Geometry and electronic structures of rare earth-doped boron-based clusters <inline-formula><tex-math id="M2">\begin{document}$ {\text{REB}}_n^ - $\end{document}</tex-math></inline-formula> (RE = La, Sc; <i>n</i> = 6, 8)

Abstract

Rare earth doped boron clusters have attracted much attention due to their special optical, electrical and magnetic properties. The geometric structures, stability, electronic properties and aromaticity of negative rare earth doped boron clusters &lt;inline-formula&gt;&lt;tex-math id="M11"&gt;\begin{document}$ {\text{REB}}_n^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M11.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M11.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; (RE = La, Sc; &lt;i&gt;n&lt;/i&gt; = 6, 8) are investigated with the artificial bee colony algorithm combined with density functional theory calculations at the PBE0/RE/SDD//B/6-311+G* level of theory. Calculations show that the ground state structures of &lt;inline-formula&gt;&lt;tex-math id="M12"&gt;\begin{document}$ {\text{REB}}_n^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M12.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M12.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; (RE = La, Sc; &lt;i&gt;n&lt;/i&gt; = 6, 8) are all of &lt;i&gt;C&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; symmetry, and the doped lanthanide atom is located in a “boat-shaped” structure at the top center. By comparing with the experimental photoelectron spectra, it is confirmed that the ground state structure of &lt;inline-formula&gt;&lt;tex-math id="M13"&gt;\begin{document}$ {\text{LaB}}_{8}^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M13.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M13.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is a “zither-like” three-dimensional structure, and the ground state structure of &lt;inline-formula&gt;&lt;tex-math id="M14"&gt;\begin{document}$ {\text{ScB}}_{8}^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M14.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M14.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is an “umbrella” structure with C&lt;sub&gt;&lt;i&gt;7V&lt;/i&gt;&lt;/sub&gt; symmetry formed by the scandium atom at the “umbrella handle”. The electron localization between RE-B is not as good as that between B—B. The simulated photoelectron spectra have similar spectral characteristics to the experimental results. The lowest energy structures of &lt;inline-formula&gt;&lt;tex-math id="M15"&gt;\begin{document}$ {\text{LaB}}_{6}^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M15.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M15.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M16"&gt;\begin{document}$ {\text{ScB}}_{6}^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M16.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M16.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; are σ-π double aromatic clusters, and the structures exhibit aromaticity. The density of states of low-energy isomers shows that the open shell &lt;inline-formula&gt;&lt;tex-math id="M17"&gt;\begin{document}$ {\text{ScB}}_{8}^ - $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M17.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20240962_M17.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; density of states spectrum exhibits spin polarization phenomenon, which is expected to assemble magnetic material components. These studies contribute to understanding the evolution of structure and properties of nanomaterials, and provide important theoretical support for designing nanomaterials with practical value.