Less attention has been paid to methods based on the Kohn-Sham orbital energy levels. These include Koopmans-type approaches based on asymptotically-correct XC functionals, or alternatively self-interaction-corrected eigenvalues, as well as methods based on fractional occupations. The latter are the methods considered here. Fractionaloccupancy SCF calculations have their historical basis in Slater's transition method (STM). The formal basis for fractional-electron SCF theory was established later, based on an ensemble expression for the chemical potential of an open quantum system. Within DFT, fractional-electron approaches are connected to problems at the heart of modern functional development: self-interaction, delocalization error, and the derivative discontinuity. Fractional-electron methods have also been used in the context of correlated wave functions. The STM approach and its subsequent generalizations compute electron binding energies directly from Kohn-Sham orbital eigenvalues. Because these one-particle energy levels can directly measure chemical shifts, these methods may hold some advantages for modeling complex systems or experiments, including transient spectroscopy at x-ray or extreme ultraviolet wavelengths. To model a pumpprobe experiment with the ∆SCF approach, where (for example) an optical pump pulse first prepares a valence excited state, which is subsequently interrogated using an x-ray probe, one would need to construct a core-hole within a ∆SCF calculation of the optically-excited state. In our experience, ∆SCF calculations for valence excited states are rather fragile and this composite calculation therefore runs a significant risk of variational collapse to the ground state.