<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>,<i>3</i>x-ray-absorption edges of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>compounds:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Sc</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ti</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>(octahedral) symmetry (1990)

The ${L}_{2}$,3 x-ray-absorption edges of 3${d}^{0}$ compounds are calculated with use of an atomic description of the 2${p}^{6}$3${d}^{0}$ to 2${p}^{5}$3${d}^{1}$ excitation, with the inclusion of the crystal field. For reasons of clarity, we confine ourselves to ${d}^{0}$ compounds in octahedral symmetry, but the same approach is applicable to all other ${d}^{N}$ compounds in any point-group symmetry. The experimental spectra of ${\mathrm{FeTiO}}_{3}$, ${\mathrm{Sc}}_{2}$${\mathrm{O}}_{3}$, ${\mathrm{ScF}}_{3}$, ${\mathrm{CaF}}_{2}$, and the potassium halides are well reproduced by the present calculations, including the previously misinterpreted small leading peaks. The splitting between the two main peaks in both the ${L}_{3}$ and ${L}_{2}$ edge are related, though not equal, to the crystal-field splitting. Comparison to experiment showed that the broadening of the main multiplet lines is different. This can be related to Coster-Kronig Auger processes for the ${L}_{2}$ edge and to a solid-state broadening which is a combination of vibrational (phononic) and dispersional broadenings. With the full treatment of the atomic multiplets, the atomic effects can be separated from solid-state effects, which offers a better description of the latter. This includes vibrational broadenings, the covalent screening of the intra-atomic Coulomb and exchange interactions, via the position of small leading peaks, and surface effects. The same general framework can be used to discuss crystal-field effects in both lower symmetries, with the possibility of polarization-dependent spectra (e.g., ${\mathrm{TiO}}_{2}$), and partly filled d bands.