1Department of Chemistry, Key Laboratory of Functional Inorganic Materials of Anhui Province, Anhui University, Hefei, 230601, PR China
2Key Laboratory of Structure and Functional Regulation of Hybrid Materials (Anhui University), Ministry of Education, Hefei, 230601, PR China

Correspondence

Qinqin Yuan and Longjiu ChengDepartment of Chemistry, Key Laboratory of Functional Inorganic Materials of Anhui Province, Anhui University,Hefei, 230601, PR ChinaKey Laboratory of Structure and Functional Regulation of Hybrid Materials (Anhui University), Ministry of Education, Hefei, 230601, PR ChinaEmail:qinqinyuan@ahu.edu.cn (Q. Yuan) andclj@ustc.edu (L. Cheng)

Funding information

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

1 | 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 XePtF6 was first synthesized by Bartlett in 1962,[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, XeF2and XeF4 are exploited as key agents to remove impurities in alloy smelting,[2] while XeO3 and XeO4 serve as useful explosive components.[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≡CH), constituting traditional covalent or ionic bonds.[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 insp3d2 hybridization, as in both inorganic XeFn (n = 2, 3, 4, 6)[2, 13, 14] and organic Xe(CCH)n(n =1, 4, 6).[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 sp3 hybridization. In 2000, by reduction of AuF3 with elemental xenon, the first complex containing noble gas-noble metal (Ng-Nm) interactions (AuXe42+[Sb4F11]2) was synthesized experimentally,[15] in which two kinds of noble element, i.e., Au and Xe, formed a strong bonding of the σ-donor type. This unique Ng-Nm bond stimulated further search for similar complexes. Soon after, Gerry 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)[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.[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 sp3 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[24-27]that induce the expanding of 5d orbital and the shrink of the 6s 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)···Au(I) aurophilic interaction, a special attractive force between Au atoms with closed-shell electronic configuration (5d10) that is thought to be a joint result of strong relativistic effects and dispersion-type electron correlations.[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 Au2I3- 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.[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.[14] One is nature to wonder, if the strongest Ng-Nm bond, i.e. Xe-Au bond, can be extended from already obtained XeAuF to heretofore unknown Xe(AuF)n (n ≥ 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)n (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)n(n = 2-4) complexes have not been reported yet.

2 | COMPUTATIONAL DETAILS

In order to select an appropriate theoretical methodology, two key structural and energetic parameters of linear XeAuF molecules,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 (e.g., PBE,[40]B3LYP,[41] M06-2X,[42]CAM-B3LYP,[43] ωB97X,[44]and LC-ωPBE-D3 [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-ωPBE-D3/def2TZVPP optimized geometry. According to the comparison results presented inTable S1 and for the sake of balancing the accuracy and cost of calculations, the LC-ωPBE-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)n (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 [46, 47] were performed with Gaussian 16 suites.[48] Basis set superposition error (BSSE) corrections are included when computing dissociation energies.[49] To deeper understand the electron structures and chemical bonding characteristics, the electron and bonding analyses including electron localization function (ELF),[50] extended transition state–natural orbitals for chemical valence (ETS-NOCV),[51, 52]reduced density gradient (RDG)[53] and quantum theory of atoms in molecules (QTAIM) methods[54-56] were conducted with the aid of Multiwfn codes.[57]

3 | RESULTS AND DISCUSSION

3.1 | Geometries and Binding Motifs

Multiple optimized structures of Xe(AuF)n(n = 2-4) were theoretically located at the LC-ωPBE-D3/def2TZVPP level and alphabetically labeled from na tonc according to their relative energies, as shown inFigure 1. The key geometrical parameters for all these predicted structures along with XeAuF were summarized in Table S2. For Xe(AuF)2, two near-degenerate isomers,2a and 2b, were found to adopt a common bent geometry with C2v 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 Au2I3- shows similar bond-bending isomerism that was characterized by an intramolecular competition between aurophilic interaction and Au-I covalent bonds.[39] Here, the slightly high-lying isomer2b simply contains two strong covalent Xe-Au bonds with a length of 2.56 Å, almost identical to that in linear XeAuF.[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. Isomer2a 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 in2b. From 2b to 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.FIGURE 1 The optimized structures of Xe(AuF)n (n = 2-4) at the level of LC-ωPBE-D3/def2TZVPP with key bond lengths (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 n = 3 complex presents three triangular conical geometries. The lowest-lying 3a isomer features C3vsymmetry 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-1. TheCs symmetric 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 3c structure devoid of aurophilic interactions has a C3v symmetry, displaying three identical Au-Au distances (4.02 Å) and bending angles (104.0°). By comparing 3b and 3c, the absence of one intramolecular aurophilic interaction raises the energy of 3cby nearly 0.1 eV. It is also worth mentioning that the Au-Au distance corresponding to the aurophilic interaction keeps almost identical for2a (2.82 Å) and 3b (2.81 Å), hinting that these aurophilic interactions are considerably close in intensity. For n = 4, the 4a (Cs) and4c (D2d) structures are both calculated to have imaginary frequencies albeit featuring aurophilic interactions, while 4b (Td) is determined as the stable local minima, which may be attributed from the synergistic effect[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 2b,3c, and 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, e.g.,2a and 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 traditional andaurophilic structures.FIGURE 2 Electron and bonding analysis of Xe(AuF)n (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.

3.2 | 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 2a,2b, 3b, 3c and 4b, were used to in-depth analyze the electronic structure, while the analysis results of the unstable species were simply listed in 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 6s electron of each Au atom is transferred to the adjacent F atom, forming an intense Au-Fσ covalent bond with each Au atom in 5d10 electron configuration. Meanwhile, the highly electronegative F atom induces a σ-hole of Au atom on the side away from the F atom (Figure S4). The electron on Xe atom will be further pushed to this σ-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 (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)n were divided into n+1 groups (Xe and nAuF, n = 2-4) to directly probe the interactions of Xe and Au. Figure 2 shows the dominating NOCV pairs selected to characterize Xe-Au bonding. Apparently, all the Xe-Au bonds are formed upon p electron transferred from Xe to Au (see pair 1) and the feedback from d orbital of Au atom to Xe (see pair 2). No orbital interactions were observed between any two Au atoms in 2b,3c and 4b, indicating the absence of aurophilic interactions. By contrast, the NOCV pairs in 2a and 3bclearly present the 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 d orbital feedback of Au in the aurophilic species, interpreting why the Xe-Au bonding intensity differs when aurophilic interactions are engaged. The hyperconjugation ofnNg → σ*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 Figure 1. When the number of AuF groups increases, the positive charge on Xe atom of traditional structures (2b3c4b) 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.FIGURE 3 Reduced density gradient (RDG) analysis of Xe(AuF)n (n = 2-4) with non-covalent interactions (NCI) isosurface set at 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) (seeFigure 3). Generally, the more negative the spike value, the stronger the corresponding interaction. Three types of spike values were captured for Xe(AuF)n (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[38], the most negative value of nearly -0.140 was reasonably attributed to the Au-F bond, which is moderately stronger in Xe(AuF)n due to the feedback fromd orbital of Au to Xe atom. The close spike values of -0.045 and -0.048 respectively in 2a and 3b arise from the isosurface denoting Au···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 2a is mildly weaker than that in 2b by comparing the corresponding spike values of -0.070 and -0.078, in good agreement with the bond lengths in 2a (2.63Å) and 2b(2.56Å). The 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 3bwith the corresponding value of -0.070 in 2a, we are convinced the aurophilic interaction is more competitive in 3b than that in 2a.TABLE 1 The Xe-Au bond lengths, along with electron densityρ(rc), Laplacian of electron density ▽2ρ(rc), electron local energy density H(rc), local kinetic energy density G(rc), and the ratio ofG(rc) andρ(rc) at the bond critical points (BCPs) of the Xe-Au bonds in Xe(AuF)n (n = 1-4) calculated at the LC-ωPBE-D3/def2TZVPP level.