1 Introduction

Gold halides have attracted considerable attention because they are extensively applied in catalysts and solid materials [1, 2]. It has been demonstrated that the relativistic effects of Au atom can facilitate 6s–5d hybridization [3]; as a result, the diverse oxidation states are available for Au atom. Also, the Au–Au bond in gold clusters frequently displays intriguing properties, such as the extremely bonding distances and aurophilic interactions [3], and Au atom exhibits similar bonding properties with hydrogen in its interaction with the other atoms [4, 5]. Due to the remarkably large electronegativity and high electron affinity of gold, it can act as a good electron acceptor [6].

Halides are also usually considered as an electron acceptor. However, the gold-containing compounds show significant covalent bonding characters and unique structural arrangements [7]. Then, one can raise the questions that what are the structural and bonding properties in gold halides? To answer these questions, there are a lot of investigations focused on exploring the geometrical characteristics and electronic properties of gold halides [8,9,10,11,12,13,14,15,16,17]. AuF6− can be named as superhalogen as the result of its electron affinity (EA) being to be 10 ± 0.5 eV [18], and can also be used as superhalogen anion to form LiAuF6 ionic salt [19,20,21]. The Au atom exhibits + 7 oxidation states in AuF7 [22], which can be synthesized by reacting AuF5 with atomic fluorine [23]. A combined study of [XAuCN]− (X = F − I) based on anion photoelectron spectroscopy and theoretical calculations revealed that the Au–F bond has strong ionic characters and the covalent bonding strength gradually increases from Au–Cl to Au–I [24, 25]. Very recently, the first-principles calculations of coinage fluorides under high pressure identified that the Au atoms in AuF4 and AuF6 stable molecular crystals have oxidation states of + 4 and + 6, respectively [26].

Nevertheless, the previous investigations regarding the structures and properties of gold halides mainly focused on the monomeric gold halides, whereas those of multiple gold halides are rare [27,28,29]. In addition, the bonding nature (ionic or covalent) of multiple gold halides is still controversial. It is interesting to study multiple gold halides because these clusters may hold very special geometrical structures and exhibit unique fascinating properties. More importantly, investigating the multiple gold halides may provide valuable information for the production of functional nanomaterials for solar cell or lithium battery. Here, we explored the structural, bonding, and superhalogen properties of isolated Au4X −/04 (X = F, Cl, Br, and I) clusters using density functional theory calculations. We found that Au4F4−, Au4Cl4−, and Au4Br −4 have similar cyclic structures and superhalogen features, and Au4I4− possesses a D4h symmetric aromatic planar structure, whereas Au4X4 neutrals adopt D2d symmetric quasi-planar eight-membered ring structures.

2 Theoretical methods

Density functional theory (DFT) within B3LYP framework [30, 31] was performed for the configuration optimizations and frequency calculations of both anionic and neutral Au4X4 (X = F, Cl, Br, and I) clusters. Previously, the B3LYP functional was also used in investigating the structures and properties of gold halides [27,28,29]. The aug-cc-pVTZ-PP basis sets [32, 33] were chosen for the Au and I atoms, whereas the aug-cc-pVTZ basis sets [34, 35] were applied for the F, Cl, and Br atoms. No symmetry constraint was used in the configuration optimizations and frequency calculations. The CALYPSO software [36] was applied for an unbiased search for initial structures of Au4X −/04 clusters. Details of obtaining the initial structures based on the CALYPSO software have been elaborated elsewhere [37,38,39,40]. Also, the structures of the neutral gold fluoride and chloride clusters reported in the previous works [27,28,29] had been considered in the structural optimization processes. To determine the lowest energy spin states of Au4X −/04 clusters, the 2, 4, and 6 spin states were taken into account for anionic clusters. As for neutral Au4X4 clusters, the 1, 3, and 5 spin states were considered. Harmonic vibrational frequency calculations were performed to verify that the obtained structures are the true minima. As for both anionic and neutral Au4X4 clusters, no imaginary frequencies were found to confirm the low-lying isomers are the genuine minima on their potential energy surfaces. The TPSSH functional [41] and B3PW91 functional [31] were also used in the configuration optimizations and frequency calculations. The TPSSH functional gives generally excellent results for a wide range of systems and properties, correcting overestimated bond lengths in molecules including clusters, hydrogen-bonded complexes, and ionic solids [41]. The B3PW91 functional performs significantly better than previous functionals with gradient corrections only and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol [31]. Also, in the previous investigations of clusters including Au atoms [42, 43], B3PW91 functional is widely applied to explore their structures and properties. Therefore, in this work, we used TPSSH and B3PW91 functionals to conduct the compared calculations with B3LYP functional. We calculated the theoretical vertical detachment energies (VDEs) by the energy differences of the neutrals and anions both using the anionic geometries, while we obtained the theoretical adiabatic detachment energies (ADEs) through the energy differences of the neutrals and anions using their each global minimum. During calculating the relative energies and ADEs of isomers, we performed zero-point energy (ZPE) corrections. The atomic dipole moment corrected Hirshfeld population (ADCH) analyses, implanted in the Multiwfn program [44], were conducted to probe the atomic charge distributions of Au4X −/04 clusters. Compared with Mulliken, natural population analysis (NPA), and atoms in molecules (AIM) charges, the ADCH charge has many advantages in handling with atomic charge distribution, such as the ADCH atomic charges are very reasonable in chemical sense, molecular dipole moment is exactly reproduced, the reproducibility of electrostatic potential (ESP) is close to the atomic charges from fitting ESP, and the computational cost of ADCH correction is almost zero [45, 46]. Theoretical calculations were performed within the Gaussian 09 [47].

3 Theoretical results and discussion

The low-lying isomers of Au4X4− anions are displayed in Fig. 1. Also, the relative energies (ΔE) and theoretical VDEs and ADEs of isomers are shown in Fig. 1. As we all known, anion photoelectron spectroscopy has been extensively used for studying atomic or molecular clusters because it can obtain the fingerprint information of both anionic and neutral species. However, the experimental photoelectron spectra of Au4X4− anions have not been reported. In this work, the photoelectron spectra of the lowest-lying isomers of Au4X4− anions were simulated based on the generalized Koopmans’ theorem (GKT) [48, 49], as displayed in Fig. 2. We hope that these theoretical results can help the experimentalists to understand the further experimental spectra. As for Au4X4 neutrals, their low-lying isomers as well as ΔE are presented in Fig. 3.

Fig. 1
figure 1

Typical low-lying isomers of Au4X4− (X = F, Cl, Br, and I) as well as their relative energies, ADEs, and VDEs obtained at the B3LYP level. The relative energies in parentheses are calculated at the TPSSH and B3PW91 levels. The bond lengths of the lowest-lying isomers of Au4X4− are given in angstrom

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Fig. 2
figure 2

Simulated photoelectron spectra of the lowest-lying isomers of Au4X4− (X = F, Cl, Br, and I). Simulated spectrum was obtained by fitting the distribution of the transition lines with the unit area Gaussian functions of 0.20 eV full widths at half maximum. The vertical lines in blue are the calculated vertical detachment energies for Au4X4− (X = F, Cl, Br, and I)

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Fig. 3
figure 3

Typical low-lying isomers of Au4X4 (X = F, Cl, Br, and I) as well as their relative energies obtained at the B3LYP level. The relative energies in parentheses are calculated at the TPSSH and B3PW91 levels. The bond lengths of the lowest-lying isomers of Au4X4 are given in angstrom

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3.1 Au4F4 −/Au4F4

One can see from Fig. 1 that the lowest-lying isomer (A) of Au4F4− is a cyclic structure, in which the four F atoms attach to the different sites of Au-capped Au3 triangle framework. The Au–F bond lengths are in the range of 1.94–2.29 Å, whereas the Au–Au bond lengths are between 2.57 and 2.77 Å. The bond angles of Au–Au–Au and Au–F−Au are 118.9° and 79.9°, respectively. Isomer A is also the lowest-lying isomer for Au4F4− at the TPSSH and B3PW91 levels. The VDE (5.67 eV) and ADE (5.26 eV) of isomer A are significantly larger than the EA of Cl (3.61 eV) [50]; as a result, Au4F4− can be classified as a superhalogen anion to form a LiAu4F4 ionic salt. We can see from Fig. 2 that the simulated photoelectron spectrum of isomer A has a relatively weak peak at 5.67 eV and a high-intensity peak at 6.17 eV. Isomers B and C are located above the lowest-lying isomer by 0.16 and 0.65 eV, respectively, calculated at the B3LYP level. The calculated relative energies are slightly different at the different theoretical levels.

The lowest-lying isomer (A′) of Au4F4 is a D2d symmetric quasi-planar ring-like structure in which the four F atoms edge-cap the four Au–Au bonds of Au4 square core, different from its corresponding anionic counterpart. The Au–F and Au–Au bond lengths are 2.07 and 3.04 Å, respectively. The bond angles of Au–Au–Au, Au–F–Au, and F–Au–F are 90.0°, 94.9°, and 175.1°, respectively. The other isomers are higher in energy than the lowest-lying isomer by at least 0.21 eV at the B3LYP level.

3.2 Au4Cl4 −/Au4Cl4

The most stable isomer (A) of Au4Cl4− is very similar to that of Au4F4− anion. The Au–Cl bond lengths are in the range of 2.28–2.53 Å, whereas the Au–Au bond lengths are between 2.62 and 2.84 Å. The bond angles of Au–Au–Au and Au–Cl–Au are 110.3° and 71.2°, respectively. Also, isomer A is the most stable isomer for Au4Cl4− at the TPSSH and B3PW91 levels. The VDE and ADE of isomer A are 5.52 and 5.19 eV, respectively, much larger than the EA of its Cl (3.61 eV) [50] building block; thus, Au4Cl4− can be considered as a superhalogen anion to form a LiAu4Cl4 ionic salt. It is reasonable to find that the simulated photoelectron spectra of Au4Cl4− and Au4F4− have similar spectral features due to their analogical structural characteristics. The other isomers are higher in energy than the lowest-lying isomer by at least 0.26 eV at the B3LYP level. The calculated relative energies among the three isomers are slightly different at the TPSSH and B3PW91 levels.

As we can see from Fig. 3, the most stable isomer of Au4Cl4 neutral (A′) is a D2d symmetric quasi-planar ring-like structure composed of four Cl–Au–Cl chain-shaped units sharing with four Cl atoms. The bonding Au–Cl distance is 2.34 Å, and the bond angles of Au–Cl–Au and Cl–Au–Cl are 89.5° and 177.8°, respectively. The dihedral angle between two Au–Cl–Au–Cl planes is 12.8°. The other isomers are higher in energy than the lowest-lying isomer by at least 0.65 eV at the B3LYP level.

3.3 Au4Br −4 /Au4Br4

The global minimum (isomer A) of Au4Br −4 resembles well with those of Au4F4− and Au4Cl4−. The Au–Br bond lengths are between 2.42 and 2.49 Å, and the Au–Au bond lengths are within the scope of 2.63–2.83 Å. The bond angles of Au–Au–Au and Au–Br–Au are calculated to be 107.7° and 66.9°, respectively. Likewise, isomer A is the most stable one for Au4Br −4 at the TPSSH and B3PW91 levels. Additionally, the VDE and ADE of isomer A are calculated to be 5.34 and 4.89 eV, respectively; they both far exceed the EA of Cl (3.61 eV) [50]; as a consequence, Au4Br −4 is also a superhalogen anion. Given that Au4Br −4 , Au4Cl4−, and Au4F4− adopt very similar geometrical structures, it is very reasonable to find their analogical photoelectron spectral patterns, as we can see from Fig. 2. The other isomers are higher in energy than the global minimum by at least 0.19 eV at the B3LYP level.

Likewise, the global minimum (A′) of Au4Br4 adopts a D2d symmetric quasi-planar ring-like structure. The bonding Au–Br distance is 2.62 Å, and the bond angles of Au–Br–Au and Br–Au–Br are 89.3° and 180.0°, respectively. The dihedral angle between two Au–Br–Au–Br planes is 7.2°. The other isomers are higher in energy than the global minimum by at least 0.98 eV at the B3LYP level. Isomer A′ is also the most stable isomer for Au4Cl4 at TPSSH and B3PW91 levels.

3.4 Au4I4 −/Au4I4

The isomer A of Au4I4− is a D4h symmetric planar structure, in which the four I atoms edge-cap the four Au–Au bonds of Au4 square core. The Au–I and Au–Au bond lengths are 2.79 and 2.74 Å, respectively. The bond angles of Au–Au–Au, Au–I–Au, and I–Au–I are 90.0°, 58.8°, and 148.8°, respectively. The VDE and ADE of isomer A are computed to be 3.07 and 2.07 eV, respectively. In the simulated photoelectron spectrum of isomer A, it reveals three peaks at 3.07, 4.30, and 5.05 eV, and several congested peaks at the high electron binding energy (EBE) region. The spectral features of Au4I4− are markedly different from those of Au4F4−, Au4Cl4−, and Au4Br −4 . The two peaks in the simulated spectrum have a large space of 1.23 eV, more likely due to the highly symmetric structure of Au4I4−. The other isomers are higher in energy than isomer A by at least 0.27 eV at the B3LYP level. Isomer A is also the most stable one for Au4I4− at the TPSSH and B3PW91 levels, and the calculated relative energies of isomers are slightly different.

The global minimum (A′) of Au4I4 is a D2d symmetric quasi-planar eight-membered ring structure, composed of four I–Au–I chain-shaped units sharing with four I atoms. The global minimum of Au4I4 neutral (A′) resembles well with those of Au4F4, Au4Cl4, and Au4Br4. The bonding Au–I distance is 2.62 Å, and the bond angles of Au–I–Au and I–Au–I are 90.7° and 179.3°, respectively. The dihedral angle between two Au–I–Au–I planes is calculated to be only 1.5°. The other two isomers are higher in energy than isomer A by at least 0.75 eV at the B3LYP level.

Here, we would like to point out that the calculated VDEs of Au4X4− decrease gradually from 5.67 to 3.07 eV with the variation from X = F to I. This is probably because of the different interactions between halogen and gold atoms due to the various properties of halogen atoms including the atomic radiuses, electronegativities, and electron affinities. In particular, the covalent interactions between Au and I atoms are weakest among these mixed clusters because the covalent bonding lengths gradually increase from Au–F to Au–I, as shown in Fig. 1. Certainly, the highly symmetric geometric structure of Au4I4− may be another reason for the lower VDE. As for Au4X4−, the Au–Au distances increase gradually from X = F to Br, suggesting that the Au–Au interactions are weaken. Moreover, the global minima of Au4X4 neutrals are consistent with the results in previous investigations [27,28,29].

On the one hand, we found that Au4F4−, Au4Cl4−, and Au4Br −4 have similar geometrical structures, spectral features, and superhalogen property, which are significantly different from Au4I4−. As for their corresponding neutral counterparts, they all adopt analogical quasi-planar eight-membered ring structures. On the other hand, among these Au–X mixed clusters, the four Au atoms incline to interact with each other and form an Au–Au bond, while the four halogen atoms prefer to bonding with the Au atoms rather than interact with each other. These suggest that the structures and properties of Au–X mixed clusters are not completely similar. In particular, Au4I4− has a D4h symmetric planar structure. The different structural evolutions between Au4X4− (X = F, Cl, and Br) and Au4I4− clusters may be due to the involved 5p orbitals of I atoms interacted with the 5d orbitals of Au atoms (see subsequent molecular orbital analyses). In particular, it is well recognized that the relativistic effect of I atom can promote s–p hybridization, giving rise to the I atom having a wide range of oxidation states from − 1 to + 7 in chemical reactions [6], even though iodine is not as reactive as its group elements F2, Cl2, and Br2. These unique properties and effects of I may lead to the structural evolution and bonding properties of Au–I mixed clusters are different from those of Au–X (X = F, Cl, and Br) clusters. The Au–I bond lengths in Au4I4− are calculated to be 2.79 Å, much longer than that (2.47 Å) in the AuI diatomic molecule [51], suggesting that the Au–I bonds are weak, in good agreement with the low calculated Wiberg bond orders of Au–I bonds (0.50). The weak covalent Au–I and Au–Au bonds in Au4I4− can be further confirmed by molecular orbital analyses.

The molecular orbitals of the lowest-lying isomer of Au4I4− are shown in Fig. 4. The SOMO is primarily made up of the \( 5d_{{x^{2} - y^{2} }} \) and 6s orbitals of Au and the 5px and 5py orbitals of I. The HOMO-1, HOMO-2, HOMO-3, HOMO-4, and HOMO-5 are mainly composed of 5d orbitals of Au atoms and 5p orbitals of I atoms. It is worth noting that there are small overlaps between 5d orbitals of Au atoms and 5p orbitals of I atoms. Also, the small mixings between the 5d orbitals of four Au atoms are found. These can confirm that the covalent Au–I and Au–Au bonds are weak. The weaker Au–I and Au–Au interactions in Au4I4−, in comparison with those in Au4F4−, Au4Cl4−, and Au4Br −4 , which may partly explain why the calculated VDE of Au4I4− is the lowest one (the calculated Wiberg bond orders of Au–X bonds (0.55–0.79) and Au–Au bonds (0.40–0.58) in Au4F4−, Au4Cl4−, and Au4Br −4 ).

Fig. 4
figure 4

Molecular orbitals of the lowest-lying isomer of Au4I4− (D4h, 2B2u, isosurface value = 0.02) at the B3LYP level

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The electron localization function (ELF) analyses of Au4I4− are shown in Fig. 5. ELF was initially proposed by Becke and Edgecombe [52] and is used to measure the probability of electron pairing. In general, the larger ELF value means more strong the covalent bond. We can clearly see from Fig. 5 that the ELF values of Au–I and Au–Au bonds are within the scope of 0.2–0.3, indicating that the covalent Au–I and Au–Au bonds are weak. This is in accordance with the analysis results of bond lengths, calculated Wiberg bond orders, and molecular orbitals. A direct calculation of bond dissociation energies of Au4I4− anion was also carried out to reinforce the statement of a weak covalent bonding for Au–I and Au–Au bonds, which suggests that the dissociation energies of Au–I and Au–Au bonds are averagely calculated to be 26.9 and 19 kcal/mol, respectively.

Fig. 5
figure 5

Electron localization functions analysis of Au4I4−

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The Au–I and Au–Au interactions can also be interpreted based on the partial density of states (PDOS), as presented in Fig. 6. As for the four Au atoms, it exhibits very small overlaps between Au4-d and Au4-s, confirming that the four Au atoms have weak aurophilic interactions. Regarding the Au–I interactions, there are small overlaps between Au4-d and I4-p states at − 2.0 to − 6.0 eV, indicating the Au–I interactions are also weak. Also, these suggest that the bonding interactions are in the order of Au–I > Au–Au. It seems that the Au–I interactions can weaken the Au–Au interactions of Au4 framework. The PDOS analyses are consistent with the molecular orbital and ELF analyses. Therefore, the weak covalent Au–I and Au–Au interactions play crucial role in thermal stabilities of Au4I4−, similar to the weak interactions in proteins [53].

Fig. 6
figure 6

Partial density of states (PDOS) of Au4I4−. Green dashed line is the Fermi level

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To probe the effective atomic charge distributions in Au4I4−, the ADCH analyses were carried out. The ADCH charges on the four Au atoms and four I atoms are + 0.11e and − 0.36e, respectively, suggesting that there are electrons transferring from the Au4 framework to these I atoms. The electron transfer can be probably explained by the stronger electronegativity of I atom (χ = 2.66) than Au atom (χ = 2.54) [54]. The electron transfer may play crucial role in stabilizing the planar structure of Au4I4−. Thus, except for the covalent character, the Au–I bonds also exhibit some ionic characters due to the transfer of 6s electrons from Au atoms to the 5p orbitals of I atoms. Overall, based on the molecular orbitals, ELF, calculated Wiberg bond orders, PDOS, and ADCH analyses, we can conclude that the D4h symmetric planar structure is stabilized by both covalent and ionic bonds.

Aromaticity stemming from electron delocalization is also used for comprehending the stability of Au4I4−. The nucleus-independent chemical shift (NICS) value of Au4I4− is computed at the B3LYP/aug-cc-pVTZ-PP level. The calculated results suggested that Au4I4− has a large NICS value of − 46.5 ppm; therefore, Au4I4− exhibits significant aromaticity. The aromatic stabilization energy (ASE) [55] and multicenter bond index [56] at the B3LYP/aug-cc-pVTZ-PP level can further identify the aromaticity of Au4I4−. The aromatic stabilization energy (ASE) is based on energy to analyze the aromaticity due to electron delocalization. The system is aromatic when the reaction energy is positive. Generally, the system is regarded to be aromatic when the ASE > 5 kcal/mol. Here, the ASE of Au4I4− is calculated as the equation of ASE(Au4I4−) = 2E(Au2I3−) − 2E(I) − E(Au4I4−) = 14.6 kcal/mol (the E is the total energy including zero-point energy (ZPE) corrections). The higher multicenter bond index refers to be the stronger aromaticity. The calculations of multicenter bond index for Au4I4− were carried out using Multiwfn program [44], and the multicenter bond index of Au4I4− is calculated to be 0.97. Most noteworthy, the typical aromatic compounds in organic chemistry such as benzene, where the HOMO exhibit mainly z-character. Here, the SOMO is mainly contributed by the \( 5d_{{x^{2} - y^{2} }} \) and 6s orbitals of Au atoms. The aromaticity may be come from the spherically symmetric 6s orbitals of Au atoms.

Here, the structures of Au4I −/04 are compared with those of Cu4I −/04 reported in our previous work [37]. Au4I4− is a D4h symmetric planar structure, slightly different from that of Cu4I4−, which is a C2h symmetric planar structure, in which the four I atoms surround with the Cu4 rhomb. As for neutrals, Au4I4 adopts a D2d symmetric quasi-planar eight-membered ring structure, while that of Cu4I4 neutral holds a D2d symmetric V-shaped structure. These suggest that the geometrical configurations of Cu and Au–I hybrid clusters are different, although the Cu and Au atoms are in the same group.

We also carried out an unbiased search for initial structures of Cu–X and Ag–X (X = F, Cl, Br, and I) hybrid clusters using CALYPSO software and optimized their geometrical structures at the B3LYP level, and the results are displayed in Figs. S1, S2, S3, and S4 (see them in Supplementary Materials). Here, it is interesting to compare the structures of Cu–X, Ag–X, and Au–X (X = F, Cl, Br, and I) hybrid clusters. As for anions, the global minima of TM4X4− (TM = Cu, Ag, and Au; X = F, Cl, Br, and I) all have a similar planar structure with the four X atoms surrounding the TM4 rhombic framework with slightly different symmetries. As for neutrals, the most stable isomers of TM4X4 (TM = Cu, Ag, and Au; X = F, Cl, Br, and I) adopt a quasi-planar eight-membered ring-like structure except for Ag4F4 and Cu4I4. Ag4F4 is a planar structure with the four F atoms surrounding the Ag4 rhombic framework, similar to its corresponding anion, and Cu4I4 adopts D2d symmetric V-shaped structure.

4 Conclusions

We carried out a DFT theoretical study of structural, bonding, and superhalogen properties of Au4X −/04 (X = F, Cl, Br, and I) clusters. We found that Au4F4−, Au4Cl4−, and Au4Br −4 anions have similar cyclic structures, spectral features, and superhalogen property, while Au4I4− anion adopts a D4h symmetric planar structure. Au4X4 (X = F, Cl, Br, and I) neutrals all has a D2d symmetric quasi-planar eight-membered ring structure. The Au–I and Au–Au bonds in Au4I4− are weak including the covalent and ionic characters. The weak covalent Au–I and Au–Au interactions can be further verified by the bond lengths, Wiberg bond orders molecular orbital, ELF, and PDOS. The large NICS value of − 46.5 ppm, aromatic stabilization energy (ASE), and multicenter bond index indicate that Au4I4− is significantly aromatic.

5 Supplementary materials

Cartesian coordinates for the low-lying isomers of Au4X −/04 , and typical low-lying isomers of Cu4X4− and Ag4X4− (X = F, Cl, Br, and I) obtained at the B3LYP level.