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\begin{document}

\title{Conversions of Localized Excess Electrons and Spin States under External
Electric Field: Inter-Cage Electron-transfer Isomer
(C\textsubscript{20}F\textsubscript{20})\textsubscript{3}\&K\textsubscript{2}}



\author[1]{ Jia-Min   Tang }%
\author[1]{Yin-Feng Wang}%
\author[1]{Tian Qin}%
\author[1]{Xue-Xia   Liu}%
\author[1]{ Zhijun  Wang}%
\author[1]{Jiangen Huang}%
\author[1]{Hua-Rong  Zhang}%
\author[1]{Kai Yang}%
\author[2]{Zhi-Ru Li}%
\affil[1]{Jinggangshan University}%
\affil[2]{Jilin University}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
By doping two potassium atoms among three
C\textsubscript{20}F\textsubscript{20} cages, peanut-shaped single
molecular solvated dielectron
(C\textsubscript{20}F\textsubscript{20})\textsubscript{3}\&K\textsubscript{2}
was theoretically presented. The triplet structures with two excess
electrons individually inside left and middle cages (isomers \textbf{I}
or \textbf{II}) are thermodynamically more stable than both open-shell
(OS) and close-shell (CS) singlet ones with lone pair of excess
electrons inside middle cage. Applying an oriented external electric
field (OEEF) of -20 \selectlanguage{ngerman}× 10\textsuperscript{-4} au (-0.1018 V/Å) or a
larger one can result in both left-to-right transfers of the two excess
electrons, and then releasing the OEEF can form new kind of inter-cage
electron-transfer isomers (\textbf{III} or \textbf{IV}). Each triplet
\textbf{I} \textasciitilde{} \textbf{IV} with three redox sits may be
new members of mixed-valent compounds, namely, Robin-Day Class II. For
electrified \textbf{I} of
(C\textsubscript{20}F\textsubscript{20})\textsubscript{3}\&K\textsubscript{2}
, the following spin states are ground state: 1) triplet state in field
ranges of -120 × 10\textsuperscript{-4} \textless{}
\emph{F}\textsubscript{x} \textless{} -30 × 10\textsuperscript{-4} au
and 30 × 10\textsuperscript{-4} \textless{} \emph{F}\textsuperscript{-4}
\textless{} 111 × 10\textsuperscript{-4} au; 2) CS singlet state in
range of \emph{F}\textsubscript{x} \selectlanguage{english}[?] 111 x 10\textsuperscript{-4} and \selectlanguage{english}[?]
-120 x 10\textsuperscript{-4} au; 3) OS singlet state in ranges of -30 x
10\textsuperscript{-4} \selectlanguage{english}[?] \emph{F}\textsubscript{x} \selectlanguage{english}[?] -5 x
10\textsuperscript{-4} au and 5 x 10\textsuperscript{-4} \selectlanguage{english}[?]
\emph{F}\textsubscript{x} \selectlanguage{english}[?] 30 x 10\textsuperscript{-4} au.%
\end{abstract}\selectlanguage{ngerman}%



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