfied in the large majority of the cases, provided the Fermi energy is located within the HOMO-LUMO gap of the molecules. The circuit rules imply that if measurements are performed on molecules with nA different anchors and nB different backbones, then properties of nA(nA + 1)nB/2 molecules can be predicted. So for example, in the case of 20 backbones and 10 anchors, 30 measurements (or reliable calculations) can provide a near quantitative estimate for 1070 measurements of other molecules, at no extra cost.

We studied the single-molecule conductance through an acid oxidant triggered phenothiazine (PTZ-) based radical junction using the mechanically controllable break junction technique. The electrical conductance of the radical state was enhanced by up to 200 times compared to the neutral state, with high stability lasting for at least two months and high junction formation probability at room-temperature. Theoretical studies revealed that the conductance increase is due to a significant decrease of the HOMO-LUMO gap and also the enhanced transmission close to the HOMO orbital when the radical forms. The large conductance enhancement induced by the formation of the stable PTZ radical molecule will lead to promising applications in single-molecule electronics and spintronics.

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