Infrared multiple photon dissociation spectroscopy of anionic copper formate clusters Coulomb explosion imaging for gas-phase molecular structure determination: An ab initio trajectory simulation study

We investigate the structure of copper formate and deuterated copper formate clusters using infrared multiple photon dissociation in combination with quantum chemical calculations. Symmetric and asymmetric C–O stretching vibrations along with C–H/C–D stretching vibrations were characterized. Fermi interactions between the C–H stretch and likely a C–O combination band and/or the overtone of a C–H in-plane bending motion have been confirmed by deuteration. The spectra reveal a strong dependence on the monodentate or bidentate binding motif of the formate ligands. Many minima are energetically accessible on the potential energy surface through rotation of the monodentate formate ligands into several almost isoenergetic local minima. While the C–H/C–D stretching vibration is heavily influenced by the charge distribution in the cluster, the C–O vibrations are largely unaffected. The C–H stretch region is not very diagnostic due to a variety of possible Fermi resonances, which also depend on the charge distribution at the formate ligand. Deuteration yields unperturbed spectra in the C–D stretch region and reveals characteristic shifts of the C–D stretching mode for the different binding motifs, with a strong dependence of the band position on the oxidation state of the copper center. The observed bands are compared with formate adsorbed on copper surfaces from the literature.


INTRODUCTION
The mechanisms behind the efficient activation of the rather inert CO 2 molecule have become an increasingly large research field. 1 In electrochemical routes, the reactive radical anion CO 2 − plays a key role, and gas phase experiments showed that it readily forms C-C bonds. [2][3][4][5][6] The radical is formed via reductive charge transfer from a transition metal center and is efficiently stabilized by solvation. [7][8][9] The underlying mechanisms are extensively investigated on an atomistic level by a combination of gas phase experiments and theory. [10][11][12][13][14][15][16][17][18][19][20] Detailed spectroscopic and structural data are available for hydrated and metal-bound CO 2 − structures. [21][22][23][24][25][26][27][28][29][30][31][32][33][34] A practical approach to CO 2 activation in power-to-fuel applications focuses on the hydrogenation through formation of a C-H bond, leading toward formic acid, methanol, or dimethyl ether. [35][36][37][38] Especially, formic acid along with the formate intermediate gained attention for large scale hydrogen storage applications under mild conditions [39][40][41] while providing the simplest form of stable, activated CO 2 . Gas phase experiments investigated the selective decomposition of formic acid using coinage metals along with how to translate these approaches into zeolites or metal organic frameworks. [42][43][44][45] Furthermore, it was shown that copper hydrides are capable of reacting with formates without significant energetic barriers. [46][47][48] We demonstrated recently that the direct formation of formic acid after initial decarboxylation on the copper formate anion Cu(II) 2 (HCO 2 )5 − via a proton-coupled electron transfer is the dominant decomposition step, while the Cu(II)(HCO 2 ) 3 − species can eliminate formic acid via a hydrogen atom transfer. 49,50 In industry-scale methanol synthesis, the formate anion is an important intermediate, and a key role is played by a copper based catalyst. [51][52][53] In model studies, a large cluster-size dependence was revealed through size-selective cluster deposition. 54,55 The copper centers act as a reducing agent and are also applied for the reduction of nitrogen and sulfur oxides or within carboxylation reactions. [56][57][58][59][60][61] It was shown in the gas phase that a single copper oxide cation transforms methane to methanol. 62 The electronic structure of copper compounds was investigated for CuO + and copper nitrate as well as copper formate in the gas phase, [63][64][65][66][67] while small, neutral copper clusters were investigated embedded in a neon matrice. [68][69][70] For bulk copper formate, there is disagreement in the literature regarding the assignment of the reported bands, involving overtones, combination bands, and even the crystal lattice contributions as interpretation. [71][72][73][74][75] In particular, the vibrational signature of the C-H bond, which is crucial for CO 2 activation, is not well understood. In spectroscopy experiments of formate adsorbed on Cu(110) or copper-based catalyst surfaces, bands in the C-H stretch region have been assigned to the combination band of the asymmetric C-O stretch with the C-H in-plane bend. [76][77][78][79][80] However, it has been noted previously that vibrations caused by the C-H modes of other species lie close and make a definitive assignment difficult. 76,80,81 To gain detailed insight into the microscopic interactions here, small atomically defined cluster ions in the gas phase provide suitable model systems as they can be irradiated for rather long times and sensitively analyzed using Infrared Multiple Photon Dissociation (IRMPD) spectroscopy. [82][83][84] The structure of the formate anion itself was recently investigated in detail theoretically 85 and experimentally, 86 solvated with water 87 or as a proton-bound formate dimer. 88 The well-defined gas phase experiments clearly revealed the peculiar features especially in the C-H stretch region arising due to Fermi resonances with the overtone of the in-plane C-H bending mode in addition to C-O combination bands, 86 contrasting some previous interpretations. [89][90][91] However, in combination with a transition metal, the bands of the formate ligands are heavily shifted compared to the isolated molecule, potentially leading to different interactions, and a severe effect on the strength and positions of Fermi resonances must be expected.
In the present study, a molecular view on the catalytically important combination of copper centers with formate ligands is obtained and compared to the adsorbed species on copper surfaces. We present Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometry experiments in combination with IRMPD spectroscopy and quantum chemical calculations of mass-selected Cu(II)m(HCO 2 ) 2m+1 − (m = 1, 2, 3) and Cu(I)n(HCO 2 ) n+1 − (n = 1, 2) cluster anions along with their deuterated analogs in the gas-phase to characterize the structure and spectroscopic properties of these nanoparticles.

EXPERIMENTAL AND COMPUTATIONAL METHODS
Isotopically enriched copper formate cluster anions are formed from solution by electrospray ionization (ESI) and introduced into a 9.4 T FT-ICR mass spectrometer, as described before. 50 For the deuterated clusters, formic acid-d of 98% purity is used (Sigma Aldrich) for the preparation of the copper formate solution. Three separate optical setups are used to investigate the mass selected clusters across a broad wavenumber range. In the range of 800 cm −1 -1400 cm −1 and 1400 cm −1 -2235 cm −1 , ZnSe optics and CaF optics are used, respectively, with an EKSPLA NT273-XIR tunable OPO laser system. For the range of 2235 cm −1 -4000 cm −1 , an EKSPLA NT277 tunable OPO laser system again with CaF optics was used. 92 The IRMPD irradiation time was varied for the best compromise between fragment intensity and avoiding saturation effects (see Table S1 of the supplementary material for the irradiation time in each case). For the evaluation of the experimental data, the IRMPD yield is calculated as the sum of the photofragment intensities divided by the sum of the photofragment plus precursor intensities corrected for decomposition caused by BIRD and collisions, divided by the calibrated wavelength-dependent laser power. 21,93,94 The maximum yield for each absorption range is normalized to 100.
For the quantum chemical modeling, the density functional theory (DFT) method B3LYP/aug-cc-pVDZ is used based on spectrum benchmarking (see Tables S2-S5 of the supplementary  material for details). Several conformers were considered, and only the energetically most favorable ones are shown. Frequencies were scaled by a factor of 0.985. The wave functions were tested for stability and all given energy differences are zero-point corrected. Gaussian Fig. 1, together with modeled spectra for the four energetically most favorable conformers. All structures exhibit a monodentate binding motif for both formate ligands, lie energetically close to each other (within 10 kJ/mol), and are interconvertible via internal rotations of the formate ligand.
The absorption band at about 1302 cm −1 is assigned as the symmetric C-O vibration, in agreement with the calculated transition at 1298 cm −1 for the energetically most stable structure. The band broadening arises due to the presence of several energetically lowlying conformers. Upon deuteration, the measured symmetric C-O stretch is shifted by 15 cm −1 to around 1287 cm −1 , and the calculated shift is 16 cm −1 . A few data points indicate a weak absorption at around 1368 cm −1 , which vanishes upon deuteration. It is difficult to distinguish it from noise due to the very low IRMPD yield, BIRD effects, and background collisions under the long irradiation time of 20 s. However, it would fit well to the in-plane C-H bending mode calculated to lie between 1356 cm −1 and 1367 cm −1 , depending on the conformer.
In the 1400 cm −1 -1700 cm −1 range, intense absorption bands are observed, with the maximum at 1644 cm −1 shifting to 1631 cm −1 upon deuteration. The band is assigned as the intense asymmetric C-O vibration, predicted computationally at 1649 cm −1 with the vibration shifting to 1640 cm −1 upon deuteration. A clear band structure with two pronounced maxima is observed, which arises from splitting by in and out of phase vibration of the two ligands in addition to the presence of several minima on the potential energy surface. A weaker but still intense band can be identified for the deuterated species at 1643 cm −1 .
From 1700 cm −1 to 2235 cm −1 , a weak absorption can be found for the deuterated species at 2055 cm −1 , which is not observed in the spectra of Cu(I)(HCO 2 ) 2 − . This is assigned to the C-D stretching absorption calculated at 2068 cm −1 .
Above 2235 cm −1 , three intense bands are found at 2610 cm −1 , 2676 cm −1 , and 2762 cm −1 with an irradiation time of only 2.5 s. Irradiation for 20 s reveals weak absorption bands of Cu(I)(HCO 2 ) 2 − at about 2952 cm −1 and 3005 cm −1 . It is striking that the band corresponding to C-H vibrations, which is expected as a counterpart to the experimentally measured C-D vibration at 2055 cm −1 , seems to be missing. Calculations predict it at 2811 cm −1 . Instead, several strong peaks are observed in this range. In addition, the deuterated spectrum also features a single band at 2923 cm −1 , which shows that not only C-H vibrations or combination bands with C-H bending are present in this region.
Let us first discuss the bands at 2920 cm −1 -3025 cm −1 . Adding the two intense, previously discussed symmetric and asymmetric C-O vibrations yields 2946 cm −1 and 2918 cm −1 for Cu(I)(HCO 2 ) 2 − and Cu(I)(DCO 2 ) 2 − , respectively. This C-O combination band fits well to the observed bands at 2952 cm −1 and 2923 cm −1 for these two species and is also reproduced by adding the harmonic frequencies from our calculations that predict 2947 cm −1 and 2922 cm −1 , respectively. We thus assign this feature to the C-O combination band of the symmetric and asymmetric stretching modes. An additional weak absorption feature at 3005 cm −1 in Cu(I)(HCO 2 ) 2 − potentially arises from a C-O combination band as well, which may merge upon deuteration with the band at 2920 cm −1 due to the slightly different interaction. A similar situation was observed in the case of the Ar-tagged isolated formate anion where the band is assigned to a C-O combination band at 2928 cm −1 with a second peak at ∼2952 cm −1 with a slightly higher wavenumber. 86 In the carbon dioxide molecule, a C-O combination band is also observed at about 3675 cm −1 with four distinguishable absorptions in the neutral species 96 and at 2895 cm −1 for the anionic species. 97 An alternative explanation is a combination of the C-H in-plane bending at about 1368 cm −1 with the asymmetric C-O stretching mode at 1644 cm −1 . Now, let us analyze the three observed bands of Cu(I)(HCO 2 ) 2 − at 2550 cm −1 -2800 cm −1 . Contrary to the spectrum of the deuterated ion, three bands in the C-H region are observed, shifted to the red from the calculated C-H transition position. The band structure arises from Fermi resonances: The energetically most favorable conformer of Cu(I)(HCO 2 ) 2 − belongs to the C 2h symmetry group with the copper atom as an inversion center. The IR-active, fundamental C-H stretching mode exhibits Bu symmetry, as well as the combination bands of symmetric and asymmetric C-O vibrations. Therefore, a Fermi resonance is allowed. Both vibrations are located in the same area of the molecule and have similar transition energies (calculated as 2811 cm −1 for the fundamental C-H stretch and about 2950 cm −1 for the C-O combination band in harmonic approximation). An interaction between the C-H stretch and the two distinguishable C-O combination bands can therefore explain two of the observed absorptions between 2550 cm −1 and 2775 cm −1 .
Additionally, the overtone of the in-plane C-H bending can be expected in the region (with twice the fundamental vibration calculated as 2712 cm −1 without considering anharmonic effects). However, the fundamental IR-active C-H bending has Bu symmetry, the overtone exhibits Ag symmetry, and a Fermi resonance between the C-H in-plane bend overtone and C-H stretch is therefore symmetry forbidden. For other conformers of Cs or C 2 symmetry group, the symmetry requirements of Fermi resonances are fulfilled with some overtones and combination bands of the inplane C-H bending exhibiting the same symmetry as the fundamental C-H stretching vibration, explaining the low-intensity band at 2550 cm −1 -2650 cm −1 .
To rule out the possibility that our calculations do not describe the C-H interaction properly, we benchmarked them against The Journal of Chemical Physics ARTICLE scitation.org/journal/jcp higher-level methods and larger basis sets, all predicting a very similar position of the C-H vibration for all included minima on the potential energy surface (see Tables S2-S4 in the supplementary  material). At the same time, there was only one experimentally measured C-D vibration band upon deuteration. According to calculations, several combination bands are plausible in the formate ion. 85 However, they all should exhibit very low IR intensities compared to the fundamental C-O and C-H stretching vibrations in the copper formate system. Therefore, Fermi resonances must be invoked to explain the series of strong absorptions, which are observed in our experiment. This is in line with the assignment of the spectrum of the argon-tagged isolated formate anion, 86 which is reported to exhibit Fermi resonances from the interaction of the in-plane C-H bending overtone at about 2675 cm −1 with the fundamental C-H vibration at 2449 cm −1 , similar to earlier studies in solution. 91,98,99 With the addition of the copper center, the fundamental C-H vibration is shifted significantly closer to the C-O combination bands. The two formate ligands with the copper center enable several different combination bands within the same symmetry group as the fundamental C-H vibration, allowing for a more complex Fermi interaction. Additional peaks within the C-H region can be expected for Cu(I)(HCO 2 ) 2 − compared to the known Fermi resonances in the isolated formate anion. Surplus bands in the C-H region arising from Fermi resonances are also well-known from studies involving absorbed formate on copper containing surfaces, with the Fermi resonance assigned as the C-H stretch interacting with the combination band of an asymmetric C-O stretch vibration and the C-H bend. [76][77][78][79][80] This interaction seems less likely than the assignment of a Fermi interaction with symmetric plus asymmetric C-O combination band as the combination band consisting of the symmetric plus asymmetric C-O stretch lies closer in energy to the fundamental C-H stretch while exhibiting a higher intensity. Furthermore, other vibrations in this energy range have previously been reported, 80 turning assignment for surface-adsorbed structures difficult. − , respectively, in range of the expected C-H stretching bands at ∼2845 cm −1 and 2949 cm −1 for the monodentate and bidentate ligands, respectively. This is considerably closer than for Cu(I)(HCO 2 ) 2 − . The lowest energy conformer of Cu(II)(HCO 2 ) 3 − exhibits C 2 symmetry with the fundamental C-H stretch exhibiting A or B symmetry for the monodentate ligands and B symmetry for the bidentate ligand. This enables a Fermi interaction on the monodentate ligands with the C-O combination band exhibiting A symmetry. Furthermore, the C-H in-plane bending overtone of the monodentate ligands exhibits A symmetry and can be expected in this range with the harmonic, doubled fundamental frequency at about 2690 cm −1 , enabling further Fermi interactions. Some of the accessible conformers have lower symmetry, which then results in even more Fermi mixing possibilities. Therefore, many intense absorptions can be expected in the C-H stretch region.
Cu(II) 2 (HCO 2 ) 5 − and Cu(II) 2 (DCO 2 ) 5 − Next, we investigated how the formate ligands interact with multiple copper centers. The experimental and calculated IR spectra of Cu(II) 2 (HCO 2 )5 − and Cu(II) 2 (DCO 2 )5 − clusters are shown in Fig. 3, while the spectra of Cu(II) 3 (HCO 2 )7 − and Cu(II) 3 (DCO 2 )7 − are depicted in Fig. S1 of the supplementary material. Absorption bands are observed in the same regions as for the smaller clusters, but the bands exhibit significantly different intensity patterns. Quantum chemical calculations show that a structure with three bridging and two monodentate formate ligands is preferred in the case of Cu(II) 2 (HCO 2 )5 − with the number of bridging ligands further increasing in Cu(II) 3 (HCO 2 )7 − . Several conformers lie within 16 kJ/mol.
For Cu(II) 2 (HCO 2 )5 − and Cu(II) 2 (DCO 2 )5 − , two absorption bands are located at 1309 cm −1 and 1370 cm −1 , shifting to 1308 cm −1 and 1342 cm −1 , respectively, upon deuteration. The observed bands lie close to the ones in Cu(II)(HCO 2 ) 3 − , showing that the bridging and bidentate binding motifs exhibit similar spectroscopic signatures. However, the maximum in the IRMPD yield itself changes to the higher energy band at 1370 cm −1 , corresponding to the symmetric C-O stretching of the bridging ligands in Cu(II) 2 (HCO 2 )5 − . The relative intensity of the symmetric C-O stretch bands correlates nicely with the number of monodentate and bridging ligands in Cu(II) 2 (HCO 2 )5 − and Cu(II) 3 (HCO 2 )7 − (see Fig. S1). According to theoretical calculations of Cu(II) 2 (HCO 2 )5 − , the symmetric C-O stretching vibrations partially mix with the C-H in-plane bending mode, predicting them at 1299 cm −1 for the monodentate ligand, 1351 cm −1 -1353 cm −1 for the two equivalent bridging ligands, and 1363 cm −1 for the third bridging ligand. These vibrations shift to 1298 cm −1 , 1328 cm −1 , and 1337 cm −1 , respectively, upon deuteration, consistent with the experimental shift of 1 cm −1 and 28 cm −1 for the mono-and bidentate ligands, respectively.
In the range of 1550 cm −1 -1700 cm −1 , a broad band can be observed with a maximum at 1660 cm −1 , corresponding to the asymmetric C-O stretching vibrations. Upon deuteration, the relative intensities change. Calculations show that the asymmetric C-O vibrations of monodentate and bridging ligands partially mix, and their positions at 1569 cm −1 -1666 cm −1 for the most favorable structure shift slightly to 1567 cm −1 -1664 cm −1 upon deuteration.
For Cu(II) 2 (DCO 2 )5 − , a band can be observed at 2141 cm −1 with a second band at 2119 cm −1 emerging in the left flank of the peak, corresponding to calculated C-D vibrations at 2134 cm −1 , 2166 cm −1 , and 2180 cm −1 for the two monodentate, the two equivalent bridging, and the third bridging ligand, respectively. Due to isomeric and thermal broadening, only the contribution of the monodentate ligands is distinguishable. of Chemical Physics In the C-H stretching region, multiple bands can be observed again with the most intense ones at 2724 cm −1 , 2812 cm −1 -2894 cm −1 , and 2922 cm −1 with another relatively intense band at 2948 cm −1 in the right flank of the latter. Upon deuteration, only a single peak remains at 2909 cm −1 , while calculations in harmonic approximation again suggest only C-H vibrations in this region. Similar to the previous case of Cu(II)(DCO 2 ) 3 − , the observed vibration of Cu(II) 2 (DCO 2 )5 − at 2909 cm −1 is consistent with a combination of the calculated symmetric and asymmetric C-O stretching bands at 2909 cm −1 (1298 + 1611), 2903 cm −1 (1328 + 1575), and 2904 cm −1 (1337 + 1567) for the monodentate, the two equivalent bridging, and the third bridging formate ligand, respectively, with the combined intensity favoring the monodentate ligands combination band. In the case of Cu(II) 2 (HCO 2 )5 − , the corresponding combination bands are calculated at 2920 cm −1 (1299 + 1621), 2929 cm −1 (1353 + 1576), and 2932 cm −1 (1363 + 1569) on the monodentate, the two equivalent bridging, and the third bridging ligands, respectively. This would be consistent with the measured band of Cu(II) 2 (HCO 2 )5 − at 2922 cm −1 . Furthermore, calculations suggest a potential overtone of the C-H in-plane bending motion in this region with the doubled fundamental frequency at 2727 cm −1 (without anharmonic effects), fitting well to the experimental band at 2724 cm −1 . However, this overtone vibration has a very weak IR intensity, which suggests that some Fermi mixing still takes place as discussed above. This is in line with the observation that none of the features can directly be assigned to the C-H stretching modes of Cu(II) 2 (HCO 2 )5 − . While the energetically lowest lying structure of Cu(II) 2

Sequential fragmentation during IRMPD
The branching ratios of the observed fragments in the C-H stretch region exhibit a pronounced frequency dependence, which provides additional insight into the nature of the absorption. The color coded calculated transition intensities I H and I D for the four conformers along with their structures for ions with hydrogen and deuterium, respectively; "m" and "br" stands for monodentate and bridging ligands between two copper centers with a bidentate binding motif, respectively [level of theory-B3LYP/aug-cc-pVDZ and a scaling factor of 0.985; relative energy is shown for Cu(I) 2 (HCO 2 ) 3 − , transition intensity scaled for convenience]. different fragmentation channels, we recorded mass spectra with Cu(II)(HCO 2 ) 3 − as the precursor for different irradiation times at 2783 cm −1 (Fig. S3). The mass spectra depending on the irradiation time clearly reveal the following sequential reactions: This observation agrees with the fragmentation sequence of the Cu(II)(HCO 2 ) 3 − anion in our previous study on fragmentation upon irradiating the asymmetric C-O stretching vibrations. 50 Within the spectra in Fig. 5, we can observe that the individual fragment yield of Cu(II)(HCO 2 ) 3 − exhibits maxima in the IRMPD yield at different energies. Therefore, the initial fragment of reaction (1) can sequentially decompose if the reactant of reaction (2) [also afterward reaction (3)] absorbs photons at the corresponding wavelength. At 2825 cm −1 , Cu(II)(HCO 2 ) 3 − yields almost exclusively Cu(II)(HCO 2 ) 2 H − with its intensity rapidly declining upon decreasing wave numbers under 2810 cm −1 where Cu(II)(HCO 2 ) 2 H − absorbs further photons. Furthermore, the formation of Cu(II)(HCO 2 )H − only occurs at the low energy flank of the band below 2790 cm −1 , reflecting the redshifted absorption of its precursor, Cu(I)(HCO 2 ) 2 − . This is consistent with the directly observed absorption maximum of Cu(I)(HCO 2 ) 2 − at 2762 cm −1 in Fig. 1.
A similar behavior can be found in the intense bands of Cu(I) 2 (HCO 2 ) 3 − in Fig. S2. Here, sequential decarboxylation up to Cu(I) 2 H 3 − can be observed, as also discussed previously. 49 The spectra reveal that the sequential fragmentation of the products is slightly redshifted within the most intense band at 2787 cm −1 after each decarboxylation step. This result suggests a redshift of the C-H stretching vibration for mixed copper hydride formate clusters compared to pure copper formate clusters, likely caused by a different charge distribution with hydride ligands carrying a lower nominal negative charge than formate anions. The activation of the C-H bonds is highly influenced by the charge distribution across the cluster.

Fingerprint of formate ligands on copper centers
Finally, we compare all observed bands with previous work on the isolated, argon-tagged formate anion in the gas phase and formate adsorbed on copper containing surfaces in Table I. As one might expect, the vibrations of the argon-tagged formate anion in the gas phase are significantly different, especially for the C-H vibrations, making the comparison difficult. However, our results correspond closely to the bands observed with formate adsorbed on copper containing surfaces. The symmetric C-O stretch of the monodentate ligand lies between 1275 cm −1 and 1309 cm −1 for the clusters, and the only reported value for a Cu(110) surface 76 lies a little below at 1266 cm −1 . This absorption is blue-shifted to 1354 cm −1 -1374 cm −1 in the clusters if both oxygen atoms of the formate ion interact with copper atoms, either in a bridging fashion or as a bidentate ligand of a single Cu(II) center. Again, the corresponding literature values [76][77][78][79][80] for bridging formate on surfaces lie with 1350 cm −1 -1358 cm −1 slightly lower. In most cases, the in-plane C-H bending mode overlaps with the symmetric C-O stretching mode, although at lower intensity in an overall weak band.
The asymmetric C-O stretching mode is observed as a strong band, covering a wide range of 1632 cm −1 -1678 cm −1 for monodentate coordination, which encloses the literature value of 1640 cm −1 -1670 cm −1 for Cu(110). 76 It undergoes a redshift upon switching to bridging coordination, with absorptions observed in the range 1565 cm −1 -1629 cm −1 . For the bridging coordination, literature values are available for formate adsorbed at Cu(II)/SiO 2 surfaces, 79,80 with 1550 cm −1 and 1580 cm −1 at slightly lower values than for the clusters.
The Fermi resonances involving the C-H stretch range lead to strong bands observed at 2610 cm −1 -2954 cm −1 in the clusters, while assignments on surfaces are limited to the region of 2848 cm −1 -2978 cm −1 . [76][77][78][79][80] The weak C-O combination bands are observed in the clusters or for argon tagged formate in the gas phase. For copper formate clusters, they are observed at 2922 cm −1 -3005 cm −1 . Their assignment is helped by deuteration, which leads to a sizable redshift of the combination bands to the range 2909 cm −1 -2936 cm −1 . Deuteration also allows for the observation of the unperturbed C-D stretching mode, which is quite sensitive to the coordination mode of the formate ligand and the charge distribution in the cluster, ranging from 2055 cm −1 to 2148 cm −1 .
The features in the C-H stretch region are difficult to assign due to many possibilities for Fermi interactions and C-O combination bands, yielding a wide range of peaks in this region. Furthermore, the Fermi interactions with the C-H stretch vibration are highly dependent on the partial charge on the formate ligand, which can significantly shift the C-H frequency, as directly observed with the C-D stretching mode. Therefore, this region is not diagnostic and it might be problematic to simply assign two peaks in a spectrum by comparison with the previously studied copper formate systems, e.g., as the combination band of an asymmetric C-O stretch vibration with a C-H wagging motion. [76][77][78][79][80] Our experiments emphasize that many vibrations in this energy range, which have previously been reported, 80 could very well be induced by copper formate species. To use the C-H/D stretching mode for diagnostic purposes, deuteration of the formate ligand is indispensable. Deuteration separates the fundamental C-D band from the combination bands, removes the Fermi interactions, and considerably simplifies the spectrum.

CONCLUSIONS
We investigated the structure and vibrations of copper formate clusters using IRMPD in combination with quantum chemical calculations. We observed symmetric and asymmetric C-O stretching vibrations. The symmetric C-O stretching region exhibits two well-separated bands depending on the bidentate or monodentate binding motif of the formate ligand with the symmetric vibrations partially mixing with the in-plane C-H bending motion. The substructure of the bands can be attributed to the presence of several minima on the potential energy surface. Through rotation of the monodentate formate ligands, many conformers with slightly shifted frequencies are energetically accessible within the experimental conditions. Additionally, many absorption bands were observed in the C-H stretching region. Upon deuteration, the C-O vibrations are slightly shifted, in agreement with calculations, clear C-D stretching vibrations emerge, and a C-O combination band in the C-H stretch region remains, with all other vibrations vanishing. The broad features in the C-H stretch range are attributed to complex Fermi mixing, likely with the C-O combination band of the formate ligands and the C-H in-plane overtone, but other possibilities are available. While the C-O vibrations are relatively unaffected by the cluster size and the oxidation state of the copper center, the position of the C-H stretch fundamental heavily shifts, depending on the charge distribution in the cluster. This is further evidenced by the shifting of the sequential fragmentation in the C-H stretching region after decarboxylation of one formate to a hydride ligand. This shift fundamentally affects the complex Fermi interactions observed in the C-H stretch region, emphasizing the need for deuteration to gain a clear, diagnostic spectral feature of this mode.

SUPPLEMENTARY MATERIAL
See the supplementary material for additional data in the form of figures and tables supporting the conclusions of the article along with xyz coordinates of the calculated structures.

ACKNOWLEDGMENTS
This work was supported by the Austrian Science Fund FWF (Project No. P28896). The computational results presented were achieved using the HPC infrastructure LEO of the University of Innsbruck. The tunable OPO systems are part of the Innsbruck Laser Core Facility, financed by the Austrian Federal Ministry of Education, Science and Research.

DATA AVAILABILITY
The data that support the findings of this study are available within the article and its supplementary material.