  The single-impurity Anderson model has been the focus of theoretical studies
of molecular junctions and the single-electron transistor, a nanostructured
device comprising a quantum dot that bridges two otherwise decoupled metallic
leads. The low-temperature transport properties of the model are controlled by
the ground-state occupation of the quantum dot, a circumstance that recent
density-functional approaches have explored. Here we show that the ground-state
dot occupation also parametrizes a linear mapping between the thermal
dependence of the zero-bias conductance and a universal function of the
temperature scaled by the Kondo temperature. Careful measurements by Grobis and
co-workers are very accurately fitted by the universal mapping. Nonetheless,
the dot occupation and an asymmetry parameter extracted from the same mapping
are relatively distant from the expected values. We conclude that mathematical
results derived from the model Hamiltonian reproduce accurately the universal
physical properties of the device. In contrast, non-universal features cannot
be reproduced quantitatively. To circumvent this limitation, \emph{ab initio}
studies of the device at high energies seem necessary, to accurately define the
model Hamiltonian. Our conclusion reinforces findings by Gross and coworkers,
who applied time-dependent density-functional theory to show that, to describe
the low-energy properties of molecular junctions, one must be able to describe
the high-energy regime.
