IR spectroscopic characterization of the co-adsorption of CO2 and H2 onto cationic Cun+ clusters

To understand elementary reaction steps in the hydrogenation of CO2 over copper-based catalysts, we experimentally study the adsorption of CO2 and H2 onto cationic Cun+ clusters. For this, we react Cun+ clusters formed by laser ablation with a mixture of H2 and CO2 in a flow tube-type reaction channel and characterize the products formed by IR multiple-photon dissociation spectroscopy employing the IR free-electron laser FELICE. We analyze the spectra by comparing them to literature spectra of Cun+ clusters reacted with H2 and with new spectra of Cun+ clusters reacted with CO2. The latter indicate that CO2 is physisorbed in an end-on configuration when reacted with the clusters alone. Although the spectra for the co-adsorption products evidence H2 dissociation, no signs for CO2 activation or reduction are observed. This lack of reactivity for CO2 is rationalized by density functional theory calculations, which indicate that CO2 dissociation is hindered by a large reaction barrier. CO2 reduction to formate should energetically be possible, but the lack of formate observation is attributed to kinetic hindering.


Introduction
The rapid development of the urbanized world has resulted in the constant growth of the atmospheric CO 2 concentration. On its own, CO 2 is a harmless molecule, which is part of the natural carbon cycle. In large concentrations, CO 2 acts as thermal isolation for our planet and is one of the main causes of global warming. Therefore, a reduction of the global carbon footprint is of great significance to reduce the societal impact of global warming. 1 Since CO 2 is non-toxic, renewable, and cheap, it has the potential to serve as a feedstock for the industrial production of value-added chemicals. The bottleneck of CO 2 utilization is its kinetic inertness due to the high CQO bonding energy of 7.8 eV. 2 Almost a century ago, syngas, a mixture of CO 2 , CO, and H 2 , was used for the first time for methanol production. 3 This reaction required a catalyst, and elevated pressure (up to 350 bar) and temperature. Ever since, the search has been ongoing for more efficient catalyst materials that can reduce production costs, increase methanol selectivity, and minimize environmental impact.
The widely used Cu/ZnO/Al 2 O 3 catalyst for commercial methanol production made it possible to reduce the reaction pressure to 50-100 bar at a temperature around 200-300 1C. 4 Wide ranges of other catalysts have been investigated; a recent summary was given by Zhang et al. 5 Overall, Cu based catalysts still show the best performance. However, the exact mechanism of methanol formation over the catalyst remains elusive. Theoretical studies have discussed several reaction paths. [6][7][8] Some require the dissociation of hydrogen before CO 2 activation, while others are initiated by direct CO 2 activation or even water involvement. It is now widely accepted that the most profitable path for hydrogenation of CO 2 to methanol over Cu-based catalysts proceeds via a formate (HCOO) intermediate. 4,6,[9][10][11][12] The surface chemistry of CO 2 as studied under high vacuum conditions has been reviewed by various authors. [13][14][15] Surface studies agree that the electronic and geometric structures determine the activity of the catalyst. 2,[16][17][18] Experimentally, it was shown that crystalline Cu(100) surfaces are relatively inert towards CO 2 . 16,19 In the Cu/ZnO catalyst, Cu atoms are dispersed and Cu + is stabilized, 20,21 where a correlation was found between the concentration of Cu + species on the catalyst surface and methanol production rates. 19,[21][22][23][24] Cu clusters deposited on a ZnO/Al 2 O 3 surface were demonstrated to significantly reduce the pressure required for methanol formation. 25,26 Concomitant density functional theory (DFT) modeling showed that the Cu clusters deposited on Al 2 O 3 and SiO 2 are slightly positively charged, which is attributed to the cluster-support interaction. 26 Theoretical studies also emphasize that the size of the deposited cluster has a large influence on its activity, with smaller clusters showing a higher activity. [26][27][28] Complete control over the structure and charge of the clusters is achieved in gas-phase studies. Here, metal clusters can mimic the catalyst active sites to study the elementary steps of methanol formation at the molecular level. Understanding the binding nature of CO 2 to different metal ions has attracted broad research interest. The chemistry between cationic metal ions and a single CO 2 molecule has been studied employing guided ion beam and flow tube reactor based mass spectrometry; [29][30][31][32][33][34][35][36] a summary can be found elsewhere. 7 IR spectroscopic studies have aimed to obtain structural insight into the solvent-driven activation of CO 2 by various metal cations. [37][38][39][40][41][42][43][44][45][46][47] The general picture that emerges is that metal cations mostly bind CO 2 molecules intact, in end-on configuration via one of the oxygen atoms through quadrupole-related electrostatic interactions.
It can thus be expected that CO 2 adsorption onto metal clusters is also dominated by a weak electrostatic interaction resulting in physisorption. However, what is unclear is how this situation changes when hydrogen atoms are present on the cluster surface. Hu et al. simulated methanol formation over a Cu 8 cluster and compared it to the Cu(100) surface. 48 According to this work, H 2 and CO 2 are co-adsorbed on the surface, where H 2 is dissociated and CO 2 is chemisorbed in the form of CO 2 À . This leads to a Langmuir-Hinshelwood type reaction between atomic hydrogen, H(a), and CO 2 À resulting in a formate intermediate. Yang et al. also found that methanol formation will proceed via a formate intermediate, both over a Cu 29 cluster, and over Cu(111). 49 However, in this study the reaction proceeds via an Eley-Rideal-type mechanism. First, H 2 dissociatively binds to the surface, and then CO 2 directly reacts with the H(a) to form formate. Another mechanism of methanol formation over Cu/ZnO catalyst is proposed by Kakumoto. 11 His calculations suggest that CO 2 is first linearly absorbed on Cu + , followed by an attack of H(a) on the C atom, leading to the formate intermediate. 11 Therefore, three alternative routes of the formation of the formate intermediate are proposed by the theoretical investigations. Previously, we have shown that the adsorption of H 2 onto cationic Cu n + (n = 4-7) clusters can lead to a significant fraction of cluster population with dissociatively bound H 2 , with a sizedependent propensity for dissociation. 50 In this work, we investigate the co-adsorption of CO 2 and H 2 on cationic Cu n + clusters employing IRMPD spectroscopy. To interpret the coadsorption spectra we compare them to equivalent spectra separately obtained for the adsorption products of the individual molecules. For H 2 adsorbed on cationic Cu n + we use spectra from our previous work; 50 for CO 2 , we present new spectra. Furthermore, we have carried out extensive DFT calculations to rationalize and corroborate our interpretations.

Experimental
The experiments are performed using a molecular beam instrument placed within the cavity of a free-electron laser (FELICE). 51 GmbH) attached to a stainless steel rod. The plasma formed in the ablation process is collisionally cooled by a carrier gas pulse consisting of a mixture of 1% Ar in He for the CO 2 experiment (to facilitate the formation of larger clusters) and of pure He for the co-adsorption experiment. The carrier gas is introduced via a pulsed valve (General Valve series 9) with a stagnation pressure of 6 bar. The created clusters are reacted with either pure CO 2 or a mixture of 1% CO 2 in H 2 , introduced approximately 50 mm downstream by a second pulsed valve with a 1 bar stagnation pressure. The reacting mixture is confined in the flow channel by a converging-diverging nozzle (diameter B0.7 mm), which is located 10 mm further downstream, through which the gas mixture eventually is expanded into vacuum, forming a molecular beam. The formed beam is subsequently collimated by a 2 mm diameter skimmer and shaped by a horizontal slit aperture (8 Â 0.45 mm) to ensure optimum overlap with the (horizontal) IR beam, which it crosses at a 351 angle; both shaping elements are electrically grounded. The irradiated cationic species are extracted by two pulsed, high voltage plates into a reflectron time-of-flight mass spectrometer and registered by a multichannel plate (MCP) detector. The experiment is operated at 10 Hz, which is double the FELICE macropulse repetition rate. Therefore, for every mass spectrum of irradiated clusters recorded, a reference mass spectrum is recorded to correct for fluctuations in cluster production. When the IR light is resonant with an optically allowed vibrational mode of the complex, the sequential absorption of IR photons can lead to fragmentation, resulting in the loss of CO 2 , H 2 , or both. The FELICE IR light employed in this work is in the 120-2100 cm À1 spectral range. Each FELICE macropulse is formed by a 10 ms duration pulse train of 1 ns spaced picosecond duration, near-transform limited optical pulses. The spectral bandwidth is adjusted to a full-width at half-maximum (FWHM) of about 0.7% of the central frequency, thus B7 cm À1 at 1000 cm À1 . The typical macropulse energy used is between 0.5-0.8 J. The use of the intracavity instrument allows performing experiments, where high pulse energies are required for photofragmentation, as one could expect for complexes where CO 2 and/or H 2 adsorb dissociatively. For systems with lower binding energies, the instrument can be positioned well out of the focus of the IR laser to reduce the IR intensity. The IRMPD spectra presented in this paper are measured out of focus. 51 This journal is © the Owner Societies 2021 Phys. Chem. Chem. Phys., 2021, 23, 26661-26673 | 26663 The IRMPD spectra for CO 2 adsorption are presented as the pulse energy-normalized depletion yield Y D , defined as where I(n) is the ion intensity of the mass channel under study with IR radiation at frequency n, I off the intensity without IR laser, and P the macropulse energy, respectively. If no fragmentation takes place, the ratio I(n)/I off is unity and Y is consequently zero.
To construct spectra for [Cu n , CO 2 , H 2 ] + , loss of H 2 from [Cu n , CO 2 , pH 2 ] + (p 4 1) and of CO 2 from [Cu n , mCO 2 , H 2 ] + (m 4 1) leads to contamination of the mass channel of interest. To account for this, we inspected the IR-induced loss and growth signals for all relevant mass channels to identify the fragmentation pathways, which are summarized in Scheme 1; they are substantiated by depletion spectra per individual mass channel in the ESI. † We then calculate the branching ratio B(n) of all clusters with m CO 2 and p H 2 molecules adsorbed to all these species plus the channel into which the [Cu n , CO 2 The IRMPD yield Y B is then obtained as the logarithmic depletion ratio of the branching ratios with and without IR irradiation: This approach assumes that no direct loss of multiple H 2 or CO 2 occurs from [Cu n , mCO 2 , pH 2 ] + (m,p 4 1) induced by IR absorption, and was used previously. 53 By employing it, ingrowth effects from higher order complexes are reduced, as are shot-to-shot fluctuations in cluster production.
To construct spectra for [Cu n , CO 2 ] + in the co-adsorption experiments, neither of the described methods is suitable. The depletion yield Y cannot be used since there is significant ingrowth from fragmentation from the different complexes into the [Cu n , CO 2 ] + mass channel. The depletion of the branching ratio also fails, because the final fragment in this case, the bare cluster, has competing ingrowth from fragmentation of [Cu n , pH 2 ] + , which will contaminate the final spectrum. Therefore, the depletion yield Y D of [Cu n , CO 2 ] + plus all species fragmenting into the [Cu n , CO 2 ] + mass channel has been calculated: Throughout the manuscript, we employ the bracketed notation introduced here to indicate no structural knowledge of the products is known, only its mass.

Computational
Quantum chemical computations were carried out using the Q-Chem 5.3 program package, 54  with different metal cluster cores and different CO 2 and H 2 binding motifs (i.e., intact and dissociated H 2 and CO 2 , CO 2 bound with its oxygen or in di-s binding mode) were systematically generated using our in-house code. This code, successfully used in other combined experimental and theoretical work on activation reactions involving metal clusters, [55][56][57][58] systematically generates the initial clusteradsorbate structures in different binding modes (see the ESI, † for the details). A publication detailing and benchmarking this software is forthcoming. The structures generated were optimized at the TPSSh/def2-TZVP + D3 level of theory. 59 All calculations were done at the lowest spin multiplicity, i.e., doublet for even and singlet for odd numbers of Cu atoms. The effect of the level of correlation for Cu 4 + with CO 2 or H 2 adducts is compared to CCSD(T)/def2-QZVPPD benchmarks, while the finite basis size in DFT computations and relativistic effects were estimated using relativistic full-potential linearized augmented wave computations (see the ESI † for the details). We explored the reaction mechanisms between stable intermediates. Harmonic vibrational frequencies of the structures were computed for comparison with the experimental spectra, and to confirm that all minima and transition structures have zero or one imaginary vibrational frequency, respectively. The stability of the Self Consistent Field solution was confirmed. Intrinsic Reaction Coordinates were computed starting from the transition structures. To compare experimental spectra to calculated spectra, the harmonic frequencies were scaled by a factor 0.968 to correct for anharmonicity of the vibrational potential and inaccuracies of the employed level of theory. This factor was determined by fitting experimental band positions of [Cu 5 , H 2 ] + , 50 to calculated band positions of the assigned isomer at the current level of theory (see Fig. S4 in the ESI †). The scaled harmonic stick spectra were then convoluted with a 20 cm À1 full-width at half-maximum Gaussian line shape function. Enthalpies and Gibbs-free energies were computed at 298 K and 1 atm using the rigid rotor harmonic oscillator approximation and treating all internal degrees of freedoms as vibrations, i.e., not considering hindered internal rotors. They are compiled in Table S1 in the ESI. †

CO 2 adsorption onto Cu n + clusters
A typical mass spectrum resulting from the reaction of cationic copper clusters Cu n + (n = 7-25) with CO 2 is shown in Fig. 1.
We have found that production of Cu n + (n = 1-4) in the presence of only a helium carrier gas yields significant signals for n r 4; the production of larger Cu n + clusters is facilitated by admixing a few % of Ar into the helium carrier gas. Since Ar readily binds to Cu n + clusters, and especially so for the smaller clusters where the total charge is distributed over only a few atoms as was shown in our previous work, 50,60 a competition between complexation of Cu n + with Ar and CO 2 results in a rather complex mass spectrum, with substantial mass overlap for the smaller cluster sizes. This overlap prevents us from completely disentangling depletion and growth for n o 7. In the mass spectrum shown, we observe that Cu n + with 7 o n o 19 binds up to two CO 2 with appreciable efficiency, and only one for n 4 19. For the whole mass range, we observe no significant binding of Cu n + with Ar, indicating that binding of CO 2 is preferred here and that the binding energy thus likely exceeds the 0.2 eV found for Ar. 60 The inset shows two mass spectra zoomed into the region of the Cu 10 + cluster, where the isotopic distributions of Cu 10 + , [Cu 9 , 2CO 2 ] + , and [Cu 10 , CO 2 ] + are visible. Upon resonant IR irradiation at a frequency of 657 cm À1 , the distribution without IR light (top trace) changes such that the intensity of the [Cu 10 , CO 2 ] + distribution reduces, coinciding with an increase of the Cu 10 + bare cluster distribution, as indicated with boxes and arrows in the bottom trace. This is indicative of photoinduced loss of CO 2 via the reaction [Cu 10 , CO 2 ] + + kÁhn -Cu 10 + , with k an unknown number of IR photons. In Fig. 2 the IRMPD spectra for [Cu n , CO 2 ] + (n = 7-25) are displayed. Whereas the adsorption of CO 2 onto extended surfaces was shown either to lead to chemisorption or carbonate formation, depending on the surface morphology, 61 clusters provide often very diverse structural motifs, and it can therefore a priori not be predicted whether the binding motif of CO 2 will be similar for each cluster size. However, inspection of the spectra for different size n tells there are no significant differences. Although the signal-to-noise ratio gradually decreases with cluster size (a result of the decrease in production efficiency), it is evident that all spectra are very similar. We therefore discuss the spectrum of one cluster size in detail as a representative example for the other sizes. Cu 10 + is chosen because a) the Cu 10 + geometry is already known from our previous work on the spectroscopy of Cu n + ÁAr clusters, 62 and b) since a direct comparison between the spectrum of Cu 10 + ÁAr and [Cu 10 , CO 2 ] + may allow to determine whether the adsorption of CO 2 -be it dissociative adsorption, molecular chemisorption or physisorption -affects the structure of the cluster itself.   3 shows the IRMPD spectrum of [Cu 10 , CO 2 ] + in the 120-1600 cm À1 spectral range (panel A) together with the IR photodissociation spectrum of Cu 10 + ÁAr. 62 Additionally, calculated spectra for two possible geometries, one with molecularly adsorbed CO 2 (panel C) and one where one of the CQO bonds has been ruptured, and the eliminated O is separately adsorbed (panel D  62 This band broadening could be caused by the higher binding energy of CO 2 compared to that of Ar, but also by the larger pulse energies employed here. Nevertheless, the similarity between the spectra of the two complexes in the 120-350 cm À1 range strongly suggests that the cluster structure is not much affected by CO 2 adsorption.
Before considering the current spectrum further, it is useful to discuss the vibrational structure of free CO 2 in the gas phase. Free CO 2 has three fundamental modes: the symmetric and anti-symmetric stretch vibrations n 1 and n 3 , and the bending vibration n 2 . Due to the symmetry of CO 2 , only n 2 and n 3 are IR-active, and they have been experimentally observed at  667 cm À1 , and 2349 cm À1 , respectively. 63 The symmetric stretch is symmetry-forbidden in IR, but not in Raman spectroscopy.
Here, not one but two bands are found, at 1388 cm À1 and 1285 cm À1 , respectively. These bands are due to a Fermi resonance between n 1 and 2n 2 . 63 A rapid look at the experimental spectrum already indicates that the band at 650 cm À1 likely corresponds to the bending vibration of free CO 2 (667 cm À1 ). Further, the series of three bands at 1185, 1274 and 1378 cm À1 are all in the region where the IR-forbidden symmetric vibrations are expected, which become IR active due to the cluster breaking the symmetry. However, for intact CO 2 only two bands are expected, namely the two characteristic bands of the Fermi dyad. It is most likely that this dyad corresponds to the bands observed at 1274 and 1378 cm À1 for [Cu 10 , CO 2 ] + .
Thus, only the band at 1185 cm À1 remains. This band cannot be a CO 2 fundamental. It is also not an overtone of the bending vibration (667 cm À1 in free CO 2 ) since this is already part of the Fermi dyad. Another possibility, a combination between the bending mode and a cluster vibration can be ruled out as none of the conceivable combination bands would have a frequency exceeding 1000 cm À1 .
To seek a plausible explanation for the 1185 cm À1 band, we turn to DFT calculations. We did not do an extensive structure search, but rather limited ourselves to two possible structures, one with CO 2 attached molecularly, and one where one of the CO bonds has ruptured, leaving a carbonyl and a separate O atom. In both cases, we assumed that the Cu 10 + structure is the one found in experiments on Cu 10 + -Ar clusters. 62 We first discuss the physisorbed species, for which the spectrum is shown in Fig. 3C. The binding energy of CO 2 to Cu 10 + in this species amounts to a mere 0.26 eV, which is only a little more than the Ar binding energy of 0.17 eV. 60 Its calculated spectrum is dominated by a strong band at 645 cm À1 , which is associated with the OQCQO bending motion. The bands at lower frequencies are the cluster vibrations, with little involvement of the CO 2 ligand, or the vibrations involving the CO 2 -cluster bond (below 70 cm À1 ). The final bands are the modes associated with the CO 2 symmetric (1352 cm À1 ) and antisymmetric (2406 cm À1 ) stretching vibrations. Since this is a calculation in the harmonic approximation, a Fermi doublet caused by anharmonic couplings is not reproduced. The symmetric stretching mode at 1352 cm À1 is falling much closer to the higher two of the three bands in the 1100-1400 cm À1 spectral range, confirming that the 1274 and 1378 cm À1 experimental bands are indeed the Fermi dyad. Nevertheless, this species still does not provide a satisfactory explanation for the 1185 cm À1 band. Further trial structures of molecularly absorbed CO 2 on Cu 10 + , all within 0.1 eV from the minimum shown here, have near-identical vibrational frequencies.
An alternative structure conceivable is that of a dissociatively adsorbed CO 2 where a separate O atom is bound to several Cu atoms, and a carbonyl CO is bound on an on-top site. While the on-top binding is typical for late transition metal surfaces, it is energetically quite unfavorable with a formation energy of 1.4 eV higher than the physisorption complex, and thus unlikely given its endothermicity. Indeed, the calculated spectrum does not give reason to suspect the species in the experiment is this structure, for instance an intense band at 378 cm À1 is not detected. Thus, we find little reason to suspect the CO 2 molecule is adsorbed in any other way than the physisorption complex shown in Fig. 3C. What is then the cause of the band at 1185 cm À1 ? For this, we have to critically evaluate the IR excitation laser and the possible presence of higher harmonics. It is well-known that any free-electron laser contains spontaneously emitted radiation at higher harmonic wavelengths, see e.g., 64 and lasing was achieved early on at the third harmonic. 65 In contrast to odd harmonics, even harmonics have zero gain on the favored on-axis TEM 00 optical mode. However, the less favorable TEM 01 was demonstrated to have gain, and eventually lasing on the second harmonic was achieved at Jefferson Lab. 66 Overall, one can thus expect that the second harmonic is present, albeit at substantially reduced intensity when compared to the harmonic. Inspection using a grating spectrometer indeed confirms that there is second harmonic radiation present with an intensity of B1% of the fundamental, making the observation of bands of similar oscillator strength as the ones discussed above unlikely. However, the one fundamental band not discussed as it is seemingly out of the spectral range probed, the CO 2 anti-symmetric stretching vibration, has a much higher intensity than, e.g., the bending mode (predicted 1203 and 17.4 km mol À1 for the physisorbed complex shown in Fig. 3C, respectively), and can thus plausibly be observed if the intensity of the second harmonic radiation is no less than three orders of magnitude lower. Thus, we assign the observed band at 1185 cm À1 to the anti-symmetric CO 2 stretching mode, which thus has its band maximum at 2370 cm À1 . This is slightly lower than the 2406 cm À1 predicted for the physisorbed Cu 10 + -CO 2 complex, shown at half its frequency and 1/100 its calculated IR intensity by the green trace in Fig. 3C, but still altogether acceptable. Unfortunately, we are unable to verify this assignment experimentally with the FEL fundamental, since this is out of the spectral range covered by FELICE. Nevertheless, we can unambiguously conclude that the Cu 10 + -CO 2 reaction product adopts a physisorption complex. Given the similarity of all spectra shown in Fig. 2, we conclude that the intermediate size cationic Cu n + clusters all weakly bind CO 2 and no significant activation takes place. Panel E shows the spectrum recorded for [Cu 4 , CO 2 ] + using pure helium as carrier gas over the 600-1600 cm À1 spectral range. It essentially shows the same four bands as observed for [Cu 10 , CO 2 ] + . The band at 630 cm À1 is somewhat broader and shows a high-frequency shoulder. The calculated IR spectrum for the Cu 4 + ÁCO 2 physisorption complex shows the two CO 2 bending and symmetric stretch vibrations at near-identical frequencies as for Cu 10 + ÁCO 2 (panel C). In summary, like the larger Cu n + clusters, CO 2 adsorbs molecularly on Cu 4 + .

Co-adsorption of H 2 and CO 2 onto Cu n + clusters
To see whether co-adsorption of H 2 can activate CO 2 , we have examined the products formed upon reacting Cu n + (n = 4-7) with a gas mixture of H 2 and CO 2 . In the resulting mass spectrum, presented in Fig. 4, it is evident that apart from masses indicative for binding of the individual CO 2 and H 2 molecules, also co-adsorption complexes [Cu n , mCO 2 , pH 2 ] + , typically with m = 1,2 and p = 1-4, are formed. The ion intensity of the complexes formed upon the adsorption of a single H 2 molecule for n = 4 and 5 is much lower than that of the bare cluster, while for n = 6 and 7 it is the opposite. Complexes with p 4 1 are always much lower in intensity than complexes with a single H 2 adsorbed. For the sole adsorption of CO 2 , only the product [Cu 4 , CO 2 ] + is significantly higher in intensity than [Cu 4 , CO 2 , pH 2 ] + . For other complexes, the intensity of just CO 2 adsorbed on the cluster is lower than for the co- In contrast, CO 2 binds more strongly to Cu 4 + as also suggested by the intensity distribution of the measured mass channels.  Fig. 3E is reproduced. In that experiment, no higher-order complexes were present and, therefore, this spectrum does not suffer from ingrowth. This spectrum of [Cu 4 , CO 2 ] + obtained during the co-adsorption experiment is fairly similar to that from Fig. 3E, but there are some minor differences. The spectrum in green exhibits two additional lowintensity bands. The band attributed to the CO 2 bending vibration at 644 cm À1 gets a small shoulder at 704 cm À1 and the band at 1186 cm À1 probably originates from the  antisymmetric stretch of CO 2 probed with the second harmonic of FELICE. Similar bands were found in the data presented earlier in Fig. 2 for the Cu n + (n = 7-25). The [Cu 4 , CO 2 ] + spectrum obtained from the co-adsorption experiments also has an additional feature at 1573 cm À1 , but we interpret this as an artifact, just like the noisy (and in fact negative) signal just above 1600 cm À1 . Therefore, the reference spectrum seems more reliable and we conclude that CO 2 is bound to Cu 4 + in end-on configuration, in the same manner as on Cu n + (n = 7-25  50 To verify and rationalize this, we compare the experimental spectrum of [Cu 4 , CO 2 , H 2 ] + to calculated spectra of different isomers in Fig. 6. In the structure search, it was found that the majority of structures is based on the 2D rhombic geometry of the Cu 4 + cluster, which was found to be present in the molecular beam in complexes with Ar and H 2 . 50,62 The exception is formed by structure 4B, the second-lowest in energy, and the only one based on a pyramidal cluster structure. Low-energy structures are dominated by isomers where reduction of CO 2 has led to the formation of water or hydroxyl and CO; structure 4A, the lowest energy structure found, has a formate on the cluster. Only the sixth-lowest energy isomer 4F has an intact CO 2 . The energy of formation of 4F (À1.35 eV with respect to the reactants Cu 4 + , H 2 , and CO 2 ) is only 0.5 eV higher than that of 4A, suggesting CO 2 reduction is thermodynamically favored, but not by very much.
When comparing the experimental spectrum with theoretical spectra, it is evident that among the lowest energy structures 4B-E and 4G cannot be the dominant species in the molecular beam. The spectra of these structures all exhibit quite strong bands below 600 cm À1 for which no evidence is found in the experimental spectrum. Of the remaining structures, 4A can also be ruled out since it exhibits strong bands above 1500 cm À1 , while the highest frequency band on the experimental spectrum is at 1391 cm À1 . The experimental band at 641 cm À1 could be assigned to strong bands at 638, 640, or 652 cm À1 from 4I, 4J, or 4K, respectively, or to the low-intensity bands at 634 (4F) and 647 cm À1 (4H). Structure 4J appears to be ruled out due to a strong band predicted at 910 cm À1 , for which no experimental evidence is found. The band at 1391 cm À1 could be due to bands for 4F, 4H, 4I, and 4K (1372, 1307, 1361, and 1351 cm À1 ). A word of caution is in place here: these calculations are all done in the harmonic approximation, and inherently do not reproduce the CO 2 Fermi resonance, which is likely still present for isomers 4F, 4H, 4I, and 4K, and it could thus also be seen back in the bump Fig. 6 Experimental spectrum of [Cu 4 , CO 2 , H 2 ] + (top panel) compared to theoretical spectra of possible isomers. The calculated modes (black sticks) are complemented by a 20 cm À1 Gaussian convolution. The frequencies of calculated modes outside the spectral range probed (above 2100 cm À1 ) were divided by a factor of two and the intensities multiplied by 1% (green sticks) simulating the measurement with the second harmonic of FELICE. The energy relative to the free reactants of the corresponding structure is also shown.
at 1270 cm À1 . The experimental sideband of the strong 641 cm À1 resonance, centered at 713 cm À1 , appears most plausibly assigned to 4I's band predicted at 703 cm À1 . The 4I band at 1059 cm À1 could cause the experimental band at 1098 cm À1 . We cannot rule out 4K despite its band at 986 cm À1 , which could simply be too weak to detect. The experimental band at 1186 cm À1 could potentially originate from a FELICE second harmonic probing of the antisymmetric stretch of CO 2 in isomers 4I and 4K, predicted at 2418 and 2404 cm À1 , respectively.
All structures that could be responsible for the spectrum are formed by the reaction of rhombic Cu 4 + , which was found to be the most stable isomer, 62 with CO 2 and H 2 . In all cases, CO 2 is bound to the cluster in a linear end-on configuration, as was seen earlier for bare Cu n + clusters. The H 2 is either molecularly bound to the obtuse apex of the cluster with CO 2 bound to the same (structure 4K) or opposite Cu atom (4I), or dissociated on the obtuse apex and bound in-plane on bridge sites with CO 2 bound to the acute apex for 4F. All these configurations of H 2 are consistent with the previous work. 50 The presence of structure 4H is difficult to rule out or confirm: its principal bands are all consistent with the structure above 1000 cm À1 in the experimental spectrum.

Potential energy surface for the adsorption and activation reaction of CO 2 and H 2 on Cu 4 + clusters
To understand how the co-adsorption of CO 2 and H 2 proceeds and which products can be formed, the potential energy surface (PES) for this reaction is calculated and presented in Fig. 7, with the energies, ZPE corrected energies, enthalpies and Gibbs free energies in Table S1 (ESI †). The inclusion of the ZPE and the thermal effects in enthalpies play a relatively small role, while the entropy part is more important, especially when both CO 2 and H 2 are added to the cluster and the reactions progress. All structures included in the PES are numbered, the structures used for assignment of the [Cu 4 , CO 2 , H 2 ] + IRMPD spectrum in Fig. 6 are also labeled with the corresponding letters. First, the adsorption and dissociation of CO 2 over the bare cluster are evaluated in Fig. 7A. The entrance complex (2) is formed by linear CO 2 adsorbed on the obtuse apex of rhombic Cu 4 + , with a CO 2 binding energy of 0.54 eV. Adsorption on the acute apex (not shown) is only 0.08 eV higher in energy. Of all structures found, the entrance complex is thermodynamically the most favorable, followed by one (7, +0.09 eV) where CO 2 is dissociated, with CO attached to the acute apex of the still close to rhombic cluster, and the loose O on a hollow site. Although both structures are exothermic with respect to the reactants, for CO 2 to dissociate it has to overcome a barrier at +1.79 eV associated with transition state (TS3). The dissociation pathway involves a rearrangement of the cluster to allow the CO 2 molecule to bend, leading to the insertion of a Cu atom into the CQO bond in structure (4). This barrier is obviously too high to be overcome, as is experimentally evidenced above. In Fig. 7B, potential reaction paths for forming the coadsorption complexes are explored. If the entrance complex (2) reacts with the H 2 , a co-adsorption complex 4I, with intact H 2 adsorbed on the opposite obtuse apex of the cluster, can be formed barrierless as indicated by the blue route. This complex is more favorable than (2) by 0.46 eV. 4I can of course also be formed by first adsorbing H 2 , and then CO 2 (route indicated in black). Entrance complex 4I can further rearrange to the slightly less favorable (0.29 eV) structure 4K, also an entrance complex, by transfer of either H 2 or CO 2 over the short axis of the cluster so that both molecules are bound on the same obtuse apex. Structure 4K can likely also be directly formed by adsorption of H 2 onto structure (2), but it requires a bending of the CO 2 ligand, which may not be energetically more favourable than the formation from structure 4I, given it is relatively low barriers. The H 2 on 4K can dissociate by crossing transition state (TS13) at 0.74 eV with respect to 4K to form complex 4H. This reaction involves a compression-elongation-type interconversion of the horizontally oriented rhombus into a vertically oriented one, via a tetrahedron in TS13, again showing the cluster's dynamic nature. Although this barrier is the highest in this reaction path, it is only 0.04 eV higher than the energy of the reactants and might be overcome at room temperature. 4H has two H atoms on bridging sites, sharing the acute apex, with CO 2 in end-on configuration in-between. This configuration is thermodynamically more favorable than 4I by 0.07 eV. There is an alternative pathway to form 4H, but it requires H 2 dissociation before CO 2 adsorption. In the current calculations, the barrier towards dissociation is at least 0.58 eV above the energy of the reactants, making it difficult to see this as a viable pathway. However, this barrier was at the PBE/QZV4P level calculated to be only 0.15 eV, making the reaction much more plausible. In fact, structure (22) was one of the assigned species for the spectrum of H 2 adsorbed onto Cu 4 + . 50 To investigate this somewhat better, we benchmarked this barrier for the two functionals PBE, TPSSh with various (larger) basis sets and with CCSD(T) (ESI †). We find that the level of correlation and relativistic effects each lead to an error of B0.2 eV in the computed relative energies, and that the barrier height is very sensitive to the structures. Given the earlier assignment of (22) to a H 2 adsorption product of Cu 4 + , 50 we assume that this route is open in the current experiment, too. The adsorption of CO 2 onto structure (22) will directly lead to 4H, that onto structure 17 to 4F, at À1.35 eV the lowest energy structure in this PES.
To summarize: complexes 4H, 4I, 4K, and 4F, which are viable candidate structures for assignment of the experimental bands, can all be formed relatively easily. Each pathway leads to the formation of complexes with linear CO 2 bound in end-on configuration. Structures 4I and K are formed most easily, requiring no H 2 dissociation, whereas formation of structure 4H can proceed via several paths, which often requires the crossing of a relatively high, but not insurmountable, barrier. The energetically most feasible (black) route for 4H also allows the formation of structures 4I and 4K. Of these, the former is the most stable, and appears the most important candidate for assignment. The energetically most favorable structure, 4F, also requires dissociation (purple route).
The co-adsorption complexes discussed above (4F, I-K) could of course also lead to dissociation of CO 2 . However, if we assume that the corresponding barrier is similar to the one calculated for CO 2 on bare Cu 4 + (Fig. 7A), it can be expected that, even starting from the lowest energy structure 4F, the transition state lies around 1 eV higher than the reactants. Therefore, the energetic gain from the adsorption of H 2 is not enough to overcome this barrier, and dissociation of CO 2 will not be examined further.
In contrast, the barrier for CO 2 reduction to formate, which is energetically also more favorable than CO 2 dissociation, is almost isoenergetic with the reactants, making this route more plausible than dissociation. A reduction pathway starting from 4H is illustrated in Fig. 7C. Here, the CO 2 ligand leans over to one of the bridging H atoms, abstracting it to form HCOO (formate), which then rotates along the Cu-O-C bond to bind via the second O atom in a Z 2 bidentate configuration to Cu 4 + .
An additional minimum and transition state were located on the potential energy surface (see Fig. S11 in the ESI †), however the minimum is shallow and thus expected to play a negligible role in the reaction. Since many routes in Fig. 7B lead to the formation of 4H, it acts as a 'gateway' structure for the formation of formate. Although we can rule out CO 2 reduction as the dominant pathway in the current experiments, the pathway calculated suggests it is not entirely out of reach. While the decreased entropy of the formate adduct compared to the free reactants has certainly an adverse effect, its Gibbsfree energy is still negative (see Table S1 in the ESI †), so its formation is thermodynamically allowed at 298 K. Thus, we can speculate that its formation under thermalized conditions in an ion trap only requires moderate temperatures. Because several computational studies of CO 2 hydrogenation to methanol over Cu clusters suggest that the methanol formation proceeds via formate, 11,48,49 this opens up the possibility to complete a full catalytic cycle over Cu 4 + .
IR spectroscopy of [Cu n , CO 2 ,H 2 ] + (n = 5-7) The experimental spectra for the co-adsorption of CO 2 and H 2 onto Cu n + (n = 5-7) are presented in Fig. 8  1068, 1118, and 1335 cm À1 in the spectrum of the coadsorption product; other bands visible in the [Cu 5 , H 2 ] + spectrum are likely hidden in the shoulders of the strong CO 2 bands. Interestingly, a new potential band is observed for the co-adsorption product around 1640 cm À1 . This band is absent in the experimental spectra of the individual complexes or in the calculated spectra of complexes with H 2 . This might be indicative of a reaction between CO 2 and H 2 on the cluster surface, but we are unable to assign this band without calculated structures. Nevertheless, based on a comparison between experimental spectra alone, it is clear that the spectrum is dominated by the vibrations of both molecularly and dissociatively chemisorbed H 2 together with CO 2 adsorbed in the end-on configuration as it is found for Cu 4 + .  Fig. 6.
The green trace on the [Cu 7 , CO 2 ] + spectrum is the reference spectrum from Fig. 3 obtained during individual CO 2 adsorption experiments.
hidden in the elevated baseline of overlapping bands. The exception is formed by the band at 1453 cm À1 in [Cu 6 , H 2 ] + spectrum, which is absent in the co-adsorption spectrum or shifted by more than 50 cm À1 forming the shoulder of an asymmetric band at 1377 cm À1 . The origin of this band in the [Cu 6 , H 2 ] + spectrum is still unclear, and even after an extensive search no structure was found that could explain it. 50 Nevertheless, we conclude that Cu 6 + binds CO 2 in end-on configuration with H 2 co-adsorbed. Finally, the spectrum for [Cu 7 , CO 2 , H 2 ] + is compared to its counterparts in Fig. 8 (right panels). The spectrum of the coadsorption product is better resolved than those for [Cu n , CO 2 , H 2 ] + (n = [4][5][6], showing bands at 646, 766, 1117, 1182, 1264 and 1377 cm À1 . The band at 1377 cm À1 has shoulders peaking at 1402 and 1444 cm À1 . The spectrum for [Cu 7 , CO 2 ] + is in good agreement with the spectrum presented in Fig. 2, reproduced as a green trace in Fig. 8, and shows bands that are probably the same as the band 646, 1264 and 1377 cm À1 observed for [Cu 7 , CO 2 , H 2 ] + . The strongest band for [Cu 7 , H 2 ] + at 784 cm À1 , can be linked to the 766 cm À1 band for [Cu 7 , CO 2 , H 2 ] + , slightly shifted but still clearly visible. The same is valid for the 1135 and 1488 cm À1 bands of [Cu 7 , H 2 ] + , which correspond to a band at 1117 cm À1 and a shoulder of the 1377 cm À1 band for [Cu 7 , CO 2 , H 2 ] + . The [Cu 7 , H 2 ] + bands at 1255 and 1386 cm À1 lie fairly close to the Fermi dyad of CO 2 and therefore probably overlap. The only unexplained low-intensity bands in the [Cu 7 , CO 2 , H 2 ] + spectrum are found at 1182 and potentially at 1622 cm À1 . We speculate that the band at 1182 cm À1 is caused by the antisymmetric stretch of CO 2 excited by the second harmonic of FELICE (found at 1185 cm À1 in Fig. 3). We have no clear explanation for the 1622 cm À1 band, but due to its weakness, we do not regard this as crucial. We conclude again that CO 2 binds only weakly to Cu n + clusters (n = 4-7), even when H 2 is co-adsorbed.

Conclusion
We have recorded experimental IRMPD spectra for the products resulting from reacting Cu n + (n = 4-7) clusters with CO 2 , and with CO 2 and H 2 simultaneously. The spectra of the clusters with only CO 2 adsorbed are indicative for simple physisorption of the CO 2 molecule in an end-on configuration, leaving the CO 2 fundamental vibrations largely unchanged. This is in agreement with DFT calculations, which predict the activation of CO 2 by cationic clusters is hindered by a barrier of at least 2.33 eV relative to the energies of the reactants. This inactivity of Cu n + cations towards CO 2 is also consistent with previous calculations, suggesting that CO 2 only gets activated by a significant amount of charge transfer that goes hand in hand with stronger bonding. When both H 2 and CO 2 co-adsorb onto the clusters, CO 2 activation is not achieved either. No size-dependent effects have been observed in the binding of CO 2 to either bare and H 2 preloaded clusters. On the other hand, co-adsorption of CO 2 does not affect the cluster size dependence of H 2 adsorption as identified in ref. 50. DFT calculations of the reaction pathway for CO 2 reduction over Cu 4 + in which dissociative adsorption of H 2 leads to H(a) being formed that could react with CO 2 after migration from its absorption site on the cluster, thereby following a Langmuir-Hinshelwood type mechanism. The transition states along this reaction path are only slightly higher than the energy of the reactants, but the barriers might be in the order of 1 eV. This suggests that, although CO 2 reduction under the current experimental conditions may not be feasible or dominant, it could be observed at only slightly higher temperatures and longer reaction times that can be provided by an ion trap. If such experiments would be successful, a study of the efficiency of CO 2 reduction on more complex cluster materials could provide an understanding of e.g., the promotor materials in the real catalyst.

Conflicts of interest
There are no conflicts to declare.