We have quantified the performance of various densityfunctional approaches for computing K-shell electron binding energies corresponding to ionization of C(1s), O(1s), N(1s), and F(1s) orbitals. As a baseline, we provide comprehensive benchmarks for the ∆SCF or "full core hole" approach, although our real interest lies in methods based on Slater's transition concept, using fractional-occupancy SCF calculations. This provides a means to compute core-level transition energies directly from Kohn-Sham orbital energy levels and may therefore be more amenable to chemical insight into the nature of chemical shifts in x-ray transitions, which could be rationalized in terms of shifting molecular orbital energy levels. The convenience of STM-based methods also represents a first step towards modeling transient x-ray experiments directly in terms of one-particle energy levels.