The impact of optical excitation on the binding in complexes of the cationic gold dimer: Au2+N2${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $ and Au2+N2O${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $

Abstract

The vibrationally resolved òΣ⁺ ← $${\tilde{\rm{X}}}^{2} $$Σ⁺ transitions of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ are reported together with a detailed characterization of important geometric and electronic properties, enabling a deep understanding of the bonding mechanism at the molecular level. Comparison with time‐dependent density functional theory calculations reveals that the ligand stabilizes the $${\mathrm{Au}}_{2}^{+}$$ entity in the $${\tilde{\rm{X}}}^{2} $$Σ⁺ state by donating electron density into the half‐filled bonding orbital leading to the strengthening of the $$\text{Au-Au}$$, $$\text{N-N}$$, and $$\text{N-O}$$ bonds. This effect is reversed in the òΣ⁺ state, where the $$\text{Au-Au}$$ bonding orbital is already filled and the ligand destabilizes the $$\text{Au-Au}$$ bond by donating into the antibonding orbitals of $${\mathrm{Au}}_{2}^{+}$$. The spectral detail obtained provides a deep understanding of the interplay of multiple electronic states in gas‐phase metal‐complex cations, opening the door for a systematic approach in the study of excited state reactivity in organometallic chemistry.

Key points

High‐resolution spectroscopic characterization of $${\mathrm{Au}}_{2}^{+}\text{L}$$ complexes by photodissociation of mass‐selected ions in the optical range and determination of fundamental molecular constants and ligand binding energies Detailed insight into geometric and electronic structure of ground and excited state of catalytically relevant gold cluster cations Effect of ligands on chemical bonding and reactivity of $${\mathrm{Au}}_{2}^{+}$$ in ground and excited electronic state

INTRODUCTION

An understanding of the interaction of gold with ligands at the molecular level is of fundamental interest in inorganic and organometallic chemistry.^1-3 In particular, the interaction of excited states of metal clusters with ligands is important because these states may interact differently with the ligands than the ground state, opening up new possibilities for molecular activation and/or reactivity changes that could be selectively switched on or off by light. Another example is the concept of two (or multiple) state reactivity that based on the distinct state-dependent reactivity of transition metals, together with a spin-crossover during the course of a reaction.⁴ Correlations between cluster reactivity and electronic properties, such as ionization and excitation energies or HOMO-LUMO gaps, have been reported long ago, for example, for the binding of $${\text{H}}_{\text{2}}$$ or $${\text{N}}_{\text{2}}$$, and are suggested to indicate intermediate electronic transitions during the reaction.^5-7 Here, we present vibrationally resolved electronic spectra of the $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ complexes that provide deep insight into the electronic properties of the ground and first excited electronic states.

The importance of gold lies not only in its catalytic properties but also in its role as a model system for developing an appropriate theoretical description of strong relativistic effects. These relativistic effects and their influence on ligands and their binding motifs have been the topic of numerous studies.^1,8,9 $${\mathrm{Au}}_{2}^{+}$$ specifically was shown to catalyze the formation of ethylene,^10,11 an observation that was later called into question and it was speculated that the observation could be explained by an excited state participating in the reaction.^12-14 The ligands considered herein are also of fundamental interest. $${\text{N}}_{\text{2}}\text{O}$$ is a potent greenhouse gas and a better understanding of its metal-based catalytic reduction is desirable.^15,16 $${\text{N}}_{\text{2}}$$ is abundantly available and efficient reduction to its bioavailable form, $${\text{NH}}_{\text{3}}$$, is an important chemical challenge.^17-19

The optical properties of $${\mathrm{Au}}_{2}^{+}$$ and $${\mathrm{Au}}_{2}^{+}\text{Ar}$$have been reported previously.^20,21 The first excited state of $${\mathrm{Au}}_{2}^{+}$$ (A²Σ_u⁺) is formed from the ground state (X²Σ_g⁺) by excitation from an antibonding 5dσ* orbital into the half-filled bonding 6sσ orbital. As a result, the Au-Au bond distance decreases significantly upon electronic A ← X excitation. The X and A states of $${\mathrm{Au}}_{2}^{+}$$ are described well using standard time-dependent density functional theory (TD-DFT) as is apparent from the similarity between computed and measured excitation spectra.

The manifold bonding and activation mechanisms of $${\text{N}}_{\text{2}}\text{O}$$ by transition metals have been described previously and $$\text{N}$$ coordination as well as back donation from the metal d-orbital into the LUMO of $${\text{N}}_{\text{2}}\text{O}$$ were identified to be the most critical components of the interaction.² The reactions of $${\mathrm{Au}}_{n}^{+}$$ clusters with $${\text{N}}_{\text{2}}\text{O}$$ have been studied in a Penning trap²² and $${\mathrm{Au}}_{n}^{+}{\text{N}}_{\text{2}}\text{O}$$ complexes have been characterized via IR action spectroscopy.^23,24 While the reactions in a Penning trap revealed several gas-phase pathways (especially dissociative charge transfer yielding $${\text{NO}}^{\text{+}}$$), the structural IR investigation of the ground state showed no indication of dissociation apart from simple $${\text{N}}_{\text{2}}\text{O}$$ loss.^23,24 The latter studies also showed the $$\text{N}$$-bound isomer to be formed predominantly, with the $$\text{O}$$-bound isomer being substantially less stable. Many metal–$${\text{N}}_{\text{2}}$$ complexes have been studied,²⁵ and the strong $${\text{N}}_{\text{2}}$$ bond was found to be activated in $${\text{Au-N}}_{\text{2}}$$ complexes.²⁶ On the other hand, $${\text{N}}_{\text{2}}$$ interaction with $$\text{Fe(III)}$$ oxoacetates was found to strengthen the $${\text{N}}_{\text{2}}$$ bond.²⁷ This nonclassical behavior was explained by a lack of π back donation and delocalization of the antibonding 4σ($${\text{N}}_{\text{2}}$$) orbital, an effect that has also been described for isoelectronic $$\text{CO}$$ in metal–$$\text{CO}$$ complexes.^28,29 Our study focuses on the effects of $${\text{N}}_{\text{2}}$$ and $${\text{N}}_{\text{2}}\text{O}$$ ligands on the X and A states of $${\mathrm{Au}}_{2}^{+}$$, identifying the resulting binding motifs in each state and any changes in N₂ and $${\mathrm{Au}}_{2}^{+}\text{L}$$ activation upon metal complexation (Figure 1). The detailed insight into the potential energy surface of these fundamental metal–ligand complexes arises from recent instrumental improvements, which allow us to measure vibronic spectra in unprecedented detail.^20,30,31

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RESULTS AND DISCUSSION

Vibronic spectra of $${\mathrm{Au}}_{2}^{+}\text{L}$$ ($${\text{L=N}}_{\text{2}}$$ and $${\text{N}}_{\text{2}}\text{O}$$) have been measured in the 0.8–1.5 eV range (Figure 2) via electronic photodissociation (EPD) of mass-selected clusters in a quadrupole/time-of-flight tandem mass spectrometer.^20,31 Both clusters decay exclusively via loss of the ligand and the $${\mathrm{Au}}_{2}^{+}$$ fragment is detected. Parent clusters are generated via laser vaporization (532 nm, 3 mJ/pulse, ∼0.5 mm diameter) of a turning and translating $$\text{Au}$$ rod. $${\text{N}}_{\text{2}}$$ and $${\text{N}}_{\text{2}}\text{O}$$ are added to the $$\text{He}$$ expansion gas in fractions of 0.1 %. For cluster generation, the plasma is expanded through a reaction channel (l = 3 cm, d = 4 mm) and a conical nozzle cooled by liquid $${\text{N}}_{\text{2}}$$. After passing through a skimmer, $${\mathrm{Au}}_{2}^{+}\text{L}$$ complexes are mass-selected in a quadrupole and guided into the extraction region of a reflectron time-of-flight mass spectrometer. Before extraction, they are overlapped with a laser pulse emitted from a tuneable optical parametric oscillator (bandwidth ≤10 cm^–1, 10¹⁵–10¹⁶ photons/cm²) to induce dissociation. The photodissociation cross section is then determined as a function of photon energy from the relative parent and fragment ion signals, using an overlap factor of ion and photon beam of α = 0.6 as estimated from power-dependent measurements.³¹ The EPD spectra provide a good measure for the total absorption cross section if competing relaxation processes can be neglected. To aid the spectral assignment and to obtain deeper insight into the electronic structure of the complexes, DFT calculations are performed. The $$\tilde{\rm{X}}$$ and à states of $${\rm{Au}_{2}^{+}}$$L are optimized at the CAM-B3LYP/cc-pVTZ level,^32,33 including GD3BJ empirical dispersion and ECP60MDF effective core potentials,³⁴ as implemented in GAUSSIAN16 (Figure 1 and Table 1).³⁵ D₀ and E_a values reported herein are the zero-point corrected dissociation and adiabatic excitation energies. Previous studies have shown that the lowest excited state of $${\mathrm{Au}}_{2}^{+}$$ is described very well at this level of theory, giving a difference in E_a of less than 0.1 eV.²⁰ The lowest energy electronic states were found to have doublet multiplicity for all complexes studied here with quartet states lying more than 2.5 eV higher in energy and thus ignored henceforth.

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TABLE 1 Experimental properties of the ground and first excited state of $${\rm{Au}_{2}^{+}} $$, $${\rm{Au}_{2}^{+}} {\rm{N}}_{2} $$, and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ compared to computed values

	Experiment	CAM-B3LYP/cc-pVTZa
	$${\rm{Au}_{2}^{+}}$$N2	$${\rm{Au}_{2}^{+}}$$N2O	$${\rm{Au}_{2}^{+}}$$N2	$${\rm{Au}_{2}^{+}}$$N2O	N2	N2O	$${\rm{Au}_{2}^{+}}$$
State	$${\tilde{\rm{X}}}^{2} $$Σ+	Ã2Σ+	$${\tilde{\rm{X}}}^{2} $$Σ+	Ã2Σ+	$${\tilde{\rm{X}}}^{2} $$Σ+	Ã2Σ+	$${\tilde{\rm{X}}}^{2} $$Σ+	Ã2Σ+	X1Σg+	$$\tilde{\rm{X}}$$1Σg+	X2Σg+	A2Σu+
Ea / eV		0.910(1)		0.90(5)		0.975		0.953
Ev / eV		1.07(2)
Re(Au-L) / Å	ΔRe($$\tilde{\rm{X}}$$, Ã) = 0.25(4)b			2.067	2.264	2.068	2.219
re(Au-Au) / Å	Δre($$\tilde{\rm{X}}$$, Ã) = −0.09(4)b			2.606	2.459	2.607	2.458			2.635	2.447
D0($${\rm{Au}_{2}^{+}}$$-L) / eV	<0.91		1.05(3)		0.89	0.64c	1.06	0.86c
ω1 / cm–1					2501	2514	2496	2476	2501d	1359	140	193
ω2 / cm–1	290(2)	216(5)			285	219	1452	1460		637
ω3 / cm–1	147(2)	179(2)		230(10)	138	180	245	220		2404
ω4 / cm–1	Δ(ω4‘‘,ω4‘) = 39(2)		170(10)	243	205	133	170
ω5 / cm–1					44	49	617	633
ω6 / cm–1							104	106
ω7 / cm–1			Δ(ω7‘‘,ω7‘) = –4(2)			26	27
ω2χ2 / cm–1		0.89(5)
ω3χ3 / cm–1		0.8(1)
χ23 / cm–1		0.85(5)
kAu-Aub / 102 N m–1	2.3(1)	3.9(2)			2.04	4.01	2.01	3.86
kAu-Lb / 102 N m–1	2.0(1)	1.0(1)			1.95	1.00	2.06	1.41

The EPD spectra of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ are compared in Figure 2 to the spectrum of $${\rm{Au}_{2}^{+}}$$Ar reported previously.²⁰ $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ shows a long progression starting at E_a = 7340(5) cm^–1. Isolated peaks have a full width at half maximum (FWHM) of 5 cm^–1, which corresponds to the laser bandwidth and allows to give a lower limit for the excited state lifetime. Together with the information that no delayed decay is observed in the reflectron after laser excitation, we can estimate that the excited state lifetime lies in between 2×10^–6 and 1×10^–12 s. About 13 quanta in the main progression (ν₂ = 213 cm^–1) are observed together with 2–3 quanta in a second mode (ν₃ = 176 cm^–1), as well as some peaks arising from hot bands. By comparison with the $${\rm{Au}_{2}^{+}}$$spectrum and the TD-DFT calculations, the progressions are assigned to the symmetric and antisymmetric stretch vibrations ν₃ and ν₂, their hot bands, and some small contributions from hot bands of the degenerate ν₄ mode (SOMO ← HOMO-1, Figure 3 and Table S2). A Dunham fit yields harmonic frequencies and (cross) anharmonicities of the à state (Table 1). The A state of $${\mathrm{Au}}_{2}^{+}$$ is formed by moving an electron from the antibonding 5dσ^∗ orbital into the half-filled bonding 6sσ orbital (Figure 1), effectively increasing the $$\text{Au-Au}$$ bond order from 0.5 to 1.5. The resulting àstates of $${\rm{Au}_{2}^{+}}$$L, therefore, show a 0.15 Å shorter Au-Au bond length than the $$\tilde{\rm{X}}$$ state. At the same time, the $${\rm{Au}_{2}^{+}}$$-L bond strength decreases, resulting in an increase in intermolecular distance (+0.2 and +0.15 Å for L = N₂ and N₂O). The harmonic frequencies and atomic masses can be used to estimate the force constants of the Au-Au and the Au-N₂ bonds (Table 1) as described in the Supporting Information. The Au-Au force constant increases by a factor of 1.7(2) upon excitation, consistent with an increased bond order. The $${\rm{Au}_{2}^{+}}$$-N₂ force constant halves upon excitation. Both changes result in substantial geometry changes that are reflected in extended Franck–Condon (FC) progressions of the vibration corresponding to this change, which is mainly the antisymmetric Au-Au-L stretch mode (ν₂ for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and ν₃ for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$) and to a lesser extent the symmetric $$\text{Au-Au-L}$$ stretch (ν₃ for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and ν₄ for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$, Figure 1).

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Comparison of the simulated FC spectrum of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ to the measured EPD spectrum shows good agreement in the main progression (ν₂) after correction for anharmonicity (Figure 3) and a small origin shift of –0.065 eV. The calculated geometry change is slightly overestimated, resulting in larger intensity toward the high-energy side of the spectrum. The simulations also slightly overestimate the contribution from ν₃. The observed hot bands stem from ν₃ and ν₄. We observe the 2ⁿ3₁^m transitions with m = 0 and 1 and the 2ⁿ4₁¹ transitions, from which we determine ω₃''  =  143(2) cm^–1 and Δ(ω₄'', ω₄')  =  39(2) cm^–1. These compare well to the computed values of 138 and 38 cm^–1, respectively. Interestingly, we do not observe a hot band in the lowest energy vibration, ν₅(π). If this made a substantial contribution to the spectrum, the peaks would be broader because a difference of 5 cm^–1 between ω₅' and ω₅'' is at the lower end of the instrumental resolution. Possibly, lower frequency modes cool more efficiently than those with higher energy, an effect also seen in the $${\rm{Au}_{2}^{+}}$$Ar spectra,²⁰ but not in the spectra of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$. Comparison between EPD spectra of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ recorded at 100 and 300 K (Figure S1), indeed, reveals significant broadening, albeit not as much as would be expected at 300 K. Another explanation is that Δ(ω₅'', ω₅') is significantly smaller than the calculated value of 5 cm^–1. Significantly, the whole NIR spectrum of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ lies above its D₀ value and thus is obtainable via single-photon EPD. A Birge–Sponer plot of the main progression (ν₂) of $${\rm{Au}_{2}^{+}}$$N₂ (Figure S2) results in ω₂ = 216.3 cm^–1 (the value given in Table 1 comes from the Dunham expansion) and D₀  =  1.5 eV. The ω₂ frequency agrees well with calculations but D₀ is overestimated probably due to coupling of the Au-Au and Au-L local modes and strong deviation from the Morse potential assumed (Figure S3).²⁰

The EPD spectrum of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ in Figure 2 is not as easily assigned as that of $${\rm{Au}_{2}^{+}}$$N₂. It shows fewer and broader peaks (FWHM ∼30 cm^–1) with lower peak intensity, and a clear band origin cannot be identified. It is noteworthy that the shape of the first peaks changes with nozzle temperature (Figures 2 and S1). The calculated $${\rm{Au}_{2}^{+}}$$–N₂O dissociation energy (D₀ = 1.06 eV, 8550 cm^–1) occurs within the observed band system, and several experimental observations confirm this result. First, the pronounced vibronic progression is significantly shorter than for $${\rm{Au}_{2}^{+}}$$N₂. Second, its total integrated intensity is significantly weaker, despite the same calculated oscillator strength, indicating that the low-frequency part of the absorption spectrum is not observed by EPD. This could be because the ligand binding energy exceeds the photon energy and thus prevents single-photon EPD from vibrationally cold ions. Third, the strong temperature dependence near the onset of the progression suggests that we observe mainly hot bands in this range. These results allow us to determine the experimental dissociation energy to D₀ = 1.05(3) eV, lying somewhere between the temperature-dependent peak at 8486 cm^–1 and the lowest observable signal at around 8200 cm^–1, in excellent agreement with the predicted value (1.06 eV, 8550 cm^–1). The band origin (E_a) of the à ← $$\tilde{\rm{X}}$$ transition cannot be determined as precisely. However, an estimate can be made by comparing to the $${\rm{Au}_{2}^{+}}$$L spectra with L = Ar and N₂. Their observed E_a values lie 523 and 610 cm^–1 below the calculated energies. Assuming a similar difference for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$, one can compare the vibrational progressions of the two complexes by plotting the $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ trace such that both calculated E_a’s overlap (blue trace in Figure S5, the 178 cm^–1 shift is the difference in E_a’s). One can see that the $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ progression then resembles the last part of the $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ progression. An even better agreement between the two spectra is achieved by shifting the progression further (red trace in Figure 4 for a 691 cm^–1 shift). We thus estimate E_a to lie between 7000 and 7500 cm^–1 (i.e., E_a = 0.90(4) eV).

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An FC simulation at 100 K is compared to the measured $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ spectrum in Figure 4. The FC spectrum is shifted by –1060 cm^–1, such that the relative peak heights at the higher energy side overlap with the experimental spectrum. However, because the calculation might overestimate the geometry change as in $${\rm{Au}_{2}^{+}}$$N₂, this shift is somewhat arbitrary and a firm assignment of vibrational quanta has to remain open. Nevertheless, some safe conclusions can be drawn. The observed peaks stem from the main symmetric and antisymmetric stretch vibrations ν₃ and ν₄, in accordance with $${\rm{Au}_{2}^{+}}$$N₂. Their harmonic frequencies are not as precisely determined as those for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ because of the missing initial part of the progression. Assuming a similar anharmonicity as that for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ (Figure S3) and a start of the observed progression at around v₃ = 10–12, we obtain ω₃ = 230(10) and ω₄ = 170(10) cm^–1. The larger width of the $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ peaks compared to those of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ is explained by the fact that the lowest energy vibration (ν₁) has a harmonic frequency of only ν₁ = 26 cm^–1 (compared to 44 cm^–1 for $${\rm{Au}_{2}^{+}}$$N₂) and is thus more strongly populated at the same internal temperature. Additionally, the difference in ω₅'' and ω₅' is probably larger than the calculated 1 cm^–1. Using a Boltzmann distribution at 100 K, a difference in ω₅'' and ω₅' of –4(2) cm^–1 can explain the observed line widths.

The binding energies of 0.89 and 1.06 eV computed for $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and $${\mathrm{Au}}_{2}^{+}{\text{N}}_{\text{2}}\text{O}$$ in the $$\tilde{\rm{X}}$$ state are relatively low compared to those for related $${\text{Au}}^{\text{+}}\text{L}$$ complexes.¹ As can be seen from the orbitals in Figure 1, a significant part of bonding comes from electron delocalization. In common with $${\mathrm{Au}}_{2}^{+}$$ and $${\mathrm{Au}}_{2}^{+}\text{Ar}$$, both complexes show a strong decrease in $$\text{Au-Au}$$ distance upon à ← $$\tilde{\rm{X}}$$ excitation because the transition is mostly located on $${\mathrm{Au}}_{2}^{+}$$.^20,21 Usually, one would use the shift of the $$\text{Au-Au}$$ stretch frequency to estimate a change in $$\text{Au-Au}$$ binding energy or force constant. Here, this is not easily possible because of very strong mixing with the $$\text{Au-L}$$ stretch mode, which changes with ligand and electronic excitation. Considering the calculated $$\text{Au-Au}$$ distance, the $$\text{Au-Au}$$ bond becomes stronger upon excitation consistent with the increased bond order of $${\mathrm{Au}}_{2}^{+}$$. The ligand changes the situation somewhat. While the $$\text{Au-Au}$$ distance decreases in the $$\tilde{\rm{X}}$$ state by ligation from 2.635 to 2.623, 2.606, and 2.608 Å in $${\mathrm{Au}}_{2}^{+}$$, $${\mathrm{Au}}_{2}^{+}\text{Ar}$$, $${\mathrm{Au}}_{2}^{+}{\text{N}}_{\text{2}}$$, and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$, respectively, the trend is less pronounced and reversed in the à state (2.447, 2.455, 2.459, and 2.459 Å). This result can be understood by considering that L donates electron density into the half-filled, bonding 6sσ orbital of $${\mathrm{Au}}_{2}^{+}$$, thereby stabilizing the dimer. In the à state, however, this orbital is filled and L cannot stabilize the $$\text{Au-Au}$$ bond further. Instead, any electron density transfer from L to $${\mathrm{Au}}_{2}^{+}$$ either contributes to the partially occupied antibonding 5dσ^∗ orbital or the empty 6sσ^∗ orbital of $${\mathrm{Au}}_{2}^{+}$$, resulting in an increase in the $$\text{Au-Au}$$ distance upon ligation. This effect is weaker than the stabilizing effect in the $$\tilde{\rm{X}}$$ state, probably due to the larger energy mismatch between the donating ligand orbitals and the antibonding $${\mathrm{Au}}_{2}^{+}$$ orbitals. These interactions also explain the lower ligand binding energy in the à state compared to the $$\tilde{\rm{X}}$$ state (Table 1).

We can also consider the impact of $${\mathrm{Au}}_{2}^{+}$$ on the properties of the ligands. The calculated $${\text{N}}_{\text{2}}$$ stretch frequency in free $${\text{N}}_{\text{2}}$$ is the same as that in the $$\tilde{\rm{X}}$$ state of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ (2501 cm^–1). In the à state of $${\mathrm{Au}}_{2}^{+}{\text{N}}_{\text{2}}$$, it is slightly higher at 2514 cm^–1. A similar 17 cm^–1 increase was observed in $$\text{Fe(III)}$$ oxoacetate$${\text{-N}}_{\text{2}}$$ complexes and explained by delocalization of the antibonding 4σ*($${\text{N}}_{\text{2}}$$) orbital.²⁷ The $$\tilde{\rm{X}}$$ state wavenumber can be explained by the fact that only the nonbonding lone pair of $${\text{N}}_{\text{2}}$$ participates in the $${\mathrm{Au}}_{2}^{+}{\text{-N}}_{\text{2}}$$ bond. The small à state increase could be caused by the aforementioned delocalization or by the small induced dipole.

The computed N₂O symmetric and antisymmetric stretch frequencies shift blue by almost equal amounts in the $$\tilde{\rm{X}}$$ and à states of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ compared to those of bare N₂O. A similar blue shift in the antisymmetric stretch of Au⁺N₂OAr was explained by σ-donation from the antibonding 7σ* orbital of N₂O to the metal center.²⁴ Our calculations predict a small increase in the N-N distance upon ligation and a stronger decrease in the N-O distance in the $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ complex compared to bare N₂O. The calculated force constants for the N-N and N-O stretch vibrations increase by 6% and 12% upon ligation, respectively, showing that the strengths of both the N-N and the N-O bonds slightly increase but the effect is stronger on the N-O side. The difference in the N₂O structure in the $$\tilde{\rm{X}}$$ and à states of the complex is small and thus indicates that the binding mechanism of N₂O to $${\mathrm{Au}}_{2}^{+}$$ does not change upon excitation. This behavior can be explained in accordance with the case of Au⁺N₂OAr.²⁴ Electron density from the 7σ*  N-N antibonding orbital of N₂O is donated into the half-filled bonding σ orbital of $${\mathrm{Au}}_{2}^{+}$$. The 6σ* N-O antibonding orbital also loses electron density, probably into the 7σ N-N orbital, resulting in a strengthening of the N-N, N-O, and Au-Au bonds. Note that we do not observe the higher lying O-bound $${\rm{Au}_{2}^{+}}$$ON₂ isomer^23,24 and thus do not discuss it here.

Comparing the two ligands, both N₂ and N₂O have a similar effect on $${\rm{Au}_{2}^{+}}$$, that is, strengthening the Au-Au bond. The effect is strongest in the $$\tilde{\rm{X}}$$ state of $${\rm{Au}_{2}^{+}}$$N₂, resulting in an increase in the adiabatic excitation energy compared to $${\rm{Au}_{2}^{+}}$$Ar and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ despite an increase in binding energy in the $$\tilde{\rm{X}}$$ and à states of $${\rm{Au}_{2}^{+}}$$Ar, $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ to $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ (Figure S4). The ligands, however, are affected differently. While the bond strength in N₂ barely changes, the N-O and the N-N bonds in N₂O are strengthened in both the $$\tilde{\rm{X}}$$ and à states.

CONCLUDING REMARKS

In summary, gas-phase $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ and $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ complexes have been characterized by measuring their high-resolution vibronic à ← $$\tilde{\rm{X}}$$ spectra occurring in the near infrared (NIR) range. The analysis provides unprecedented insight into the effects of electronic excitation on the chemical bonding in these prototypical metal–ligand complexes at the molecular level. An extended vibrational progression in the Au-Au-N₂ antisymmetric stretch indicates that the Au-Au bond order increases markedly upon à ← $$\tilde{\rm{X}}$$ excitation, while the Au-N₂ bond length increases. For $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$, the band origin of the à state lies below the dissociation energy of the $$\tilde{\rm{X}}$$ state, providing an accurate experimental value for the important dissociation energy of D₀ = 1.05(3) eV. Interestingly, the Au-Au bond is also strengthened upon ligation, in both cases due to electron density transfer into a bonding σ orbital of $${\rm{Au}_{2}^{+}}$$ originating either from a lower lying antibonding orbital or from the ligand. Interestingly, the ligand effect is reversed in the excited state, because the bonding σ orbital is filled and electron transfer from the ligand occurs into antibonding orbitals, thereby, weakening the Au-Au bond upon ligation. The ligand binding energy decreases upon à ← $$\tilde{\rm{X}}$$ excitation due to weaker bonding interactions in the excited state.

The N-N bond in N₂ is nearly unaffected by binding to $${\rm{Au}_{2}^{+}}$$, either in the $$\tilde{\rm{X}}$$ and à state of $${\rm{Au}_{2}^{+}} {\rm{N}_{2}} $$ because the electron density donated to $${\rm{Au}_{2}^{+}}$$ stems from a nonbonding N₂ lone pair orbital. Although we have no direct experimental indication for back donation (we do not observe any internal ligand vibration), our calculations indicate that both N₂O bonds in $${\rm{Au}_{2}^{+}} {\rm{N}_{2}{\rm{O}}} $$ are strengthened. As a result, no molecular activation of N₂ or N₂O arises from binding to $${\rm{Au}_{2}^{+}}$$ in either the $$\tilde{\rm{X}}$$ or à state. In fact, the metal–ligand interaction in the à state is even weaker than in the $$\tilde{\rm{X}}$$ state. The situation will be different for ligands that can readily donate electron density from bonding orbitals into the half-filled SOMO of $${\rm{Au}_{2}^{+}}$$ or, when the à state is considered, into the energetically displaced antibonding orbitals of $${\rm{Au}_{2}^{+}}$$. To this end, this high-resolution spectroscopic approach will allow us to characterize reactive complexes, such as $${\rm{Au}_{p}^{+}}$$C_nH_m,^10-14 providing detailed insight into photocatalysis of metal-organic reactions at the spectroscopic level.

AUTHOR CONTRIBUTIONS

Marko Förstel: conceptualization; formal analysis; investigation; methodology; project administration; software; supervision; validation; visualization; writing—original draft; writing—review and editing. Nima-Noah Nahvi: formal analysis; investigation; software; validation; writing—review and editing. Kai Pollow: conceptualization; formal analysis; investigation; software; validation; writing—review and editing. Taarna Studemund and Alice E. Green: investigation; writing—review and editing. André Fielicke: methodology; resources; writing—review and editing. Stuart R. Mackenzie: conceptualization; funding acquisition; methodology; writing—review and editing. Otto Dopfer: conceptualization; funding acquisition; investigation; methodology; project administration; resources; supervision; validation; writing—original draft; writing—review and editing.

ACKNOWLEDGMENTS

This project was supported by Deutsche Forschungsgemeinschaft (DFG, DO 729/9). We thank Roland Mitric for helpful discussions. Financial support is also gratefully acknowledged from the Oxford-Berlin Research Partnership (OXBER_STEM5: A Collaborative Approach to Understanding Nitrogen Oxide Reduction at Metal Centres). AEG and SRM gratefully acknowledge EPSRC programme grants EP/L005913 and EP/T021675. Corrections added on October 7, 2022 after first online publication: Ethic Statement was missing.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

ETHICS STATEMENT

The authors confirm that they have followed the ethical policies of the journal.

PEER REVIEW

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References

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