Impact of the U parameter on the predicted defect chemistry of materials: The example of PuO 2 ± x

Density functional theory (DFT) provides a powerful tool for describing the electronic properties of materials, however, self-interaction errors in semilocal functionals complicate the accurate modeling of correlated materials. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>DFT</a:mi> <a:mo>+</a:mo> <a:mi>U</a:mi> </a:mrow> </a:math> method is a popular and computationally cost-effective solution for mitigating self-interaction; though, this reduces the aspect of DFT calculations, as the outcome now becomes dependent on the user's choice of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>U</b:mi> </b:math> parameters. Atomistic modeling of plutonium dioxide ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>PuO</c:mi> <c:mn>2</c:mn> </c:msub> </c:math> ) is employed to provide insight into its evolution in storage or into its properties as mixed-oxide fuel. There is no single <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>U</d:mi> </d:math> parameter that can reproduce all the experimental properties of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>PuO</e:mi> <e:mn>2</e:mn> </e:msub> </e:math> accurately and, as such, it is important that the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>U</f:mi> </f:math> parameter is selected with careful consideration. In this work, we use noncollinear <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>DFT</g:mi> <g:mo>+</g:mo> <g:mi>U</g:mi> </g:mrow> </g:math> simulations to thoroughly examine the defect chemistry of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>PuO</h:mi> <h:mn>2</h:mn> </h:msub> </h:math> using <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>U</i:mi> <i:mo>=</i:mo> <i:mn>4</i:mn> </i:mrow> </i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mn>7</j:mn> <j:mspace width="0.28em"/> <j:mi>eV</j:mi> </j:mrow> </j:math> , in order to understand the implication the choice of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi>U</l:mi> </l:math> parameter can have on the predicted defect chemistry. We find that both <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>U</m:mi> </m:math> parameters predict the same intrinsic defect chemistry, with the main discrepancy being on the preferred charge state of the oxygen vacancies: <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mo>+</n:mo> <n:mn>2</n:mn> </n:mrow> </n:math> for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mi>U</o:mi> <o:mo>=</o:mo> <o:mn>4</o:mn> <o:mspace width="0.28em"/> <o:mi>eV</o:mi> </o:mrow> </o:math> and neutral for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mi>U</q:mi> <q:mo>=</q:mo> <q:mn>7</q:mn> <q:mspace width="0.28em"/> <q:mi>eV</q:mi> </q:mrow> </q:math> . Additionally, we show that the choice of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mi>U</s:mi> </s:math> can impact the defect formation energies and preferred charge states of a dopant. When uranium is placed onto a plutonium lattice site, it tends to favor the neutral and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mrow> <t:mo>+</t:mo> <t:mn>1</t:mn> </t:mrow> </t:math> charge state (indicative of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:msup> <u:mrow> <u:mi mathvariant="normal">U</u:mi> </u:mrow> <u:mrow> <u:mn>4</u:mn> <u:mo>+</u:mo> </u:mrow> </u:msup> </u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"> <w:msup> <w:mrow> <w:mi mathvariant="normal">U</w:mi> </w:mrow> <w:mrow> <w:mn>5</w:mn> <w:mo>+</w:mo> </w:mrow> </w:msup> </w:math> ) with <y:math xmlns:y="http://www.w3.org/1998/Math/MathML"> <y:mrow> <y:mi>U</y:mi> <y:mo>=</y:mo> <y:mn>4</y:mn> <y:mspace width="0.16em"/> <y:mi>eV</y:mi> </y:mrow> </y:math> , whereas with <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML"> <ab:mrow> <ab:mi>U</ab:mi> <ab:mo>=</ab:mo> <ab:mn>7</ab:mn> <ab:mspace width="0.16em"/> <ab:mi>eV</ab:mi> </ab:mrow> </ab:math> the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML"> <cb:mrow> <cb:mo>−</cb:mo> <cb:mn>1</cb:mn> </cb:mrow> </cb:math> and neutral charge states are more stable.