## Introduction

Homogeneous catalysis by gold complexes has been undergoing a remarkable development over the past decade, in particular, for alkyne activation1,2,3,4,5,6,7. Numerous reaction intermediates have been proposed, but in general it is a challenge to directly observe and characterize these transient species. Clearly, the nature of the bonding between the Au centre and its substrates is critical to the understanding of the mechanisms of homogeneous gold catalysis. Well-defined gold complexes can serve as model systems to probe the Au-substrate bonding. However, although it is generally known that the strong relativistic effects8 give rise to the many unique chemical properties for gold9,10,11, there is a scarcity of experimental studies of the Au–C bonding in organogold complexes that are most relevant to understanding the viability of catalytic intermediates and mechanisms12,13. As a powerful experimental technique to probe the electronic structure and chemical bonding of molecules, photoelectron spectroscopy has been used to study a series of Au–CN complexes recently14,15 but has not been applied to any organogold complexes.

Here we present the first photoelectron spectroscopy investigation of a series of Au(I)–alkynyl complexes, LAuCCH (L=Cl, I, CCH), accompanied by ab initio calculations, to probe the nature of the Au–C bonding. Vibrationally resolved photoelectron spectra suggest that the Au–C bonding in LAuCCH is extremely strong. Theoretical calculations show that the Au–C bond in ClAu–CCH is one of the strongest known gold bond with a dissociation energy of 5.01 eV. Further theoretical studies find that the Au–C single bond in ClAuCCH is even stronger than the known Au=C double bond in ClAu=CH2 and the Au≡C triple bond in ClAu≡C, uncovering an unprecedented inverse correlation between bond strength and bond orders for gold. Such strong LAuC≡CH bonding implies that the formation of terminal alkynyl–gold is thermodynamically favourable, which is known to have important roles in alkyne activation.

## Results

### Photoelectron spectroscopy

We produced the LAuCCH complexes (L=Cl, I, CCH) by electrospray ionization of an acetonitrile solution dissolved with HC≡C–MgCl and gold iodide. The photoelectron spectra were obtained for these Au(I) complexes at various temperatures and several detachment laser wavelengths. Figure 1 presents the room temperature spectra of LAuCCH (L=Cl, I, CCH) measured at 157 nm. Higher-resolution spectra for the low-binding energy features were obtained at lower photon energies (245 and 266 nm) for vibrationally cold anions at 20 K, as shown in Fig. 2.

The 157-nm spectrum of ClAuCCH displays six major detachment bands labelled with letters (X, A–E; Fig. 1a). The X and A bands are vibrationally resolved in the 20 K spectrum at 245 nm (Fig. 2a). The observed vibrational frequency of the X band (380 cm−1) corresponds to the ClAu stretching mode in the neutral ground state of ClAuCCH. Two vibrational progressions are resolved in the A band: a low-frequency mode of 360 cm−1 mainly corresponding to ClAu stretching and a high-frequency mode of 1960, cm−1, which should be due to the C≡C stretching. The 157-nm spectrum of IAuCCH also exhibits six major detachment bands (Fig. 1b). For the 245-nm spectrum of IAuCCH at 20 K (Fig. 2b), only a very short progression of the C≡C stretching mode with a frequency of 1,860 cm−1 is discernible for the X and A bands. The relatively broad peak widths of the X and A bands suggest that there are unresolved low-frequency vibrational excitations, most probably because of the low-frequency I–Au stretching, similar to the ClAu stretching observed in the ClAuCCH spectrum. The 157-nm spectrum of Au(CCH)2 reveals five major detachment bands (Fig. 1c), where the X and A bands overlap and the D band is weak and broad. For Au(CCH)2 at 20 K, spectra are taken at both 266 nm (Fig. 2c) and 245 nm (Fig. 2d). A vibrational progression with a frequency of 480 cm−1 is observed for the X band, corresponding to the Au–C stretching mode in the neutral Au(CCH)2 ground state. Two vibrational progressions are observed for the A band (Fig. 2d) with frequencies of 450 and 1,850 cm−1, respectively. The lower frequency mode should be due to the Au–C stretching and the higher-frequency mode due to the C≡C stretching in the first excited state of neutral Au(CCH)2. The spectral features and vibrational structures for Au(CCH)2 are similar to those for ClAuCCH.

The adiabatic detachment energies (ADEs), vertical detachment energies (VDEs) and the resolved vibrational frequencies of the X and A bands for all three complexes are summarized in Table 1, where they are compared with the theoretical calculations. The VDEs and assignments for all the observed features are given in Supplementary Table S1. We note that the Au–C vibrational frequency observed in the spectra of Au(CCH)2 is larger than the Au–C frequency observed in the photoelectron spectra of Au(CN)2 reported previously (400 cm−1)14. This observation is surprising, suggesting that that Au–CCH bond may be even stronger than the Au–CN bond in their corresponding neutral ground states.

### Quantum chemical calculations and spectral interpretation

High-level theoretical calculations were performed for the three Au(I) complexes and their corresponding neutrals using both density functional theory (DFT) and ab initio wavefunction theory. The optimized geometries for the three complexes are all linear in both charge states, as shown in Supplementary Table S2, where all bond lengths are given at two levels of theory. Figure 3 shows the isocontour surfaces of the Kohn–Sham molecular orbitals (MOs) of LAuCCH. When spin-orbit (SO) coupling effects are included, the π- and δ-orbitals split into two levels, as illustrated qualitatively in Supplementary Fig. S1. The valence MOs and electronic structures of all three complexes are similar (Fig. 3). The highest occupied MO (HOMO) is of π-symmetry, consisting of antibonding combinations between the Au dπ orbitals and CCH π-bonding orbital (and halogen pπ orbitals for ClAuCCH and IAuCCH). The SO splitting gives rise to the 2Π3/2 ground state and the 2Π1/2 first excited state for neutral LAuCCH, corresponding to the X and A bands in the photoelectron spectra (Fig. 2), respectively. The calculated ADEs and VDEs are compared with the experimental observations in Table 1 for the X and A bands and Supplementary Table S1 for all observed transitions. The calculations at the CCSD(T) level without SO corrections appear to overestimate the ADEs and VDEs by ~0.1−0.3 eV relative to the experimental data. Because of the contribution of the halogen pπ orbital to the HOMO, the SO splitting is the largest in IAuCCH among the three complexes. The simulated spectra using the calculated VDEs are given in Supplementary Fig. S2, which are in qualitative agreement with the experimental spectra shown in Fig. 1. Vibrational frequencies for the neutral ground state of LAuCCH are calculated (Supplementary Table S3) and confirm the assignments of the observed vibrational structures. In particular, the calculated Au–C vibrational frequency (476 cm−1) for Au(CCH)2 agrees well with the observed frequency of 480 cm−1. The calculated Au–C stretching is 492 cm−1 for ClAuCCH and 473 cm−1 for IAuCCH, consistent with the strong Au–C bonding.

### Unusually strong and L-dependent Au–C bond in LAuCCH−

As shown in Fig. 3, the HOMO-5 for the three Au(I) complexes is a strong π-bonding orbital, whereas the HOMO is an antibonding π-orbital. Thus, there is no net π-bonding between Au and the CCH ligand. The Au–CCH bonding comes mainly from HOMO-6, which is a σ-MO from the overlap of the Au $5{\text{d}}_{{\text{z}}^{\text{2}}}$ and the sp hybrid orbital on CCH. The Au–CCH interaction can be characterized by a single σ-bond, as supported by the bond order analyses (Table 2)16. This bonding picture is consistent with the fact that the alkynyl ligand is known to be a good σ- and π-donor but a poor π-acceptor because of the high energy of its antibonding π*-orbitals17,18,19. The covalent interaction between Au and the alkynyl ligand is more clearly illustrated in the electron localization functions presented in Fig. 4.

However, the strong Au–C stretching vibrational frequency of 480 cm−1 observed in the photoelectron spectrum of Au(CCH)2 in Fig. 2 suggests that the Au–C bond is unusually strong in the neutral Au(CCH)2 ground state. This frequency is >400 cm−1 frequency observed for the Au–C stretching in the photoelectron spectrum14 of Au(CN)2, a well-known and highly stable Au(I) complex used to extract gold for centuries20. This observation led us to suspect that the Au–CCH bonding might also be stronger than the Au–CN bonding in their respective anionic complexes. We calculated the dissociation energy of AuX2→Au++2X at the ADF/PBE level (see Methods) and found that indeed this quantity for X=CCH (15.07 eV) is higher than that for X=CN (14.62 eV). We further calculated the bond dissociation energy (De) for LAu–CCH→LAu+CCH and found that De strongly depends on the ligand L (Supplementary Table S4); the De for L=Cl is significantly higher than that for L=HCC and I. This is known as the trans-effects18,19. The more electronegative L ligands polarize the Au(I) centre and strongly enhance the Au–C bond in LAu–CCH. We subsequently calculated the De for a series of Au(I) complexes, as given in Supplementary Table S4. Except for FAu–CCH and ClAuCH3, the De of ClAu–CCH is the highest. The De shown in Supplementary Table S4 represents heterolytic bond cleavage processes, producing two closed shell and stable fragments. Heterolytic bond cleavages are usually used when considering the bonding in donor–acceptor-type complexes21. We further computed the heterolytic De of ClAuCCH, ClAuCN and ClAuCH3 at the CCSD(T)/AVTZ level and obtained 5.01, 4.52 and 5.64 eV, respectively (Supplementary Table S5), which are similar to those at the DFT level (Supplementary Table S4). We also computed the homolytic dissociation energies for ClAu–CCH, ClAuCN and ClAuCH3 to produce two open shell species: ClAu and a radical ·CCH, ·CN and ·CH3, respectively, as 5.83, 6.23 and 3.52 eV at the CCSD(T) level (Supplementary Table S5). To eliminate possible charge effects, we further considered the De of the three neutral complexes, ClAuCCH (→ ClAu+·CCH), ClAuCN (→ ClAu+·CN) and ClAuCH3 (→ ClAu+·CH3), which can be viewed to consist of a one-electron Au–C bond. The De of ClAu–CCH is the highest among the three species with a value of 3.19 eV, which would yield an estimated 6.32 eV for a two-electron Au–C bond, comparable to the 5.01 eV donor–acceptor bond energy. Interestingly, the De of ClAuCH3→ClAu+·CH3 is very low, only 1.33 eV, suggesting a strong charge effect in the donor–acceptor interaction in the ClAuCH3 anionic complex. These analyses suggest that the ClAuCCH complex represents one of the strongest Au–C bonds. The donor–acceptor De of 5.01 eV for ClAu–CCH at the CCSD(T) level is an extremely high bond energy, even higher than that of ClAuCN by ~0.5 eV (Table 2 and Supplementary Table S5).

### Inverse correlation between bond order and bond strength

To understand the nature of the strong Au–C bond in ClAu–CCH, we compare it with the multiple Au–C bonds in Table 2. It is known that Au forms a double bond with carbene22,23 in [Au=CH2]+ and a triple bond24,25 with C in [Au≡C]+. The neutral forms of the species containing the multiple Au–C bonds have been studied by complexing with halogen counter ions26,27. We have calculated the bond lengths and De for the Au–C double bond in ClAu=CH2 and triple bond in ClAu≡C, and have compared them with those of ClAu–CCH in Table 2, which also lists literature values for [Au=CH2]+ and [Au≡C]+. The isosurfaces of the MOs of ClAu=CH2 and ClC≡Au are given in Supplementary Fig. S3, from which one can get a glimpse of the multiple bond nature of these two molecules. The data in Table 2 reveal remarkably that the Au–C single bond in ClAu–CCH is even stronger than the Au=C and Au≡C multiple bonds, although the bond lengths of the multiple bonds are shorter. The Au=C and Au≡C multiple bonds were suggested in previous theoretical studies on the bases of the short AuC bond lengths and MO analyses (also see Supplementary Fig. S3)22,23,24,25,26,27. The current bond-order analyses generally support the formal bond-order designations (Table 2), although the numerical values are usually smaller28. It is interesting to note that the Cl complexation in ClAu=CH2 and ClAu≡C slightly weakens the Au–C multiple bonds, whereas it strengthens the Au–C single bond in ClAu–CCH.

The Au–C bond length decreases with increasing bond order from the single bond in ClAu–CCH to the double bond in ClAu=CH2, and the triple bond in ClAu≡C. However, the De of the single Au–C bond in ClAu–CCH is about 1.5 eV higher than that of the Au=C double bond in ClAu=CH2, which in turn is stronger by about 0.2 eV than the Au≡C triple bond in ClAu≡C (Table 2). This remarkable inverse correlation between bond strength and bond order/bond length is unprecedented for gold. The breakdown of bond strength and bond length correlation has been seen in F-substituted ethane or other heavier group-14 species, such as in C2H6−nFn or Sn2H6−nFn, mainly because of the Pauli repulsion of the inner-shell electrons between the heavier elements29,30,31,32. Inverse correlation of bond strength and bond order is very rare. A weak inverse correlation between bond order and bond strength is known in CH2=XH2 (X=Si, Ge, Sn and Pb) and some metal–metal multiple bonded species29,33. The inverse correlation between bond order and bond strength in the Au–C species can be attributed to the strong relativistic effects of Au, which result in extremely short double and triple bond lengths, leading to strong Pauli repulsion between the inner-shell electrons of Au and C.

## Discussion

The Au–C bond in the LAu–CCH complexes (L=Cl, I, CCH) is shown here to be one of the strongest Au–ligand bond known. The ancillary ligand is found to strongly influence the strength of the Au–C bond, consistent with the fact that the catalytic efficiency of LAu(I) complexes is highly dependent on the nature of L. The strong Au–C bond in Au(I) alkynyl complexes weakens and activates the C≡C triple bond and prepares it for the subsequent C–C coupling reactions. The remarkable inverse correlation between bond order and bond strength in the Au–C complexes underlies the strength of the Au–alkynyl bond and furthers our understanding of the expanding gold chemistry.

## Methods

### Experiments

The experiment was done using a magnetic-bottle photoelectron spectroscopy apparatus equipped with an electrospray ionization source34 and a cryogenically cooled ion trap35. The LAuCCH (L=Cl, I, CCH) complexes were prepared by electrospray of an acetonitrile solution dissolved with the Grignard-type HCC–MgCl compound and gold iodide. The electrospray source was purged with a flow of N2 gas and the produced anions were accumulated in a Paul trap operated both at room temperature and low temperatures36. The desired anion was mass selected by a time-of-flight mass spectrometer. Photoelectron spectra were obtained using three detachment lasers, 157 nm from an F2 excimer laser, 245 nm from a dye laser and 266 nm from a Nd:YAG laser. The experiment was calibrated by the known spectra of Au and I. The electron kinetic energy resolution of the current magnetic-bottle photoelectron analyser was about ΔE/E=3%, that is, 30 meV for 1 eV electrons.

### Theory and computation

The calculations were performed using DFT and ab initio wavefunction theory. The DFT calculations were done using the generalized gradient approximation with PBE exchange-correlation functional37 and hybrid B3LYP functional38,39 as implemented in the Amsterdam Density Functional program (ADF 2010.01)40. The Slater basis sets with the quality of triple-ζ plus two polarization functions (TZ2P) with the frozen core approximation applied to inner shells were used. The scalar relativistic (SR) and SO coupling effects were taken into account by the zero-order-regular approximation (ZORA)41. Geometries were fully optimized at the SR-ZORA level and single-point energy calculations were performed with the inclusion of the SO effects. Vibrational frequency calculations were carried out at the SR-ZORA level with PBE functional. To confirm the ADE and the first VDE (VDE1), high-level CCSD(T) single-point energy calculations were performed using the MOLPRO 2008 program42 at the B3LYP-optimized geometries from Gaussian 09 (ref. 43). In the MOLPRO and Gaussian 09 calculations, the aug-cc-pVTZ basis set was used for all atoms44,45 except the cc-pVTZ-PP basis set for Au46 and I47, and the Stuttgart SR effective core potential was used for heavier elements I47 and Au48.

The optimized geometries for anionic and neutral LAuCCH (L=Cl, I, CCH) are all linear (Supplementary Table S2), and are confirmed as minima through frequency analyses at the DFT level with PBE and B3LYP functionals. The calculated VDEs (Supplementary Table S1) were obtained using generalized Koopmans’s theorem by aligning the VDE1 with the experimental value49. The ADE and VDE1 were also calculated using the single-point CCSD(T)50 calculations with the B3LYP-optimized geometries (Table 1).