Kinetics of the reaction of CO3˙-(H2O)n, n = 0, 1, 2, with nitric acid, a key reaction in tropospheric negative ion chemistry.

A significant fraction of nitrate in the troposphere is formed in the reactions of HNO3 with the carbonate radical anion CO3˙- and the mono- and dihydrated species CO3˙-(H2O)1,2. A reaction mechanism was proposed in earlier flow reactor studies, which is investigated here in more detail by quantum chemical calculations and experimental reactivity studies of mass selected ions under ultra-high vacuum conditions. Bare CO3˙- forms NO3-(OH˙) as well as NO3-, with a total rate coefficient of 1.0 × 10-10 cm3 s-1. CO3˙-(H2O) in addition affords stabilization of the NO3-(HCO3˙) collision complex, and thermalized CO3˙-(H2O) reacts with a total rate coefficient of 6.3 × 10-10 cm3 s-1. A second solvent molecule quenches the reaction, and only black-body radiation induced dissociation is observed for CO3˙-(H2O)2, with an upper limit of 6.0 × 10-11 cm3 s-1 for any potential bimolecular reaction channel. The rate coefficients obtained under ultra-high vacuum conditions are smaller than in the earlier flow reactor studies, due to the absence of stabilizing collisions, which also has a strong effect on the product branching ratio. Quantum chemical calculations corroborate the mechanism proposed by Möhler and Arnold. The reaction proceeds through a proton-transferred NO3-(HCO3˙) collision complex, which can rearrange to NO3-(OH˙)(CO2). The weakly bound CO2 easily evaporates, followed by evaporation of the more strongly attached OH˙, if sufficient energy is available.


Introduction
The CO 3 À radical anion is an important intermediate in the tropospheric chemistry of anions. 1,2 Quantitative modeling by Kawamoto et al. 3 places the fractional abundance of CO 3 À core ions in the troposphere in the range of 0.9-2.3%, quite comparable to HSO 4 À core ions close to the ground, while the overwhelming majority of negative ions have an NO 3 À core.
However, a significant fraction of NO 3 À (H 2 O) is formed in the reaction of CO 3 À (H 2 O) with HNO 3 . 3 In recent years, ions in the troposphere have received increased attention in the form of charged aerosol particles. 4 In a series of laboratory experiments, the CLOUD collaboration at CERN has recently shown that ions play an important role for aerosol nucleation and cloud formation in the troposphere. [5][6][7][8] The formation of CO 3 À in atmospheric conditions was described by Fehsenfeld, Ferguson and co-workers in the 1970s. 9 In the first step electrons react with O 2 and an additional collision partner M to form O 2 À , reaction (1). Ozonide O 3 À is formed by charge transfer to an ozone molecule, reaction (2). The ozonide anion finally transfers O À to a carbon dioxide molecule, forming CO 3 À and O 2 , reaction (3).
The properties of CO 3 À itself were intensively studied by spectroscopy. Matrix isolation techniques were applied by Jacox et al., 10 and a number of other groups used photodissociation techniques to characterize CO 3 À . [11][12][13][14] The O 2 C-O À bond dissociation energy was determined by Johnson, Viggiano and co-workers via photodissociation and high level quantum chemical calculations to be 269 AE 5 kJ mol À1 . [15][16][17] Despite its key role in tropospheric anion chemistry, 18 only a small number of gas phase reactions were studied. [19][20][21][22][23] These are mostly reactions with nitrogen oxides, leading to formation of nitrate NO 3 À . 3,24-27 Reactions of CO 3 À (H 2 O) 0,1,2 with formic, acetic, propionic, butyric, glyoxylic, pyruvic and pinonic acid were investigated in a flow tube experiment by Arnold et al. 28,29 They reported as initial step mostly proton transfer giving the deprotonated acids as products. For propionic acid and larger, they also observed clustering with CO 3 À and formation of radical species, e.g. CH 3 CH( )COO À from propionic acid. 28,29 However, we recently showed that the reaction with formic acid proceeds mostly via oxidation of formic acid to carbon dioxide and water. 30 The deprotonation product HCOO À was re-assigned to the reaction of formic acid with HCOO À (OH ), an intermediate in the oxidation reaction that is formed in small concentrations. A similar pattern emerged for the reaction of CO 3 À with HCl.
A flow tube study by Dotan et al. 24 established an upper limit for the rate of 3 Â 10 À11 cm 3 s À1 , without observing any products. Recent studies in our laboratory reveal that this reaction proceeds via formation of a short lived, very reactive Cl À (OH ) intermediate that reacts fast with a second HCl molecule, producing HCl 2 À and Cl 2 À as final products. 31 The rate of the first step is 4.2 Â 10 À12 cm 3 s À1 , consistent with the upper limit given by Dotan et al. 24 Interestingly, hydration dramatically accelerates the rate to 2.7 Â 10 À10 cm 3 s À1 for CO 3 À (H 2 O), resulting in the reactive Cl À (HCO 3 ) radical species. 31 Nitric acid [21][22][23]32 and methane sulfonic acid 20 show efficient reactions with CO 3 À . The gas phase ion chemistry of HNO 3 was extensively investigated by Fehsenfeld and coworkers. 21 They reported a reaction rate coefficient of 8 Â 10 -10 cm 3 s À1 for reaction (4), measured by the flowing afterglow technique.
Möhler and Arnold investigated the reaction of HNO 3 with CO 3 À and CO 3 À (H 2 O) in a flow-reactor triple quadrupole mass spectrometer in the presence of 1.7 mbar N 2 and 0.3 mbar O 2 as buffer gas. 22 22 Catoire and co-workers used the CO 3 À + HNO 3 reaction for testing their flowing afterglow setup and observed the same primary products as Möhler and Arnold. 22,32 Since no mass selection was available for the reactant ions, the exact sequence of reactions generating the observed products, in particular the role of the [NO 3 ,OH ] À and the influence of an additional water molecule on the reactivity, remained unclear. Because of its central role in tropospheric negative ion chemistry, 1,3 we investigated the reaction of CO 3 À (H 2 O) n , n = 0, 1, 2, with HNO 3 by FT-ICR mass spectrometry and quantum chemical calculations. Each cluster size was studied separately with mass-selected ions. The extremely low pressure in the FT-ICR instrument leads to product distributions different from the flow reactor studies, due to the absence of stabilizing collisions.
A key problem in gas-phase reactivity studies with HNO 3 is the inherent instability of this substance. HNO 3 decomposes in concentrated aqueous solutions. In earlier studies on the reactivity of ionic water clusters, [33][34][35] we worked with aqueous concentrated solutions of HNO 3 , which yields a mixture of HNO 3 and H 2 O in the reaction region, with traces of the decomposition product HONO. The observed reaction products confirmed that the abundance of HONO was less than 3% of the HNO 3 partial pressure. To identify reactions where HONO might play a role, we use quantum chemical calculations to identify thermochemically allowed reaction pathways. In addition, structural as well as thermochemical information is obtained for stationary points on the reaction potential energy surface. Together, a consistent picture of the reaction mechanism evolves.

Computational and experimental details
The ion-molecule reaction profiles were simulated with density functional theory at the M06-2X/6-311++G(d,p) level of theory employing the Gaussian09 program suite. 36 The energies of all optimized geometries were corrected with zero-point energy obtained from harmonic vibration analyses. Local minima and transition structures on the potential energy surface were confirmed with absence of and presence of one imaginary frequency, respectively. The local minima associated with each transition structure were verified by the intrinsic reaction coordinate (IRC) method. Spin density distributions were evaluated at the same level of theory and shown as isosurfaces at a value of 0.01 a.u. Table S1 in ESI, † compares the used methods/basis sets with experimental values. The coordinates are given in Table S4 (ESI †). The experiments were performed on a modified Bruker/ Spectrospin CMS47X FT-ICR mass spectrometer as described in detail elsewhere. [37][38][39] The spectrometer is equipped with a Bruker Infinity Cell, an APEX III data station, a 4.7 Tesla magnet and an external laser vaporization ion source. CO 3 À was produced in the laser vaporization ion source [39][40][41][42] via expansion of a helium/water/oxygen/carbon dioxide mixture using a zinc target for the production of electrons. As vaporization laser a frequency doubled Nd:YAG laser at a pulse energy of B5 mJ at 10 Hz was used. All produced anionic species were transferred into the ICR cell, where they can be stored for several seconds or minutes. The ion of interest, CO 3 À or CO 3 À (H 2 O) 1,2 , was then isolated via resonant excitation of unwanted ions prior to measuring the kinetics. A constant background pressure of HNO 3 and H 2 O (concentrated aqueous solution, 70% HNO 3 , Sigma-Aldrich) was introduced into the ultrahigh vacuum region via a leak valve. Due to the inherent instability of HNO 3 , also traces of HONO were present, which are formed from the NO 2 decomposition product on thin films of H 2 O and HNO 3 , as present in the vacuum system. 43 Mass spectra were taken after different reaction delays relative to the end of the fill and isolation cycle. The intensities were extracted from the mass spectra. A rate coefficient matrix defines the allowed reaction channels and the data was fitted using a genetic algorithm that optimizes the rates from the matrix based on a pseudo-first order rate law. Relative rate coefficients were extracted from this fit. The stability of the fit was tested by systematically changing each parameter in 5 to 10 steps of AE5% from its optimized value, and re-optimizing all other parameters. The resulting error was plotted against the modified parameter. These plots are available as supporting information in Fig. S8 and S9 (ESI †). All rate coefficients reported in the results section showed stable, well-converged minima.
These pressure-dependent pseudo-first order rate coefficients are converted to pressure-independent bimolecular rate coefficients. An aqueous 70% HNO 3 solution is close to the azeotropic point and the chemical composition in the gas phase is therefore close to 70% HNO 3 and 30% water. As the cold cathode pressure gauge shows different sensitivity toward HNO 3 and H 2 O, the measured pressure was corrected taking the different sensitivity into account. The HNO 3 partial pressure was taken as 70% of the corrected total pressure. More details on the kinetic analysis and pressure correction are available in ESI. † The accuracy of the absolute rates is estimated to be AE40% due to uncertainties in the pressure determination. The noise level is derived from the baseline of each mass spectrum.

Results and discussion
Calculated reaction potential energy surface The potential energy surface (PES) corresponding to the reaction mechanisms suggested by Möhler and Arnold 22 is shown in Fig. 1. The calculations show that a barrierless proton transfer takes place upon formation of the collision complex 1, which can be written as NO 3 À (HCO 3 ). Rearrangement of the HCO 3 unit to CO 2 + OH within the complex faces a significant barrier of 81 kJ mol À1 via TS1 located at À63 kJ mol À1 relative to the separated reactants. Evaporation of CO 2 from complex 2, which can be written as NO 3 À (OH )(CO 2 ), requires only 33 kJ mol À1 , leading to the observed NO 3 À (OH ) product. Further evaporation of the OH radical requires 68 kJ mol À1 , making the overall reaction with À3 kJ mol À1 below the entrance channel almost thermoneutral.
The water binding energies in CO 3 À (H 2 O) 1,2 are 62 kJ mol À1 and 52 kJ mol À1 for the first and second molecule, respectively. Upon collision with HNO 3 , the water molecules from CO 3 À (H 2 O) and CO 3 À (H 2 O) 2 evaporate due to the energy released upon formation of the collision complex, since the transition states for rearrangement prior to water evaporation lie significantly higher in energy, see Fig. S1 (ESI †). For CO 3 À (H 2 O), the pathway to NO 3 À (OH ) + CO 2 formation is still accessible, while bare NO 3 À formation is clearly out of reach, lying 59 kJ mol À1 above the CO 3 À (H 2 O) + HNO 3 entrance channel. The second water molecule reduces the available energy further, only the formation of the NO 3 À (HCO 3 ) complex 1 is thermochemically allowed, with a moderate exothermicity of À30 kJ mol À1 .
Experimental results and discussion CO 3 À . The kinetics of the reaction of CO 3 À with HNO 3 is displayed in Fig. 2. A mass spectrum is available in Fig. S5 (ESI †). The decay of the CO 3 À ion intensity follows a pseudofirst order kinetics behavior. Primary reactions for pure CO 3 À with the reaction mixture lead to formation of HCO 3 À , NO 3 À , and NO 3 À (OH ). Rate coefficients for all reactions are given in Table 1. Compared to the flow reactor studies, the reaction is an order of magnitude slower, with an overall rate for all reaction channels of 1.0 Â 10 À10 cm 3 s À1 . Fehsenfeld et al. 21 reported a value of 8 Â 10 À10 cm 3 s À1 in their flowing afterglow, while Möhler and Arnold 22 agreed with their value of 1.3 Â 10 À9 cm 3 s À1 within error limits with Guimbaud et al., 32 who reported 1.2 AE 0.3 Â 10 À9 cm 3 s À1 . Obviously, stabilizing collisions with the buffer gas in the flow reactor studies increase the efficiency of the reaction. The nitrate-hydroxyl radical complex arises from the reaction with gaseous HNO 3 according to reaction (5). Formation of HCO 3 À requires a hydrogen atom transfer (HAT), which is significantly endothermic for HNO 3 , reaction (6). We therefore assign this small product to traces of HONO, reaction (7),  . If we assume collision efficiency for reaction (7), a partial pressure below 1 Â 10 À10 mbar of the HONO background is sufficient to explain the observed abundance of HCO 3 À .
Formation of NO 3 À via reactions (8) or (9) (11) or (12), respectively. Ligand exchange is also possible with HONO as well as HNO 3 , reactions (13) and (14), respectively. Since reactions (12) and (14) compete with each other, with reaction (14) being both more exothermic and mechanistically favorable, ligand exchange with water is the most plausible origin of the NO 3 À (H 2 O) product, reaction (11). Reaction (13) validates the presence of HONO in the reaction mixture.

Reaction
Rate coefficient k abs /cm 3 s À1 a Assuming either reaction (11) or (12). b Thermalized fraction of CO 3 À (H 2 O). c Cold fraction of CO 3 À (H 2 O); the accuracy of the absolute rates is estimated to be AE40% due to uncertainties in the pressure determination.

Paper PCCP
We also observe traces of NO 2 À , which are assigned to dissociative electron attachment. When working with negative ions, some free electrons are usually trapped in the ICR cell, 44 which react with HNO 3 according to reaction (15). 21 In turn, NO 2 À is converted with near collision rate to NO 3 À via proton transfer from HNO 3 , reaction (16).
e À + HNO 3 -NO 2 À + OH (15) NO 2 À + HNO 3 -NO 3 À + HONO (16) Fig. 3 shows the kinetics of the monohydrated species, mass spectra are displayed in Fig. S6 (ESI †). The scenario is quite complex, with a pronounced deviation of the CO 3 À (H 2 O) intensity from pseudo-first order behavior, for which a linear graph in the semi-logarithmic plot is expected.
To describe the observed curvature, the population of this species is divided into two fractions, which correspond to the initially cold ions directly from the supersonic expansion, and the thermalized ions after heating by ambient black-body radiation and collision with the reaction gas. These effects are included in the kinetic model by allowing the cold fraction to be converted to the thermalized fraction, with a unimolecular rate treated as a fit parameter. Heating ultimately leads to formation of CO 3 À via black-body infrared radiative dissociation (BIRD), [45][46][47][48][49][50][51][52][53][54][55][56][57][58] reaction (17), with a lifetime of 3 s for the thermalized fraction. This reaction is not allowed for the cold fraction in the kinetic model, see Table S2 (ESI †). Since the major part of the CO 3 À (H 2 O) population is already thermalized at nominally t = 0 s, and the thermalized fraction reacts overall much faster than the cold fraction, the intensity drop of CO 3 À (H 2 O) is faster in the beginning, and levels off at later times because the conversion from the cold to the hot fraction becomes rate limiting, which explains the observed curvature. The formation of NO 3 À (OH ) is observed with an appreciable rate, and can be assigned to collisions with HNO 3 , reaction (18). Also the transition state for CO 2 formation is below the entrance channel, see Fig. 1, thus reaction (18) is fully consistent with the calculations. The same is true for the ligand exchange product NO 3 À (HCO 3 ) formed via reaction (19). NO 3 À is exclusively formed from the thermalized fraction of CO 3 À (H 2 O) as a primary product in the kinetics. With HNO 3 as the reaction partner, reaction (20) is with DH 0 = +59 kJ mol À1 significantly endothermic. However, the thermalized fraction of CO 3 À (H 2 O) already contains almost enough energy for dissociation. Together with the internal energy of the HNO 3 collision partner, the energy required for reaction (20) is available in the system. Reactions (18)-(20) yield a total rate coefficient of 6.3 Â 10 À10 cm 3 s À1 for the reaction of thermalized CO 3 À (H 2 O) with HNO 3 , 37% of the flow reactor value of 1.7 Â 10 À9 cm 3 s À1 reported by Möhler and Arnold. 22 All secondary reactions as well as NO 2 À formation via dissociative electron attachment proceed as discussed above.  Fig. 4, mass spectra are available in Fig. S7 (ESI †). The major reaction channel is, as might be expected, loss of a water molecule due to BIRD, reaction (21). There is again formation of NO 2 À via reaction (15), but otherwise no primary products are observed from CO 3 À (H 2 O) 2 . The noise level of the kinetics, however, places a high upper limit of 6.0 Â 10 À11 cm 3 s À1 on the rate coefficient for the direct reaction of CO 3 À (H 2 O) 2 with HNO 3 . According to the thermochemical arguments discussed above, the most likely product of such a

Conclusions
The mechanism of the reaction of HNO 3 with CO 3 À (H 2 O) n , n = 0, 1, 2, is very similar to the previously studied HCl reaction. 31 With bare CO 3 À , the reaction is relatively slow, and the proton-transfer intermediate NO 3 À (OH ) is the unambiguously identified primary product, corresponding to Cl À (OH ) in the HCl reaction. Also NO 3 À is directly formed, but with even lower rate. Formation of NO 3 À (OH ) is accelerated for CO 3 À (H 2 O), but again slowed down by a second water molecule in the hydration shell. The rate is clearly dependent on the number of water molecules solvating CO 3 À , and overall significantly lower than in the flow reactor studies previously reported in the literature, indicating a strong pressure dependence.

Conflicts of interest
There are no conflicts to declare.