Errors in the Slater transition state method for spin-polarized calculations of localized core levels

In analogy to the Slater transition state method for calculating ionization energies, which takes account of electronic relaxation effects, one may construct an unrelaxed transition state method, which gives Xα ionization energies which are the analog of Koopmans’ theorem ionization potentials of Hartree–Fock theory. As the unrelaxed method is more algebraically tractable, it can be analyzed in detail. Comparisons of unrelaxed transition state energies and unrelaxed Xα total energy differences for LCAO calculations reveal an anomalous error for spin-polarized localized core orbitals. This discrepancy is shown to arise from poor convergence of the series used to derive the transition state energy. Similar discrepancies are shown to exist in relaxed transition state calculations.