Localization versus hybridization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math> states in actinide and lanthanide dioxides probed in core-level photoemission spectra

The degrees of the localization and hybridization of the valence <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>f</a:mi></a:math> states/covalency of the chemical bonding in actinide and lanthanide dioxides were investigated using the atomic, crystal-field multiplet and Anderson impurity model (AIM) approaches to calculate actinide <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>5</b:mn><b:mi>d</b:mi></b:mrow></b:math> and lanthanide <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>3</c:mn><c:mi>d</c:mi></c:mrow></c:math> x-ray photoemission spectra (XPS). The actinide <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>5</d:mn><d:mi>d</d:mi></d:mrow></d:math> XPS can be largely described within atomic, crystal-field multiplet theory due to an extended multiplet structure as a result of the strong interaction of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>5</e:mn><e:mi>f</e:mi></e:mrow></e:math> electrons with a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>5</f:mn><f:mi>d</f:mi></f:mrow></f:math> core hole. The multiplet structure was found to be quite sensitive to the oxidation state of actinides. In turn, the lanthanide <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>3</g:mn><g:mi>d</g:mi></g:mrow></g:math> XPS description requires the AIM type of calculations due to significant <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mn>4</h:mn><h:mi>f</h:mi></h:mrow></h:math>–O <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>2</i:mn><i:mi>p</i:mi></i:mrow></i:math> hybridization effects. As a result derived from the analysis of the XPS spectra, an increase in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>f</j:mi></j:math>-shell occupancy in the ground state due to the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mi>f</k:mi></k:math>–O <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mn>2</l:mn><l:mi>p</l:mi></l:mrow></l:math> hybridization and covalency of the chemical bonding appears to be higher in lanthanide dioxides as compared to actinide dioxides.