\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[greek,ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{Theoretical Study of Multi-Coordinated Xe(AuF)n (n = 2-4): Intriguing
Bond-bending Isomerism}



\author[1]{Dongze Luo}%
\author[1]{Qinqin Yuan}%
\author[1]{Longjiu Cheng}%
\affil[1]{Anhui University}%


\vspace{-1em}



  
  \date{May 07, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
This work reports a theoretical study of a novel family of
multi-coordinated noble gas (Ng) complexes, Xe(AuF)n (n = 2-4).
Geometrical optimization at the LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP level locates two
types of structures based on the bond-bending isomerism induced by an
intramolecular competition between Xe-Au covalent bonding and Au\selectlanguage{ngerman}···Au
aurophilic interactions. They both comprise a center Xe atom serving as
an electron donor binding to AuF moieties, but pronouncedly differ in
the Au-Au distance and Au-Xe-Au bending angle. Comprehensive chemical
bonding analysis undisputedly demonstrates that aurophilic interactions
exist and affect the strength of Xe-Au bonds whose covalent nature is
evident. By scanning the potential energy surface of Xe(AuF)2 with
arbitrary one atom being substituted by its analogue, we found only
Xe(AuF)2 and Xe(AuCl)2 feature bond-bending isomerism, due to the highly
electronegative F/Cl atom inducing strongly covalent Xe-Au bond via
electron donation-feedback mechanism. The present work predicts
multi-coordinated Ng-metal complexes and demonstrates the bond-bending
isomerism, which could be an interesting addition and call out more
attentions to the research field of Ng chemistry.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\emph{ORIGINAL ARTICLE}\textbf{Journal Section}

\section*{\texorpdfstring{Theoretical Study of Multi-Coordinated
Xe(AuF)\textsubscript{\emph{n}} (\emph{n} = 2-4): Intriguing
Bond-bending
Isomerism}{Theoretical Study of Multi-Coordinated Xe(AuF)n (n = 2-4): Intriguing Bond-bending Isomerism}}

{\label{theoretical-study-of-multi-coordinated-xeaufn-n-2-4-intriguing-bond-bending-isomerism}}

\textbf{Dongze Luo\textsuperscript{1}\textbar{}} \textbf{Qinqin
Yuan\textsuperscript{1*}} \textbf{\textbar{} Longjiu
Cheng\textsuperscript{1,2*}}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
\textbf{Abstract} This work reports a theoretical study of a novel
family of multi-coordinated noble gas (Ng) complexes,
Xe(AuF)\textsubscript{\emph{n}} (\emph{n} = 2-4). Geometrical
optimization at the LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP level locates two types of
structures based on the bond-bending isomerism induced by an
intramolecular competition between Xe-Au covalent bonding and Au\selectlanguage{ngerman}···Au
aurophilic interactions. They both comprise a center Xe atom serving as
an electron donor binding to AuF moieties, but pronouncedly differ in
the Au-Au distance and Au-Xe-Au bending angle. Comprehensive chemical
bonding analysis undisputedly demonstrates that aurophilic interactions
exist and affect the strength of Xe-Au bonds whose covalent nature is
evident. By scanning the potential energy surface of
Xe(AuF)\textsubscript{2} with arbitrary one atom being substituted by
its analogue, we found only Xe(AuF)\textsubscript{2} and
Xe(AuCl)\textsubscript{2} feature bond-bending isomerism, due to the
highly electronegative F/Cl atom inducing strongly covalent Xe-Au bond
via electron donation-feedback mechanism. The present work predicts
multi-coordinated Ng-metal complexes and demonstrates the bond-bending
isomerism, which could be an interesting addition and call out more
attentions to the research field of Ng chemistry. \textbf{K E Y W O R D
S} Noble gas complex, Aurophilic interaction, Bond-bending isomerism,
Chemical bond analysis\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

\textsuperscript{1}Department of Chemistry, Key Laboratory of Functional
Inorganic Materials of Anhui Province, Anhui University, Hefei, 230601,
PR China

\textsuperscript{2}Key Laboratory of Structure and Functional Regulation
of Hybrid Materials (Anhui University), Ministry of Education, Hefei,
230601, PR China

\subsection*{Correspondence}

{\label{correspondence}}

Qinqin Yuan and Longjiu Cheng\emph{Department} \emph{of Chemistry, Key
Laboratory of Functional Inorganic Materials of Anhui Province, Anhui}
\emph{University,Hefei,} \emph{230601,} \emph{PR} \emph{ChinaKey
Laboratory of Structure and Functional Regulation of Hybrid Materials
(Anhui University), Ministry of Education, Hefei, 230601, PR
China}Email:\emph{qinqinyuan@ahu.edu.cn} (Q. Yuan)
and\emph{clj@ustc.edu} (L. Cheng)

\subsection*{Funding information}

{\label{funding-information}}

the National Natural Science Foundation of China (21873001), and by the
Foundation of Distinguished Young Scientists of Anhui Province.

\subsection*{1 \textbar{} INTRODUCTION}

{\label{introduction}}

Noble gas (Ng) atoms have proven capable of forming chemical
interactions ranging from weak van der Waals forces to strong covalent
bonds and ionic bonds, though they are traditionally considered to
feature chemical inertness arising from the fully occupied valence
shell. In fact, since XePtF\textsubscript{6} was first synthesized by
Bartlett in 1962,\textsuperscript{{[}1{]}} numerous Ng complexes have
been discovered and investigated, triggering ongoing and growing
attentions. Ng complexes are important in understanding and developing
the bonding theory and related chemistry, as well as in various research
and industrial applications. For instance, XeF\textsubscript{2}and
XeF\textsubscript{4} are exploited as key agents to remove impurities in
alloy smelting,\textsuperscript{{[}2{]}} while XeO\textsubscript{3} and
XeO\textsubscript{4} serve as useful explosive
components.\textsuperscript{{[}3{]}}From a chemical bonding perspective,
the Ng complexes uncovered so far can be generally divided into two
types according to the formation mechanism differentiated by how the Ng
atoms donating electrons. The former refers to those formed from that Ng
atoms interact with highly electronegative atoms (F, Cl, Br, O, N) or
groups (C\selectlanguage{english}[?]CH), constituting traditional covalent or ionic
bonds.\textsuperscript{{[}4-12{]}} At present, Ng atoms have been found
to bind to electronegative parts with a coordination number up to 6 and
Ng atom itself is in\emph{sp\textsuperscript{3}d\textsuperscript{2}}
hybridization, as in both inorganic XeF\emph{\textsubscript{n}}
(\emph{n} = 2, 3, 4, 6)\textsuperscript{{[}2, 13, 14{]}} and organic
Xe(CCH)\emph{\textsubscript{n}}(\emph{n} =1, 4,
6).\textsuperscript{{[}11, 12{]}} The latter type, however, represents
those where Ng atoms donate electrons to metal atoms (Cu, Ag, Au) to
form coordinated structures through van der Waals interactions or
covalent bonds with Ng in \emph{sp\textsuperscript{3}} hybridization. In
2000, by reduction of AuF\textsubscript{3} with elemental xenon, the
first complex containing noble gas-noble metal (Ng-Nm) interactions
(AuXe\textsubscript{4}\textsuperscript{2+}{[}Sb\textsubscript{4}F\textsubscript{11}{]}\textsubscript{2})
was synthesized experimentally,\textsuperscript{{[}15{]}} in which two
kinds of noble element, \emph{i.e.}, Au and Xe, formed a strong bonding
of the \selectlanguage{greek}\emph{σ}-\selectlanguage{english}donor type. This unique Ng-Nm bond stimulated further
search for similar complexes. Soon after, Gerry \emph{et al.} observed a
series of linear molecules comprising such bonds via laser ablation of
metals in explosion of buffer Ng. These species share a general formula
of NgNmX (Ng = Ar, Kr, Xe; Nm = Cu, Ag, Au; X = F, Cl,
Br)\textsuperscript{{[}16, 17-23{]}} and comprise Ng-Nm bonds that are
short and rigid. In particular, the Xe-Au bond in XeAuF ranked the
strongest Ng-Nm bond and was specially characterized with covalent
character.\textsuperscript{{[}21{]}}Given that a Ng atom like Xe owns
fully occupied valence shell and can thus afford as many as eight
electrons to form four equivalent \emph{sp\textsuperscript{3}} orbitals,
it is reasonable to forge multi-coordinated Ng structures via
interactions with metals, yet such multi-coordinated complexes have
hardly been reported. Gold outstands as a promising role in the study of
Ng chemistry and in constructing brand-new multi-coordinated Ng
structures. As a heavy atom, gold possesses strong relativistic
effects\textsuperscript{{[}24-27{]}}that induce the expanding of
5\emph{d} orbital and the shrink of the 6\emph{s} orbital. Accordingly,
Au exhibits a higher electron affinity compared to other noble metals
like Ag or Cu, which was readily verified in complexes like NgNmX, where
Ng-Au bond is saliently stronger than Ng-Ag and Ng-Cu bond. Another
unique property of gold is the Au(I)\selectlanguage{ngerman}···Au(I) aurophilic interaction, a
special attractive force between Au atoms with closed-shell electronic
configuration (5\emph{d}\textsuperscript{10}) that is thought to be a
joint result of strong relativistic effects and dispersion-type electron
correlations.\textsuperscript{{[}28-38{]}} Aurophilic interactions exert
profound effects on the configuration of related molecular structures.
For example, in a prior synergetic photoelectron spectroscopy (PES) and
theoretical study of gaseous
Au\textsubscript{2}I\textsubscript{3}\textsuperscript{-} cluster,
aurophilic interaction was found to compete with Au-I covalent bonding,
leading to the formation of two ``bond-bending isomers'' with
approximately degenerate energies.\textsuperscript{{[}39{]}}Therefore,
equipped with these peculiar characteristics, Au indubitably proves an
ideal candidate for further pursuing novel multi-coordinated Ng-metal
structures. However, although many efforts have been devoted to
generating and investigating Ng complexes, the understanding of relevant
structures and bonding remains controversial and obscure. In fact, it
has become one of key issues to search for new Ng complexes, especially
the multi-coordinated Ng-metal species, and explore the underlying
bonding mechanism. Ng atoms, in particular those having larger radiuses,
are capable of coordinating several atoms or groups
simultaneously.\textsuperscript{{[}14{]}} One is nature to wonder, if
the strongest Ng-Nm bond, \emph{i.e.} Xe-Au bond, can be extended from
already obtained XeAuF to heretofore unknown
Xe(AuF)\textsubscript{\emph{n}} (\emph{n} \selectlanguage{english}[?] 2), in light of the fact
that the diameter of Xe atom is large enough to spatially satisfy more
AuF groups. To address this question and gain more insights into the
Ng-metal bonding nature, this work theoretically predicts and
characterizes a series of novel multi-coordinated Ng complexes,
Xe(AuF)\emph{\textsubscript{n}} (\emph{n} = 2-4), by performing quantum
chemical calculations, serving as an essential complement to the
research field of Ng chemistry. To the best of our knowledge, such
multi-coordinated Xe(AuF)\emph{\textsubscript{n}}(\emph{n} = 2-4)
complexes have not been reported yet.

\subsection*{2 \textbar{} COMPUTATIONAL
DETAILS}

{\label{computational-details}}

In order to select an appropriate theoretical methodology, two key
structural and energetic parameters of linear XeAuF
molecules,\emph{i.e.}, the length and dissociation energy of Xe-Au bond
obtained separately from previous experimental work and CCSD(T)
calculations, are employed to benchmark several computational approaches
including DFT with different functionals (\emph{e.g.},
PBE,\textsuperscript{{[}40{]}}B3LYP,\textsuperscript{{[}41{]}}
M06-2X,\textsuperscript{{[}42{]}}CAM-B3LYP,\textsuperscript{{[}43{]}}
\selectlanguage{greek}ω\selectlanguage{english}B97X,\textsuperscript{{[}44{]}}and LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3
\textsuperscript{{[}45{]}}) and MP2. During the evaluation, def2TZVPP
basis set were used for DFT calculations, while MP2 and CCSD(T)
computations are performed with def2-QZVP basis set. All the
dissociation energies are acquired based on the LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP
optimized geometry. According to the comparison results presented
in\textbf{Table S1} and for the sake of balancing the accuracy and cost
of calculations, the LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP method, whose outputs are very
close to the judgment criteria, was chosen for further geometry
optimization and single-point energy calculations of
Xe(AuF)\textsubscript{\emph{n}} (\emph{n} = 2-4). Geometry optimizations
were carried out without any symmetry constraints. Vibrational frequency
analysis was performed at the same level to ensure that the optimized
structures were true minima, and obtained frequencies were used to
calculate the zero-point vibrational energies (ZPEs). All the DFT, MP2
and CCSD(T) calculations and natural bonding orbital (NBO) analysis
\textsuperscript{{[}46, 47{]}} were performed with Gaussian 16
suites.\textsuperscript{{[}48{]}} Basis set superposition error (BSSE)
corrections are included when computing dissociation
energies.\textsuperscript{{[}49{]}} To deeper understand the electron
structures and chemical bonding characteristics, the electron and
bonding analyses including electron localization function
(ELF),\textsuperscript{{[}50{]}} extended transition state--natural
orbitals for chemical valence (ETS-NOCV),\textsuperscript{{[}51,
52{]}}reduced density gradient (RDG)\textsuperscript{{[}53{]}} and
quantum theory of atoms in molecules (QTAIM)
methods\textsuperscript{{[}54-56{]}} were conducted with the aid of
Multiwfn codes.\textsuperscript{{[}57{]}}

\subsection*{3 \textbar{} RESULTS AND
DISCUSSION}

{\label{results-and-discussion}}

\subsubsection*{3.1 \textbar{} Geometries and Binding
Motifs}

{\label{geometries-and-binding-motifs}}

Multiple optimized structures of
Xe(AuF)\textsubscript{\emph{n}}(\emph{n} = 2-4) were theoretically
located at the LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP level and alphabetically labeled
from \emph{n}\textbf{a} to\emph{n}\textbf{c} according to their relative
energies, as shown in\textbf{Figure 1}. The key geometrical parameters
for all these predicted structures along with XeAuF were summarized in
\textbf{Table S2}. For Xe(AuF)\textsubscript{2}, two near-degenerate
isomers,\textbf{2a} and \textbf{2b}, were found to adopt a common bent
geometry with \emph{C}\textsubscript{2v} symmetry, in which the center
Xe atom binds to both AuF units but with different sizes of Au-Xe-Au
angle. A prior case study of
Au\textsubscript{2}I\textsubscript{3}\textsuperscript{-} shows similar
bond-bending isomerism that was characterized by an intramolecular
competition between aurophilic interaction and Au-I covalent
bonds.\textsuperscript{{[}39{]}} Here, the slightly high-lying
isomer\textbf{2b} simply contains two strong covalent Xe-Au bonds with a
length of 2.56 \selectlanguage{ngerman}Å, almost identical to that in linear
XeAuF.\textsuperscript{{[}21{]}} This covalent bonding favors a obtuse
Au-Xe-Au bent angle of 104.4°, a value that resembles the angle of water
molecules and supports the water-like bent configuration.
Isomer\textbf{2a} is more stable with 0.077 eV lower in energy due to
the additional intramolecular Au···Au aurophilic interaction arising
from the saliently smaller Au-Au distance of 2.82 Å compared to that of
4.05 Å in\textbf{2b}. From \textbf{2b} to \textbf{2a}, the bond angle of
Au-Xe-Au pronouncedly shrinks from 104.4° to 64.9°, the bond length of
Xe-Au is mildly elongated from 2.56 Å to 2.63 Å, while the length of
Au-F bonds maintains almost unchanged.\textbf{FIGURE 1} The optimized
structures of Xe(AuF)\emph{\textsubscript{n}} (\emph{n} = 2-4) at the
level of LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP with key bond lengths (\selectlanguage{ngerman}Å) and angles (°)
noted in black. The natural population analysis (NPA) charges on Xe, Au
and F are shown in red. The structural symmetries and relative energies
(in eV) are given under each structure (Xe, pink; Au, dark cyan; F,
purple). The structures framed by dotted lines have imaginary
frequencies at this level. The \emph{n} = 3 complex presents three
triangular conical geometries. The lowest-lying \textbf{3a} isomer
features \emph{C}\textsubscript{3v}symmetry and three intense aurophilic
interactions between every two of the three Au atoms but is calculated
to have an imaginary frequency of -29.05 cm\textsuperscript{-1}.
The\emph{C}\textsubscript{s} symmetric \textbf{3b} structure lies 0.241
eV higher in energy and contains one single aurophilic interaction
between the Au1 and Au2 atoms that are separated by 2.81 Å and exhibit a
bending angle of 64.5° with respect to the center Xe atom. The other Au3
atom resides 4.05 Å apart from each of these two Au atoms, with two
Au-Xe-Au angles equaling to 102.7°. The rest \textbf{3c} structure
devoid of aurophilic interactions has a \emph{C\textsubscript{3v}}
symmetry, displaying three identical Au-Au distances (4.02 Å) and
bending angles (104.0°). By comparing \textbf{3b} and \textbf{3c}, the
absence of one intramolecular aurophilic interaction raises the energy
of \textbf{3c}by nearly 0.1 eV. It is also worth mentioning that the
Au-Au distance corresponding to the aurophilic interaction keeps almost
identical for\textbf{2a} (2.82 Å) and \textbf{3b} (2.81 Å), hinting that
these aurophilic interactions are considerably close in intensity. For
\emph{n} = 4, the \textbf{4a} (\emph{C}\textsubscript{s}) and\textbf{4c}
(\emph{D}\textsubscript{2d}) structures are both calculated to have
imaginary frequencies albeit featuring aurophilic interactions, while
\textbf{4b} (\emph{T}\textsubscript{d}) is determined as the stable
local minima, which may be attributed from the synergistic
effect\textsuperscript{{[}58{]}} that all eight outer electrons of Xe
participate in interacting with four AuF ligands in a perfectly
symmetrical manner, forming a regular tetrahedral configuration like
that of well-known methane. Overall, these predicted structures
informally fall into two types based on whether intramolecular
aurophilic interactions exist. One type is that Au simply forms
conventional covalent bonding patterns to Xe and that different AuF
moieties are connected through a central Xe atom via Xe-Au interactions.
The calculated Au-Xe bond length for \textbf{2b},\textbf{3c}, and
\textbf{4b} structures equal to 2.56, 2.55 and 2.53 Å, respectively,
appreciably shorter compared to the sum of covalent radii of bare Au and
Xe atoms, suggesting the covalent Xe-Au bonding nature. By comparison,
the other type features both Xe--Au covalent and Au···Au aurophilic
interactions. The isomers of this type, \emph{e.g.,}\textbf{2a} and
\textbf{3b}, shows a much closer Au-Au distance (2.82 and 2.81Å), in
contrast to the former type with Au-Au distance up to 4.0 Å. The lengths
of Xe-Au bonds for the Au involved in aurophilic interaction are also
slightly elongated, while the Au-F bonds maintain basically identical in
length. For the sake of simplicity of discussion, these two types of
isomers are each named as \emph{traditional} and\emph{aurophilic}
structures.\textbf{FIGURE 2} Electron and bonding analysis of
Xe(AuF)\emph{\textsubscript{n}} (\emph{n} = 2-4). The left shows results
of the extended transition state (ETS) method combined with the natural
orbitals for chemical valence (ETS-NOCV), while the right visualizes the
electron localization function (ELF) pictures.

\subsubsection*{3.2 \textbar{} Electronic structures and chemical bonding
analysis}

{\label{electronic-structures-and-chemical-bonding-analysis}}

Noting that some of the structures are computed to be unstable with
imaginary frequencies, only the rest stable isomers, namely
\textbf{2a},\textbf{2b}, \textbf{3b}, \textbf{3c} and \textbf{4b}, were
used to in-depth analyze the electronic structure, while the analysis
results of the unstable species were simply listed in \textbf{Figure
S1-S3} for necessary reference. As a matter of fact, for all these
multi-coordinated structures, Au atoms are in the +1 oxidation state.
The \emph{6s} electron of each Au atom is transferred to the adjacent F
atom, forming an intense Au-F\selectlanguage{greek}\emph{σ} \selectlanguage{english}covalent bond with each Au atom in
5\emph{d}\textsuperscript{10} electron configuration. Meanwhile, the
highly electronegative F atom induces a \selectlanguage{greek}\emph{σ}-\selectlanguage{english}hole of Au atom on the
side away from the F atom (\textbf{Figure S4}). The electron on Xe atom
will be further pushed to this \selectlanguage{greek}\emph{σ}-\selectlanguage{english}hole and constitute covalent
Xe-Au bonding. This generalizes how the electron donation-feedback
mechanism works within the formation of Xe-Au bonds. To better
understand the chemical bonding nature and to obtain a qualitative
bonding picture, ETS-NOCV analysis and EFL analysis were jointly
performed (\textbf{Figure 2}) to elucidate the electronic structures.
ELF directly visualize the probability of finding an electron in the
vicinity of another reference electron. On the other hand, ETS-NOCV
method has been long established useful in investigating orbital
interactions by decomposing the orbital interaction energy into the
contribution of each NOCV pair. The density of each NOCV pair
corresponds to its contribution to the electron density. Here,
Xe(AuF)\emph{\textsubscript{n}} were divided into \emph{n}+1 groups (Xe
and \emph{n}AuF, \emph{n} = 2-4) to directly probe the interactions of
Xe and Au. \textbf{Figure 2} shows the dominating NOCV pairs selected to
characterize Xe-Au bonding. Apparently, all the Xe-Au bonds are formed
upon \emph{p} electron transferred from Xe to Au (see pair 1) and the
feedback from \emph{d} orbital of Au atom to Xe (see pair 2). No orbital
interactions were observed between any two Au atoms in
\textbf{2b},\textbf{3c} and \textbf{4b}, indicating the absence of
aurophilic interactions. By contrast, the NOCV pairs in \textbf{2a} and
\textbf{3b}clearly present the \emph{d} orbital interaction between the
specific Au atoms that forms aurophilic interaction, which was also
visually confirmed by the rendered ELF image in Figure 2. Moreover, the
ETS-NOCV analysis suggests stronger \emph{d} orbital feedback of Au in
the aurophilic species, interpreting why the Xe-Au bonding intensity
differs when aurophilic interactions are engaged. The hyperconjugation
of\emph{n}Ng - \selectlanguage{greek}\emph{σ}\selectlanguage{english}\textsuperscript{*}Nm, on the other hand, results
in electron density transferring from the lone pair electron of Ng to
the antibonding orbital of NmX moiety, thereby endowing the Ng atom
moderate positive charge with the X atom getting slightly negative,
aligning with the NPA analysis in \textbf{Figure 1}. When the number of
AuF groups increases, the positive charge on Xe atom of traditional
structures (\textbf{2b}-\textbf{3c}-\textbf{4b}) gradually increases
from 0.35 to 0.45 and then to 0.49, implying a rise in the contribution
of electron pairs of Xe, while the positive charge on Au and F keeps
nearly unchanged.\textbf{FIGURE 3} Reduced density gradient (RDG)
analysis of Xe(AuF)\emph{\textsubscript{n}} (\emph{n} = 2-4) with
non-covalent interactions (NCI) isosurface set at \emph{s} = 0.3. In
addition, to quantitatively investigate the related chemical bonding
strength, Reduced density gradient (RDG) analysis was conducted to
obtain the peak spike values of non-covalent interactions (NCI)
(see\textbf{Figure 3}). Generally, the more negative the spike value,
the stronger the corresponding interaction. Three types of spike values
were captured for Xe(AuF)\emph{\textsubscript{n}} (\emph{n} = 2,3,4)
from the crossing point of the RDG image with horizontal axis. The two
side values approximately equal to -0.140, and -0.045, respectively,
whereas the middle value occupies an appreciably broader range from
-0.066 to -0.082. Noting that the spike value in neutral AuF was
reported as -0.138\textsuperscript{{[}38{]}}, the most negative value of
nearly -0.140 was reasonably attributed to the Au-F bond, which is
moderately stronger in Xe(AuF)\emph{\textsubscript{n}} due to the
feedback from\emph{d} orbital of Au to Xe atom. The close spike values
of -0.045 and -0.048 respectively in \textbf{2a} and \textbf{3b} arise
from the isosurface denoting Au\selectlanguage{ngerman}···Au interaction on account of they only
showing up in these aurophilic structures. Given above, the middle spike
value that spans from -0.066 to -0.082 is concluded to represent Au-Xe
bonding, in which the smaller values refer to those where Au
participates in aurophilic interactions. Obviously, the Xe-Au bonding
strength in \textbf{2a} is mildly weaker than that in \textbf{2b} by
comparing the corresponding spike values of -0.070 and -0.078, in good
agreement with the bond lengths in \textbf{2a} (2.63Å) and
\textbf{2b}(2.56Å). The \textbf{3b} structure comprises two kinds of
Xe-Au spike values respectively of -0.080 and -0.066, representing two
different Xe-Au interactions classified according to whether the Au atom
is involved in aurophilic interactions. Moreover, the spike values of
Xe-Au bonding in traditional structures slightly reduce from -0.078 to
-0.080 and then to -0.082 as the number of AuF increases, consistent
with the decrease in bond length of Xe-Au (from 2.56 to 2.55 and to 2.53
Å) and the enhancement of Xe-Au bonding intensities. Furthermore, by
comparing the largest spike value of Xe-Au bond equaling to -0.066 in
\textbf{3b}with the corresponding value of -0.070 in \textbf{2a}, we are
convinced the aurophilic interaction is more competitive in \textbf{3b}
than that in \textbf{2a}.\textbf{TABLE 1} The Xe-Au bond lengths, along
with electron density\selectlanguage{greek}\emph{ρ}\selectlanguage{english}(\emph{r}\textsubscript{c}), Laplacian of
electron density
V\textsuperscript{2}\selectlanguage{greek}\emph{ρ}\selectlanguage{english}(\emph{r}\textsubscript{c}), electron local
energy density \emph{H}(\emph{r}\textsubscript{c}), local kinetic energy
density \emph{G}(\emph{r}\textsubscript{c}), and the ratio
of\emph{G}(\emph{r}\textsubscript{c})
and\selectlanguage{greek}\emph{ρ}\selectlanguage{english}(\emph{r}\textsubscript{c}) at the bond critical points
(BCPs) of the Xe-Au bonds in Xe(AuF)\textsubscript{\emph{n}} (\emph{n} =
1-4) calculated at the LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP level.\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\textbf{Complex} & \textbf{R\textsubscript{Xe-Au}} &
\selectlanguage{greek}\emph{ρ}\selectlanguage{english}\textbf{(\emph{r}\textsubscript{c})} &
\emph{V\textsuperscript{2}ρ}\selectlanguage{greek}\selectlanguage{english}\textbf{(\emph{r}\textsubscript{c})} &
\emph{H}\textbf{(\emph{r}\textsubscript{c})} &
\emph{G}\textbf{(\emph{r}\textsubscript{c})} &
\emph{G}\selectlanguage{greek}\textbf{(\emph{r}\textsubscript{c})/\emph{ρ}(\emph{r}\textsubscript{c})}\selectlanguage{english}\tabularnewline
\midrule
\endhead
\textbf{1} & 2.57 & 0.077 & 0.178 & -0.023 & 0.068 &
0.883\tabularnewline
\textbf{2a} & 2.63 & 0.068 & 0.155 & -0.018 & 0.057 &
0.838\tabularnewline
\textbf{2b} & 2.56 & 0.069 & 0.160 & -0.018 & 0.058 &
0.841\tabularnewline
\textbf{3b \textsuperscript{*}} & 2.63/2.55 & 0.069/0.079 & 0.159/0.196
& -0.018/-0.025 & 0.058/0.073 & 0.841/0.924\tabularnewline
\textbf{3c} & 2.55 & 0.079 & 0.197 & -0.025 & 0.074 &
0.937\tabularnewline
\textbf{4b} & 2.53 & 0.082 & 0.209 & -0.027 & 0.079 &
0.963\tabularnewline
\bottomrule
\end{longtable}

* The two values in each box for the 3b structure correspond to the
Xe-Au1 and Xe-Au3 bonds, respectively.

\subsubsection*{\texorpdfstring{3.3 \textbar{} Covalent character
investigation of Xe-Au bonds in Xe(AuF)\textsubscript{\emph{n}}
(\emph{n} =
2-4)}{3.3 \textbar{} Covalent character investigation of Xe-Au bonds in Xe(AuF)n (n = 2-4)}}

{\label{covalent-character-investigation-of-xe-au-bonds-in-xeaufn-n-2-4}}

The bonding character of Ng-Nm interactions has been one of hot issues
of the related research field. To further explore the chemical bonding
nature of Xe-Au bonds in Xe(AuF)\textsubscript{\emph{n}} (\emph{n} =
2-4), quantum-theory-of-atoms-in-molecules (QTAIM) analysis is
performed, aimed at providing extra evidence for a bond path among all
bonding interactions with a bond critical point (BCP) and a significant
accumulation of electron density within the bond (see electron
density\selectlanguage{greek}\emph{ρ} \selectlanguage{english}\textsubscript{bcp} in \textbf{Table 1} ). Typically, at
the BCP of a certain chemical bond, high electron density\selectlanguage{greek}\emph{ρ}
\selectlanguage{english}(\emph{r} \textsubscript{c}) and negative Laplacian electron density
V\textsuperscript{2}\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{r} \textsubscript{c}) values define
a covalent bond, but this criterion does not always work especially when
heavier atoms are involved. The energy density\emph{H} (\emph{r}
\textsubscript{c}), ratio of local kinetic energy density \emph{G}
(\emph{r\textsubscript{c}} ) and electron density\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{r}
\textsubscript{c}), however, are more proper parameters in these cases.
Covalent bonds are characterized by BCPs with negative\emph{H} (\emph{r}
\textsubscript{c}) and\emph{G} (\emph{r} \textsubscript{c})/\selectlanguage{greek}\emph{ρ}
\selectlanguage{english}(\emph{r} \textsubscript{c}) lower than 1, while those with
positive\emph{H} (\emph{r} \textsubscript{c}) and\emph{G} (\emph{r}
\textsubscript{c})/\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{r} \textsubscript{c}) exceeding 1
usually denote closed-shell interaction.\textsuperscript{{[}59{]}} Based
on this criterion, the\emph{H} (\emph{r} \textsubscript{c}) and\emph{G}
(\emph{r} \textsubscript{c})/\selectlanguage{greek}\emph{ρ} \selectlanguage{english}(\emph{r} \textsubscript{c})
values at all BCPs suggest explicit covalent nature of the Xe-Au bonds
for the whole series of predicted structures. Moreover, as mentioned in
the RDG analysis, the electron density between Xe and Au atoms are
slightly bigger in traditional structures (\textbf{2b} , \textbf{3c}
and\textbf{4a} ). Topological analysis was additionally performed for
linear NgNmX (Ng = He, Ne, Ar, Kr and Xe; Nm = Cu, Ag and Au; X = F, Cl,
Br and I) molecules and compared in \textbf{Table S3} , revealing that
the Ng-Nm bonds are gradually transformed from dispersive to covalent as
the Ng atom grows heavier and that the metal and halogen atoms are
capable of affecting the Ng-Nm bonding strength without altering the
bonding character.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{FIGURE 4} (a) Calculated geometries of \textbf{2a}
and\textbf{2b} . (b) Potential energy curves of Xe(MF)\textsubscript{2}
(M = Au, Ag, Cu). (c) Potential energy curves of
Xe(AuX)\textsubscript{2} (X = F, Cl, Br). (d) Potential energy curves of
Ng(AuF)\textsubscript{2}(Ng = Xe, Kr, Ar). All geometries used in
potential energy curve illustration were obtained by full optimization
at each bending angle under the level of LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP.

\subsubsection*{3.4 \textbar{} Competition between Ng-Nm bonds and
metallophilic
interactions}

{\label{competition-between-ng-nm-bonds-and-metallophilic-interactions}}

A fact should be addressed is that aurophilic interaction can be
generalized to a wider range of metals. The concept of metallophilic
interaction typically denotes a weak electrostatic attractive force and
is encountered mainly between adjacent low-valent closed shell
{[}(n-1)d\textsuperscript{10}s\textsuperscript{0}{]} or pseudo-closed
shell {[}(n-1)d\textsuperscript{8}ns\textsuperscript{0}{]} metal centers
like Cu(I), Ag(I), Hg(II) and so on.\textsuperscript{{[}60{]}} The
competition between Ng-Nm bonds and metallophilic interactions is
undoubtedly an interesting issue that induce the bond-bending isomerism.
A good way to dig into the competition mechanism is to observe how the
molecular structure will respond once any one of the atoms in
Xe(AuF)\textsubscript{n} varies. For this purpose, the potential energy
curves of Ng(NmX)\textsubscript{2} (Ng = Ar, Kr, Xe; Nm = Cu, Ag, Au; X
= F, Cl, Br) were calculated and illustrated in \textbf{Figure 4} , by
flexibly scanning the potential energy surface via stepwise changing the
Nm-Ng-Nm angle. In contrast to Xe(AuF)\textsubscript{2} and
Xe(AuCl)\textsubscript{2} that have two minimums on the potential energy
curve representing the coexistence of \textbf{2a} and
\textbf{2b}structures, the rest species exhibit only one minimum at a
Ng-Nm-Ng angle of approximately 60\selectlanguage{ngerman}°, indicative of the sole \textbf{2b}
isomer. This may be because only Xe(AuF)\textsubscript{2} and
Xe(AuCl)\textsubscript{2} have Xe-Au bonds that are strong enough to
compete with metallophilic interactions, thereby allowing two types of
bond-bending isomers to coexist.

The optimized structures and the key geometrical parameters of
Ng(AuF)\textsubscript{2} (Ng = Ar and Kr), Xe(NmF)\textsubscript{2} (Nm
= Ag and Cu) and Xe(AuX)\textsubscript{2} (X = Cl and Br) are calculated
as well and given in \textbf{Figure S5} . RDG analysis of these
molecules shows a salient decrease of the Ng-Nm spike value from
\textasciitilde{}0.08 to \textasciitilde{}0.06 (\textbf{Figure 3 and S6}
) once one arbitrary atom of Ng(AuF)\textsubscript{2} is substituted. It
is noteworthy that weaker Ng-Nm bonds will lead to an increased
instability of the traditional structures while have negligible effects
on metallophilic structures, highlighting the significant role of Ng-Nm
bonding strength in bond-bending isomerism.

\subsubsection*{3.5 \textbar{} Comparison among multi-coordinated Xe
complexes}

{\label{comparison-among-multi-coordinated-xe-complexes}}

As mentioned hereinbefore, in inorganic complexes
XeF\emph{\textsubscript{n}} (\emph{n} =2, 4, 6)\textsuperscript{{[}2,
14{]}} or organic complexes Xe(CCH)\emph{\textsubscript{n}} (\emph{n} =
4, 6)\textsuperscript{{[}12{]}}, Xe tends to bind with an
electronegative group via electron donation from both parts. The Xe-F
bond in XeF\textsubscript{n} exhibits traditional \selectlanguage{greek}\emph{σ} -\selectlanguage{english}covalent
character with Xe in
\emph{sp\textsuperscript{3}d\textsuperscript{n}}hybridization, forming
symmetrical geometries, \emph{e.g.} , linear\emph{D} \textsubscript{2h}
configuration for XeF\textsubscript{2}\textsuperscript{{[}2{]}}, square
planar\emph{D} \textsubscript{4h} structure for
XeF\textsubscript{4}\textsuperscript{{[}2{]}}, and square
bipyramidal\emph{O} \textsubscript{h} structure for
XeF\textsubscript{6}\textsuperscript{{[}14{]}}. Similar phenomena were
observed for the Xe-CCH bond in Xe(CCH)\emph{\textsubscript{n}}
(\emph{n} = 4, 6), but with slight difference in that this interplay is
partially ionic and partially covalent.\textsuperscript{{[}12{]}}
However, the strong covalent Xe-Au bonding in this work was formed via
the electron donation-feedback mechanism for the whole family of
Xe(AuF)\emph{\textsubscript{n}} (\emph{n} = 2-4) with Xe
in\emph{sp\textsuperscript{3}} hybridization. The comparison clearly
shows the differences regarding the formation mechanism of two types of
Ng complexes referred to in the introduction context and gives further
evidence to this work serving as an essential complement to the research
field of Ng chemistry.

\subsection*{4 \textbar{} CONCLUSION}

{\label{conclusion}}

In summary, the geometrical and electronic structures of a novel family
of multi-coordinated Ng complexes, Xe(AuF)\textsubscript{\emph{n}}
(\emph{n} = 2-4), were theoretically predicted by using
LC-\selectlanguage{greek}ω\selectlanguage{english}PBE-D3/def2TZVPP method. Two types of bond-bending isomers were
located with different Au-Xe-Au bond angles as a result of the
competition between intramolecular aurophilic interactions and Xe-Au
covalent bonds. Thorough potential energy surface scanning of
Ng(NmX)\textsubscript{2} (Ng = Ar, Kr, Xe; Nm = Cu, Ag, Au; X = F, Cl ad
Br) shows the unique bond-bending isomerism merely exists in
Xe(AuF)\emph{\textsubscript{n}} and Xe(AuCl)\emph{\textsubscript{n}} ,
since their Xe-Au bonds are strong enough to compete against aurophilic
interactions. Systematic chemical bonding analysis, \emph{e.g.} ,
ETS-NOCV, EFL, RDG, and QTAIM, between these two types of bond-bending
isomers confirms aurophilic interactions indeed exist and pronouncedly
affect the intensity of the covalent Xe-Au bonds in these
multi-coordinated Ng complexes. This work stands as an essential
complement to the research field of Ng chemistry and pave the way for
experimental progress in discovering multi-coordinated Ng complexes.

SUPPORTING INFORMATION

Comparison of the length and dissociation energy of Xe-Au bond in Xe-AuF
at different theoretical levels (Table S1); geometric parameters of
Xe(AuF)\textsubscript{n} (n = 1-4) (Table S2); QTAIM topological
analysis of linear NgMX (Ng = He, Ne, Ar, Kr, Xe; M = Cu, Ag, Au; X = F,
Cl, Br, I) molecule (Table S3); chemical bonding analysis of
isomers\textbf{3a} , \textbf{4a} and \textbf{4c} , including ETS-NOCV,
ELF and RDG methods (Figure S1-S3); surface electrostatic potential map
of AuF molecule (Figure S4); the lowest-energy structures of
Ng(MX)\textsubscript{2} (Ng = Xe, Kr, Ar; M = Cu, Ag, Au, X = F, Cl, Br)
with geometric and energic parameters; RDG analysis of
Xe(AgF)\textsubscript{2} and Xe(CuF)\textsubscript{2} (Figure S6).

ACKNOWLEDGEMENTS

This work was financed by the National Natural Science Foundation of
China (21873001), and by the Foundation of Distinguished Young
Scientists of Anhui Province. Q. Y. acknowledges support from the
start-up grants from Anhui University under No. S020318008/024. The
theoretical calculations were carried out at the High-Performance
Computing Center of Anhui University.

CONFLICT OF INTEREST

The authors declare no competing financial interest.

REFERENCES

{[}1{]} Bartlett, N. \emph{Proc Chem Soc} \textbf{1962} , 218-218.

{[}2{]} Rundle, R. J. \emph{J Am Chem Soc} \textbf{1963} , \emph{85} ,
112-113.

{[}3{]} Vent-Schmidt, T.; Goettel, J. T.; Schrobilgen, G. J.; Riedel, S.
\emph{Chem - Eur J} \textbf{2015} ,\emph{21} , 11244-11252.

{[}4{]} Turner, J. J.; Pimentel, G. C.\emph{Science} \textbf{1963} ,
\emph{140} , 974-975.

{[}5{]} Nelson, L. Y.; Pimentel, G. C. \emph{Inorg Chem} \textbf{1967} ,
\emph{6} , 1758-1759.

{[}6{]} Gerber, R. B. \emph{Annu Rev Phys Chem} \textbf{2004} ,
\emph{55} , 55-78.

{[}7{]} Khriachtchev, L.; R\selectlanguage{ngerman}äsänen, M.; Gerber, R. B. \emph{Acc Chem Res}
\textbf{2009} , \emph{42} , 183-191.

{[}8{]} Lundell, J.; Cohen, A.; Gerber, R. B. \emph{J Phys Chem A}
\textbf{2002} , \emph{106} , 11950-11955.

{[}9{]} Khriachtchev, L.; Tanskanen, H.; Lundell, J.; Pettersson, M.;
Kiljunen, H.; Räsänen, M. \emph{J Am Chem Soc} \textbf{2003} ,
\emph{125} , 4696-4697.

{[}10{]} Khriachtchev, L.; Tanskanen, H.; Cohen, A.; Gerber, R. B.;
Lundell, J.; Pettersson, M.; Kiljunen, H.; Räsänen, M. \emph{J Am Chem
Soc} \textbf{2003} , \emph{125} , 6876-6877.

{[}11{]} Feldman, V. I.; Sukhov, F. F.; Orlov, A. Y.; Tyulpina, I. V.
\emph{J Am Chem Soc} \textbf{2003} ,\emph{125} , 4698-4699.

{[}12{]} Sheng, L.; Gerber, R. B.\emph{J Chem Phys} \textbf{2006} ,
\emph{124} , 231103.

{[}13{]} Krouse, I. H.; Hao, C.; Check, C. E.; Lobring, K. C.;
Sunderlin, L. S.; Wenthold, P. G. \emph{J Am Chem Soc} \textbf{2007} ,
\emph{129} , 846-852.

{[}14{]} Jr., R. M. G.; Bartell, L. S. \emph{J Chem Phys} \textbf{1968}
, \emph{48} , 2460-2465.

{[}15{]} Seidel, S.; Seppelt, K. \emph{Science} \textbf{2000} ,
\emph{290} , 117-118.

{[}16{]} Michaud, J. M.; Gerry, M. C. L.\emph{J Am Chem Soc}
\textbf{2006} , \emph{128} , 7613-7621.

{[}17{]} Evans, C. J.; Gerry, M. C. L. \emph{J Chem Phys} \textbf{2000}
,\emph{112} , 9363-9374.

{[}18{]} Evans, C. J.; Gerry, M. C. L. \emph{Phys Chem Chem Phys}
\textbf{2000} , \emph{112} , 1321-1329.

{[}19{]} Evans, C. J.; Lesarri, A.; Gerry, M. C. L. \emph{J Am Chem Soc}
\textbf{2000} , \emph{122} , 6100-6105.

{[}20{]} Evans, C. J.; Rubinoff, D. S.; Gerry, M. C. L. \emph{Phys Chem
Chem Phys} \textbf{2000} , \emph{2} , 3943-3948.

{[}21{]} Cooke, S. A.; Gerry, M. C. L. \emph{J Am Chem Soc}
\textbf{2004} , \emph{126} , 17000-17008.

{[}22{]} Michaud, J. M.; Cooke, S. A.; Gerry, M. C. L. \emph{Inorg Chem}
\textbf{2004} , \emph{43} , 3871-3881.

{[}23{]} Thomas, J. M.; Walker, N. R.; Cooke, S. A.; Gerry, M. C. L.
\emph{J Am Chem Soc} \textbf{2004} ,\emph{126} , 1235-1246.

{[}24{]} Pyykko, P. \emph{Chem Rev}\textbf{1988} , \emph{88} , 563-594.

{[}25{]} Schmidbaur, H.; Cronje, S.; Djordjevic, B.; Schuster, O.
\emph{Chem Phys} \textbf{2005} , \emph{311} , 151-161.

{[}26{]} Yu, X. L.; Jin, T.; Wang, K.; Li, D.; Cheng, L. J. \emph{J Chem
Phys} \textbf{2022} , \emph{156} , 104103.

{[}27{]} Schmidbaur, H. \emph{Gold Bull} \textbf{2000} , \emph{33} ,
3-10.

{[}28{]} Schmidbaur, H.; Schier, A.\emph{Chem Soc Rev} \textbf{2008} ,
\emph{37} , 1931-1951.

{[}29{]} Schmidbaur, H. \emph{Gold Bull} \textbf{1990} , \emph{23} ,
11-21.

{[}30{]} Mirzadeh, N.; Privér, S. H.; Blake, A. J.; Schmidbaur, H.;
Bhargava, S. K. \emph{Chem Rev}\textbf{2020} , \emph{120} , 7551-7591.

{[}31{]} Moreno-Alcántar, G.; Turcio-García, L.; Guevara-Vela, J. M.;
Romero-Montalvo, E.; Rocha-Rinza, T.; Pendás, Á. M.; Flores-Álamo, M.;
Torrens, H.\emph{Inorg Chem} \textbf{2020} , \emph{59} , 8667-8677.

{[}32{]} Zeman, C. J.; Shen, Y.-H.; Heller, J. K.; Abboud, K. A.;
Schanze, K. S.; Veige, A. S. \emph{J Am Chem Soc} \textbf{2020} ,
\emph{142} , 8331-8341.

{[}33{]} Pyykkö, P. \emph{Chem Rev}\textbf{1997} , \emph{97} , 597-636.

{[}34{]} Pyykkö, P. \emph{Angew Chem, Int Ed} \textbf{2004} , \emph{43}
, 4412-4456.

{[}35{]} Pyykkö, P. \emph{Inorg Chim Acta} \textbf{2005} , \emph{358} ,
4113-4130.

{[}36{]} Pyykkö, P. \emph{Chem Soc Rev} \textbf{2008} , \emph{37} ,
1967-1997.

{[}37{]} Gagliardi, L.; Pyykkö, P.\emph{Angew Chem, Int Ed}
\textbf{2004} , \emph{116} , 1599-1602.

{[}38{]} Yu, X.; Li, D.; Wang, K.; Xia, T.; Xu, C.; Wu, Z.; Cheng, L.
\emph{Inorg Chem} \textbf{2022} ,\emph{61} , 1051-1058.

{[}39{]} Li, W. L.; Liu, H. T.; Jian, T.; Lopez, G. V.; Piazza, Z. A.;
Huang, D. L.; Chen, T. T.; Su, J.; Yang, P.; Chen, X.; Wang, L. S.; Li,
J. \emph{Chem Sci} \textbf{2016} ,\emph{7} , 475-481.

{[}40{]} Perdew, J. P.; Burke, K.; Ernzerhof, M. \emph{Phys Rev
Lett}\textbf{1996} , \emph{77} , 3865-3868.

{[}41{]} Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M.
J. \emph{J Phys Chem} \textbf{1994} ,\emph{98} , 11623-11627.

{[}42{]} Zhao, Y.; Truhlar, D. G.\emph{Acc Chem Res} \textbf{2008} ,
\emph{41} , 157-167.

{[}43{]} Yanai, T.; Tew, D. P.; Handy, N. C. \emph{Chem Phys Lett}
\textbf{2004} , \emph{393} , 51-57.

{[}44{]} Chai, J.-D.; Head-Gordon, M.\emph{J Chem Phys} \textbf{2008} ,
\emph{128} , 084106.

{[}45{]} Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. \emph{J Chem
Phys} \textbf{2010} , \emph{132} , 154104.

{[}46{]} Reed, A. E.; Weinhold, F. \emph{J Chem Phys} \textbf{1983}
,\emph{78} , 4066-4073.

{[}47{]} Weinhold, F. \emph{J Comput Chem} \textbf{2012} , \emph{33} ,
2363-2379.

{[}48{]} Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.;
Cheeseman, J.; Scalmani, G.; Barone, V.; Petersson, G.; Nakatsuji, H.
\emph{Gaussian Inc: Wallingford, CT} \textbf{2016} .

{[}49{]} Rosa, A.; Ehlers, A. W.; Baerends, E. J.; Snijders, J. G.; te
Velde, G. \emph{J Phys Chem}\textbf{1996} , \emph{100} , 5690-5696.

{[}50{]} Silvi, B.; Savin, A.\emph{Nature} \textbf{1994} , \emph{371} ,
683-686.

{[}51{]} Mitoraj, M.; Michalak, A.\emph{J Mol Model} \textbf{2007} ,
\emph{13} , 347-355.

{[}52{]} Mitoraj, M. P.; Michalak, A.; Ziegler, T. \emph{J Chem Theory
Comput} \textbf{2009} , \emph{5} , 962-975.

{[}53{]} Johnson, E. R.; Keinan, S.; Mori-Sanchez, P.; Contreras-Garcia,
J.; Cohen, A. J.; Yang, W. T.\emph{J Am Chem Soc} \textbf{2010} ,
\emph{132} , 6498-6506.

{[}54{]} Bader, R. F. W. \emph{Acc Chem Res} \textbf{1985} , \emph{18} ,
9-15.

{[}55{]} Bader, R. F. W. \emph{Chem Rev} \textbf{1991} , \emph{91} ,
893-928.

{[}56{]} Matta, C.; Boyd, R. J.\emph{Wiley-VCH: New York} \textbf{2007}
.

{[}57{]} Lu, T.; Chen, F. W. \emph{J Comput Chem} \textbf{2012} ,
\emph{33} , 580-592.

{[}58{]} Franc, H. S.; Wen, W. Y. \emph{Discuss Faraday
Soc}\textbf{1957} , \emph{24} , 133.

{[}59{]} Wen, M.; Li, Z. Z.; Li, A. Y. \emph{Phys Chem Chem Phys}
\textbf{2019} , \emph{21} , 26311-26323.

{[}60{]} Raju, S.; Singh, H. B.; Butcher, R. J. \emph{Dalton
Trans.}\textbf{2020,} \emph{49,} 9099-9117.

\subsection*{GRAPHICAL ABSTRACT}

{\label{graphical-abstract}}

This work predicts multi-coordinated Ng complexes
Xe(AuF)\textsubscript{\emph{n}} (\emph{n} = 2-4) and demonstrates
intramolecular bond-bending isomerism that exhibiting two types of
isomers due to the competition between Xe-Au covalent bonding and Au-Au
aurophilic interactions, with the aid of high-precision theoretical
calculations and electron and chemical bonding analysis. The present
study serve as an essential complement to the research field of Ng
chemistry and pave the way for experimental progress in discovering
multi-coordinated Ng-metal complexes.

\selectlanguage{english}
\FloatBarrier
\end{document}

