Transition voltage spectroscopy (TVS) has become an accepted quantification tool for molecular transport characteristics, due to its simplicity and reproducibility. Alternatively, the Taylor expansion view, TyEx, of transport by tunneling suggests that conductance–voltage curves have approximately a generic parabolic shape, regardless of whether the tunneling model is derived from an average medium view (e.g., WKB) or from a scattering view (e.g., Landauer). Comparing TVS and TyEx approaches reveals that TVS is closely related to a bias-scaling factor, V₀, which is directly derived from the third coefficient of TyEx, namely, the second derivative of the conductance with respect to bias at 0 V. This interpretation of TVS leads to simple expressions that can be compared easily across primarily different tunneling models. Because the basic curve shape is mostly generic, the quality of model fitting is not informative on the actual tunneling model. However internal correlation between the conductance near 0 V and V₀ (TVS) provides genuine indication on fundamental tunneling features. Furthermore, we show that the prevailing concept that V₀ is proportional to the barrier height holds only in the case of resonant tunneling, while for off-resonant or deep tunneling, V₀ is proportional to the ratio of barrier height to barrier width. Finally, considering TVS as a measure of conductance nonlinearity, rather than as an indicator for energy level spectroscopy, explains the very low TVS values observed with a semiconducting (instead of metal) electrode, where transport is highly nonlinear due to the relatively small, bias-dependent density of states of the semiconducting electrode.

The total energies and the spin states for atoms and their first ions with Z=1–86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc) energy in density-functional theory. Atoms and ions for which the ground-state density is not pure-state v-representable are treated as ensemble v-representable with fractional occupations of the Kohn-Sham system. A recently developed algorithm which searches over ensemble v-representable densities [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations. It is found that for many atoms, the ionization energies obtained with the GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab initio electronic configuration in the Kohn-Sham reference system does not always equal the configuration obtained from the spectroscopic term within the independent-electron approximation. It was shown that use of the latter configuration can prevent the energy-minimization process from converging to the global minimum, e.g., in lanthanides. The spin values calculated ab initio fit the experiment for most atoms and are almost unaffected by the choice of the xc functional. Among the systems with incorrectly obtained spin, there exist some cases (e.g., V, Pt) for which the result is found to be stable with respect to small variations in the xc approximation. These findings suggest a necessity for a significant modification of the exchange-correlation functional, probably of a nonlocal nature, to accurately describe such systems.

In the framework of Kohn-Sham density-functional theory, systems with ground-state densities that are not pure-state v-representable (PSVR) in the noninteracting reference system occur frequently. In the present contribution, an algorithm, which allows the solution of such systems, is proposed. It is shown that the use of densities which do not correspond to a ground state of their noninteracting reference system is forbidden. As a consequence, the proposed algorithm considers only noninteracting ensemble v-representable densities. The Fe atom, a well-known non-PSVR system, is used as an illustration. Finally, the problem is analyzed within finite-temperature density-functional theory, where the physical significance of fractional occupations is exposed and the question of why degenerate states can be unequally occupied is resolved.