FIGURE 4 (a) Calculated geometries of 2a and2b . (b) Potential energy curves of Xe(MF)2 (M = Au, Ag, Cu). (c) Potential energy curves of Xe(AuX)2 (X = F, Cl, Br). (d) Potential energy curves of Ng(AuF)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-ωPBE-D3/def2TZVPP.

3.4 | 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)d10s0] or pseudo-closed shell [(n-1)d8ns0] metal centers like Cu(I), Ag(I), Hg(II) and so on.[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)n varies. For this purpose, the potential energy curves of Ng(NmX)2 (Ng = Ar, Kr, Xe; Nm = Cu, Ag, Au; X = F, Cl, Br) were calculated and illustrated in Figure 4 , by flexibly scanning the potential energy surface via stepwise changing the Nm-Ng-Nm angle. In contrast to Xe(AuF)2 and Xe(AuCl)2 that have two minimums on the potential energy curve representing the coexistence of 2a and 2bstructures, the rest species exhibit only one minimum at a Ng-Nm-Ng angle of approximately 60°, indicative of the sole 2b isomer. This may be because only Xe(AuF)2 and Xe(AuCl)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)2 (Ng = Ar and Kr), Xe(NmF)2 (Nm = Ag and Cu) and Xe(AuX)2 (X = Cl and Br) are calculated as well and given in Figure S5 . RDG analysis of these molecules shows a salient decrease of the Ng-Nm spike value from ~0.08 to ~0.06 (Figure 3 and S6 ) once one arbitrary atom of Ng(AuF)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.

3.5 | Comparison among multi-coordinated Xe complexes

As mentioned hereinbefore, in inorganic complexes XeFn (n =2, 4, 6)[2, 14] or organic complexes Xe(CCH)n (n = 4, 6)[12], Xe tends to bind with an electronegative group via electron donation from both parts. The Xe-F bond in XeFn exhibits traditional σ -covalent character with Xe in sp3dnhybridization, forming symmetrical geometries, e.g. , linearD 2h configuration for XeF2[2], square planarD 4h structure for XeF4[2], and square bipyramidalO h structure for XeF6[14]. Similar phenomena were observed for the Xe-CCH bond in Xe(CCH)n (n = 4, 6), but with slight difference in that this interplay is partially ionic and partially covalent.[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)n (n = 2-4) with Xe insp3 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.

4 | CONCLUSION

In summary, the geometrical and electronic structures of a novel family of multi-coordinated Ng complexes, Xe(AuF)n (n = 2-4), were theoretically predicted by using LC-ωPBE-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)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)n and Xe(AuCl)n , since their Xe-Au bonds are strong enough to compete against aurophilic interactions. Systematic chemical bonding analysis, 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)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 isomers3a , 4a and 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)2 (Ng = Xe, Kr, Ar; M = Cu, Ag, Au, X = F, Cl, Br) with geometric and energic parameters; RDG analysis of Xe(AgF)2 and Xe(CuF)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.
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GRAPHICAL ABSTRACT

This work predicts multi-coordinated Ng complexes Xe(AuF)n (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.