  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 superconducting 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.
