CO2/O2 Exchange in Magnesium–Water Clusters Mg+(H2O)n

Hydrated singly charged metal ions doped with carbon dioxide, Mg2+(CO2)−(H2O)n, in the gas phase are valuable model systems for the electrochemical activation of CO2. Here, we study these systems by Fourier transform ion cyclotron resonance (FT–ICR) mass spectrometry combined with ab initio calculations. We show that the exchange reaction of CO2 with O2 proceeds fast with bare Mg+(CO2), with a rate coefficient kabs = 1.2 × 10–10 cm3 s–1, while hydrated species exhibit a lower rate in the range of kabs = (1.2–2.4) × 10–11 cm3 s–1 for this strongly exothermic reaction. Water makes the exchange reaction more exothermic but, at the same time, considerably slower. The results are rationalized with a need for proper orientation of the reactants in the hydrated system, with formation of a Mg2+(CO4)−(H2O)n intermediate while the activation energy is negligible. According to our nanocalorimetric analysis, the exchange reaction of the hydrated ion is exothermic by −1.7 ± 0.5 eV, in agreement with quantum chemical calculations.


■ INTRODUCTION
Because of the still increasing consumption of fossil fuels, carbon dioxide is one of the most problematic greenhouse gases produced by humankind. As CO 2 is highly thermodynamically stable, it cannot be easily activated in chemical reactions, and its utilization is very limited. 1 For the transformation of CO 2 to fuels, activation is usually achieved under high temperature and pressure conditions over heterogeneous catalysts in the Sabatier process. 2 A promising alternative is electrochemical activation of CO 2 , and the formation of formic acid in electrochemical cells has been reported as early as in 1870. 3 A key intermediate is the carbon dioxide radical anion CO 2 − , which has attracted growing attention in gas phase studies since Compton and Klots reported its stabilization by solvation. 4−6 Carbon dioxide activation in the gas phase was recently reviewed by Weber 7,8 and Schwarz. 9 Photodissociation of the C−O bond in CO 2 − (H 2 O) n has been reported by Sanov and co-workers. 10,11 In aqueous solution, spectra of CO 2 − in the UV 7,12,13 have been measured, and the symmetric stretching and bending modes have recently been identified by Raman spectroscopy. 14 In gas phase clusters, infrared spectra of CO 2 − (H 2 O) n have been obtained with up to two water molecules in the O−H stretch region. 7,15 Reactions of hydrated electrons with CO 2 directly revealed the process of reductive activation, resulting in the formation of CO 2 − (H 2 O) n . 16−21 C−H, C−C, and C−S bond formation was observed with a series of reactants. 22−26 Uggerud and coworkers have shown in elegant studies that ClMgCO 2 − complexes can be formed by collision induced dissociation of the oxalic acid complex, and studied the reactivity of reductively activated CO 2 . 27−30 Weber and co-workers investigated reductive CO 2 activation in M − (CO 2 ) n systems by infrared spectroscopy. 7,8,31 Menges et al. demonstrated the capture of CO 2 by a cationic Ni(I) complex and characterized of the activated CO 2 molecule by cryogenic infrared spectroscopy. 32 The Johnson group recently also characterized radical ion adducts between imidazole and CO 2 by vibrational spectroscopy. 33 In the present work, we are interested in the influence of metal centers on the reactivity of CO 2 − in water clusters, choosing magnesium as a well-investigated metal. Magnesium has also atmospheric relevance as roughly 5 tons of Mg as interplanetary dust enters earth's atmosphere every day. 34 By photoionization or charge transfer reactions with NO + and O 2 + , Mg + is formed, which further reacts with its surroundings in the mesosphere and lower thermosphere, inter alia, with CO 2 and O 2 . 35 Bond dissociation energies for Mg + complexes with a series of small molecules, including CO 2 , as well as the binding energies of the first four water molecules were determined by collision-induced dissociation (CID) experiments by the Armentrout group. 36,37 Williams and co-workers studied doubly charged hydrated magnesium by blackbody infrared radiative dissociation (BIRD). 38 Singly charged hydrated magnesium ions Mg + (H 2 O) n have been examined with respect to the influence of blackbody infrared radiation, photodissociation, and reactions with small molecules by FT-ICR mass spectrometry and methods of theoretical chemistry. 39−54 Duncan et al. investigated infrared photodissociation spectroscopy of Mg + (CO 2 ) n and Mg + (CO 2 ) n Ar ion−molecule complexes 55  To test this prediction experimentally, we investigate the CO 2 /O 2 exchange reaction in Mg 2+ (CO) 2 − (H 2 O) n cluster distributions along with nanocalorimetric analysis 20 of clusters n ≤ 70. Quantum chemical calculations are used to map possible reaction pathways for both bare and hydrated clusters, respectively, and to monitor the course of the exchange reaction.

■ EXPERIMENTAL AND THEORETICAL METHODS
The experiments are performed on a modified 4.7 T FT−ICR Bruker/Spectrospin CMS47X mass spectrometer 62 equipped with a Bruker infinity cell 63 and an external laser vaporization source. 64,65 A frequency doubled Nd:YAG laser (Continuum Surelite II) is used to generate Mg 2+ (CO 2 ) − (H 2 O) n ions by evaporation of isotopically enriched 24 Mg from a solid metal target and supersonic jet expansion of a hot plasma in a helium/water/CO 2 gas mixture. Twenty laser shots at 10 Hz and approximately 5 mJ pulse energy are used to generate the ions. The ions are rotationally and vibrationally cooled below room temperature due to the supersonic expansion into high vacuum, accelerated downstream from a skimmer and transferred to the ICR cell by a system of electrostatic lenses through several differential pumping stages. 66 In the ICR cell, ions are stored at room temperature in an electromagnetic trap under ultrahigh vacuum conditions in a 4.7 T magnetic field. 67 O 2 is introduced at constant backing pressure, allowing the monitoring of reaction kinetics by taking mass spectra after different reaction delays. For each mass spectrum, 20 experiment cycles are averaged.
Absolute rate coefficients k abs are obtained by analyzing the pseudo-first-order kinetic plots of different experimental runs taken over a range of pressures. The cluster distribution shrinks due to blackbody infrared radiative dissociation (BIRD) 68−76 and the exothermicity of the reaction. 58,77,78 The error of the rate coefficient was estimated to be about 30% due to the uncertainty of the pressure calibration. 79,80 The noise level of the summed intensities was calculated with the Gaussian law of error propagation from the noise level of each peak. It should be noted that the internal temperature of the clusters is given by the interplay between radiative heating and evaporative cooling. Experiments on phase transitions in water clusters place this temperature in the region of 100−200 K. 81,82 The collision rates k ADO , k HSA and k SCC are calculated using the average dipole orientation (ADO), 83,84 hard sphere average dipole orientation (HSA) and surface charge capture (SCC) models, which yield the efficiencies Φ ADO = k abs / k ADO , Φ HSA = k abs / k HSA , and Φ SCC = k abs / k SCC , respectively. 85 Nanocalorimetric analysis is performed by fitting the average cluster size ⟨n⟩ of reactant and product ions over time with a set of differential equations, which yields the average number of water molecules evaporating due to the heat of the reaction. 20,21,61 The evaporation of one H 2 O molecule removes ΔE vap = 0.45 ± 0.03 eV from the cluster. 82, 86 Selected clusters were optimized using the M06 density functional theory (DFT) functional 87 along with the def2TZVP basis set. As the DFT theory might struggle to quantitatively describe the nature of the Mg + /O 2 interaction, 88 we recalculated the structures using the complete basis set QB3 (CBS-QB3) method. 89 This method is able to reproduce values calculated at the coupled cluster level (CCSD(T)/augcc-pVQZ) as already noted elsewhere. 88 Molecular volume calculations for the HSA and SCC methods and charge analysis within the ChelpG scheme 90 were performed at the MP2/ def2TZVP level.
Molecular dynamics was run on the M06/6-31+G* potential energy surface with a time step of 30 au (∼0.75 fs). Investigated [Mg(CO 2 )(H 2 O) n ] + clusters were first thermalized at 250 K using the Nose−Hoover thermostat. Then, an O 2 molecule was added at a distance of 10 Å with respect to the cluster center of mass and a microcanonical simulation was performed. Twenty trajectories were run for each structure. A dynamics run was stopped when a neutral molecule (O 2 or CO 2 ) leaves the cluster by more than 10 Å or after 7 ps (or 12 ps when CO 4 − was formed to investigate its dissociation). We considered only runs, either reactive or nonreactive, where O 2 approached the cluster with a distance shorter than 3 Å with respect to any cluster atom.
All quantum chemical calculations were performed in the Gaussian program, 91 the Abin code was used for molecular dynamics. 92 Measured rate coefficients of reaction 1 for various average cluster sizes are collected in Table 1, calculated reaction energies for n = 0−7 are shown in Table 2.

Article
The Nonhydrated Species Mg + (CO 2 ). First, we discuss the O 2 /CO 2 reaction for n = 0, i.e., the conversion from Mg + (CO 2 ) to Mg 2+ (O 2 ) − . This reaction proceeds with a relatively high rate coefficient of k abs = 1.2 × 10 −10 cm 3 s −1 resulting in an efficiency of Φ ADO = 21%. The same reaction was previously examined in a fast flow tube-mass spectrometer at a pressure of 1.2 Torr, with a measured rate coefficient roughly five times smaller than in our experiment, 35,94 probably due to the different pressure. In the fast flow tube-mass spectrometer experiment, the [(CO 2 )Mg(O 2 )] + complex was also observed, which got stabilized in collisions with background gas. 35 Since the pressure in our chamber is 7 orders of magnitude lower than in the fast flow tube, there are nearly no collisions, resulting in immediate elimination of the CO 2 molecule.
The calculated exchange reaction energy is −0.29 eV (at the CBS-QB3 level), the respective reaction profile is shown in Figure 1. Theoretical calculations predict that Mg + (CO 2 ) is linear while Mg 2+ (O 2 ) − has C 2v symmetry, as pointed out before. 88 Analysis of atomic charges shows that these two ions have considerably different electronic structures: The bonding in Mg + (CO 2 ) can be best described as an ion-induced dipole interaction, with a charge transfer of −0.29 e from CO 2 to Mg + (q Mg = 0.71 e), because the linear CO 2 is reluctant to accept an electron. In Mg 2+ (O 2 ) − , a considerable charge transfer from Mg + to O 2 is observed (q Mg = 1.63 e).
The O 2 /CO 2 exchange reaction on Mg + is predicted to follow a direct pathway, with adsorption of O 2 followed by dissociation of CO 2 . The energy released during the formation of the [(CO 2 )Mg(O 2 )] + encounter complex (∼1.8 eV) easily induces dissociation of the CO 2 unit in the absence of stabilizing collisions. In the [(CO 2 )Mg(O 2 )] + structure, there is already a considerable charge transfer from Mg (q Mg = 1.34 e) toward O 2 (q O 2 = −0.55 e). The high stability of [CO 2 MgO 2 ] + is in agreement with its observation in the above-mentioned flow tube experiment. 35 The Mg 2+ (CO 4 ) − structure is a local minimum on the potential energy surface, with the charge on Mg calculated as q Mg = 1.68 e. However, its formation requires considerable cluster reorganization, and it is stabilized by only ∼0.2 eV ( Figure 1) relative to Mg + (CO 2 ). For energetic as well as mechanistic reasons, we do not expect an Mg 2+ (CO 4 ) − intermediate to be formed in our experiment.
The course of the Mg + (CO 2 ) + O 2 reaction was further studied by molecular dynamics (see Table 3 and the SI). Only two channels were observed during the simulation time (7 ps), viz. formation of [(CO 2 )Mg(O 2 )] + (75%) and scattering of O 2 on the Mg + (CO 2 ) ion when O 2 approaches the ion from the side of the CO 2 (25%). We observed no elimination of CO 2 on the time scale of 7 ps. This can be understood considering the high dissociation energy of CO 2 from Mg 2+ (O 2 ) − (Figure 1). According to our RRKM calculations, the rate of CO 2 dissociation is about 5 × 10 5 s −1 when disregarding thermal energy of the cluster, using energetics and frequencies calculated at the M06/def2TZVP level. Thus, on the time scale of the experiment (i.e., seconds), energy redistribution takes place and CO 2 dissociates.
The Hydrated Species Mg 2+ (CO 2 ) − (H 2 O) n . When the Mg + (CO 2 ) core is hydrated to Mg 2+ (CO 2 ) − (H 2 O) n , different reactivity patterns are observed. Figure 2 shows the mass spectra at an O 2 pressure of 6.4 × 10 −8 mbar after different delays. The corresponding reaction kinetics can be seen in    The Journal of Physical Chemistry A Article Figure 3b summarizes the average cluster size ⟨n⟩ of reactant and product as a function of time. A nanocalorimetric fit yields the number of water molecules that evaporate due to the reaction. In the first 10 s, BIRD has a large influence on the average cluster size. The BIRD rate decreases with decreasing size. 70,74 When n = 3 is reached, no further dissociation is observed on the time scale of the experiment.
A mean rate coefficient k abs = 1.5 × 10 −11 cm 3 s −1 has been obtained for n ≥ 20, with similar rate coefficients in the n = 20−55 range (see Table 1). For a cluster with 43 water molecules, reaction efficiency is predicted to be Φ HSA = 1.9% and Φ SCC = 0.9%. The actual efficiency might lie somewhere in between, i.e. about one in 70 collisions is reactive. Compared to the complex without water molecules, the exchange reaction is an order of magnitude slower.
For the quantitative nanocalorimetric analysis, only data were fitted with a starting average cluster size of n ≥ 36 to minimize the influence of the size dependent rate coefficient. The mean energy release of reaction 1 corresponds to ΔE nc (1) = 1.7 ± 0.5 eV, and the mean number of evaporated water molecules m = 3.8 as calculated for clusters with n ≥ 36 and averaged over six measurements. The energy is, within the experimental uncertainty, identical to the value of ΔE nc (2) = 1.5 ± 0.3 eV measured in a previous study for the reaction without the magnesium core, reaction 2.  Table 2. When Mg + CO 2 is hydrated by one water molecule, there are two possible isomers with different electronic structure. The more stable isomer Ia with linear CO 2 shows a very limited charge transfer, and electron density is actually transferred from CO 2 to Mg + (H 2 O) (q CO 2 = 0.29 e). In isomer Ib, which lies 0.44 eV above Ia, CO 2 is coordinated in bidentate fashion to Mg + , and a considerable charge transfer to CO 2 takes place (q CO 2 = −0.63 e).
For two water molecules, CO 2 connected to Mg + already tends to accept an electron, loses its linearity, and binds either in monodentate or bidentate fashion. The structure with linear CO 2 (IIb) is also local minimum on the potential energy surface, but is higher in energy. The bidentate motif is predicted to be the most stable one for n = 1−4. However, there is only a small energy difference between monodentate and bidentate structures. Already, for n = 7, the bidentate structure collapses during optimization into a monodentate structure. For n = 6−7, we also optimized two structures where CO 2 is not directly attached to Mg + (VId, VIIb). However, this configuration is less stable by about 0.7 eV.
For all structures with at least 2 water molecules, the charge transfer from Mg + to CO 2 is already substantial, with the CO 2 A total of 20 molecular dynamics runs on the M06/6-31+G* potential energy surface were performed for each isomer, with total time of 7 ps (prolonged to 12 ps when the CO 4 moiety is formed). The O 2 /CO 2 exchange reaction proceeds either directly on the Mg + core (for Mg 2+ (CO 2 ) − (H 2 O) 2 ) or through CO 4 − formation (for Mg 2+ (CO 2 ) − (H 2 O) 5 ).  For O 2 attached to hydrated Mg + , bidentate binding seems to be more favorable, but the difference relative to the monodentate structure is negligible for n > 3. For n = 6−7, structures without direct O 2 −Mg + interaction were also considered (VIc, VIIb). These structures are only about 0.25 eV less stable with respect to structures with Mg +coordinated O 2 . At the same time, an HO 2 radical might be formed (VIIb), with the proton transfer favored by the strongly polarizing Mg 2+ center.
The calculated energies released in the O 2 /CO 2 exchange reaction 1 amount to about (−1.8 − −1.6) eV for n ≥ 2, while n = 0, 1 feature lower exothermicity (see Table 2). In other words, the reaction energy seems to converge already for n = 2, with only limited changes with ongoing hydration, irrespective whether a water molecule is added in the first or second solvation shell. This can be traced to similar hydration energies for clusters with CO 2 and O 2 . The calculated reaction energy agrees within error limits with the experimentally measured value.
In a previous publication, 21 a prominent role of the CO 4 − ion was suggested for reaction 2, as previously predicted by Weber. 7 CO 4 − formation on a hydrated Mg 2+ (CO 2 ) − center is also strongly exothermic, with a release of 1.6−1.7 eV for n > 1.
For both O 2 /CO 2 exchange reaction and CO 4 − formation on Mg 2+ (CO 2 ) − (H 2 O) n , reaction exothermicity increases considerably for n > 1. However, the exchange reaction on a hydrated cluster is found to proceed much slower in the experiment, compared to reactivity of bare Mg + (CO 2 ). This effect must be caused by water molecules already in the first hydration layer, as a small rate coefficient is observed even for n = 7 where the second hydration layer does not contain more than three water molecules. To determine the reaction mechanism and the role of the Mg + ion in the process, we investigated the exchange reaction using both time-independent calculations and molecular dynamics simulations.
In Figure 5, we analyze reaction mechanisms through relaxed scans along the potential energy surface. Three reaction mechanisms were considered. For two reactions proceeding through direct charge transfer (a, b), we follow the CO 2 angle as the reaction coordinate. For CO 2 − , an angle of about 135°is expected, neutral CO 2 is linear. In Mg 2+ (CO 2 ) − (H 2 O) 5 Va (Figure 5a), the reaction is hindered by the reorganization of the hydrogen bonded network, with a barrier below 0.2 eV. When the CO 2 molecule starts to linearize, its charge diminishes, it is pushed out of the cluster and an HO 2 moiety is formed. For Mg 2+ (CO 2 ) − (H 2 O) 6 with CO 2 in the second solvation shell (Figure 5b), the reaction barrier further decreases and could not be determined unequivocally. Again, the charge transfer leads to linearization of CO 2 and formation of an HO 2 moiety. The third reaction scenario proceeds through formation of CO 4 − and direct CO 2 /O 2 exchange on the Mg + center ( Figure  5c). The pathway does not require a high activation energy (∼0.1 eV) and lies well under the entrance channel energy; however, a suitable initial structure with a low O 2 ...Mg distance has to be reached. We also considered oxygen atom exchange between O 2 and CO 2 on the Mg center, the respective barrier was however found to exceed the entrance channel energy and we do not expect this process to take place.
To understand the role of hydration and the difference between reactivity of singly and doubly coordinated CO 2 , we study reactivity of Mg 2+ (CO 2 ) − (H 2 O) n clusters toward O 2 using molecular dynamics. Three structures were selected, IIa, Va, and Vb. Because of the expected low efficiency of the reaction, we performed the dynamics at 250 K, i.e. at higher temperature than the internal temperature of the clusters of about 100−200 K. The results are collected in Table 3, selected videos of MD runs are provided in the Supporting Information.
When we compare reaction channels observed for Mg + (CO 2 ) and Mg 2+ (CO 2 ) − (H 2 O) 2 , a strong influence of hydration can be observed. First, the ratio of scattering reactions increases about twice due to water molecules hindering the approach to the Mg + core. Second, complexation observed for Mg + (CO 2 ) is here substituted by the exchange reaction that is seen in 35% of cases (note the high reaction energy of about −1.8 eV in Table 2). In one case, formation of a long-living CO 4 − was observed. For isomers Va and Vb, we saw similar reaction channels. Scattering of O 2 from the ion is the most important channel (70% and 85%, respectively), followed by CO 4 − formation (15% for both isomers). For isomer Va, dissociation of CO 4 − to form a Mg 2+ (O 2 ) − core is observed in two dynamic runs, following the reaction pathway suggested in Figure 5c. Finally, a Mg + (CO 2 ) core with a loosely attached O 2 was also observed for Va (5%).
Ligand exchange through CO 4 − formation is the only reaction channel observed for isomers Va and Vb to produce a Mg 2+ (O 2 ) − (H 2 O) 5 cluster. Because of the hydration of the Mg + core, no direct O 2 /CO 2 exchange reaction without CO 4 − formation is documented. The charge exchange suggested in Figure 5a was not seen, probably due to the short time of the respective nonreactive collision. Molecular dynamics results also explain why the exchange reaction proceeds much slower, although the reaction exothermicity increases considerably. After hydration of Mg + (CO 2 ), the O 2 molecule must approach the cluster from a suitable direction to form CO 4 − . In calculations, we observe an increase in scattering probability by a factor of ∼3 when passing from a bare Mg + (CO 2 ) ion to Mg + (CO 2 )(H 2 O) n with n = 5, compared to a factor of ∼5 in the experiment when comparing n = 0 and n ∼ 7.
Another indication of the increased importance of proper orientation of the impacting O 2 molecule are the results for CO 2 − (H 2 O) n . The metal-free species exhibit a 2−3 times higher rate constant for CO 2 /O 2 exchange 21 than Mg 2+ (CO 2 ) − (H 2 O) n . Without the Mg + core, we might expect CO 2 − located on the cluster surface up to larger cluster sizes, thus increasing the reaction cross section. The nanocalorimetric analysis on the CO 2 − (H 2 O) n clusters leads to ΔE nc = 1.5 ± 0.3 eV, 21 which is slightly lower compared to the present experiment on the Mg + core. This supports the assumption that CO 2 − is located on the surface of the CO 2 − (H 2 O) n cluster and bound to a low number of water molecules, resulting in a lower evaporation energy. The measured efficiency is also 50% higher for CO 2 − (H 2 O) n than for Mg 2+ (CO 2 ) − (H 2 O) n . The presence of Mg + makes the exchange reaction less effective due to the solvation of the Mg 2+ (CO 2 ) − core in the clusters.

■ CONCLUSION
We studied singly charged hydrated magnesium cations with carbon dioxide, Mg 2+ (CO 2 ) − (H 2 O) n , in reaction with neutral molecular oxygen. The reaction is efficient, resulting in an exchange reaction of CO 2 to O 2 . For n = 0, an absolute rate coefficient k abs = 1.2 × 10 −10 cm 3 s −1 is measured. For hydrated clusters, the reaction is slower, and we obtained an average of k abs = 1.5 × 10 −11 cm 3 s −1 for hydration by 20−55 water molecules. This behavior can be rationalized by two different reaction scenarios. For n = 0, direct CO 2 /O 2 exchange on the Mg + core is observed. With hydration, CO 4 − formation seems to be necessary for the reaction to proceed, as indicated by molecular dynamics simulations. Although CO 4 − formation and subsequent dissociation to O 2 − and CO 2 on the hydrated Mg + core are considerably more exothermic compared to the reaction on a bare Mg + ion, hydration at the same time lowers the reaction cross section for CO 4 − formation on the cluster. This is also indirectly supported by a higher reaction constant observed for the same reaction without the Mg + core. 21 For the hydrated clusters, we determined the reaction enthalpy by a nanocalorimetric analysis to be 1.7 ± 0.5 eV, in agreement with the calculated value.