Communication: Charge transfer dominates over proton transfer in the reaction of nitric acid with gas-phase hydrated electrons

The reaction of HNO3 with hydrated electrons (H2O)n − (n = 35–65) in the gas phase was studied using Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and ab initio molecular dynamics simulations. Kinetic analysis of the experimental data shows that OH−(H2O)m is formed primarily via a reaction of the hydrated electron with HNO3 inside the cluster, while proton transfer is not observed and NO3 −(H2O)m is just a secondary product. The reaction enthalpy was determined using nanocalorimetry, revealing a quite exothermic charge transfer with −241 ± 69 kJ mol−1. Ab initio molecular dynamics simulations indicate that proton transfer is an allowed reaction pathway, but the overall thermochemistry favors charge transfer.

and at the same time it readily undergoes dissociative electron transfer in the gas phase. [11][12][13] Charge transfer leading to NO 2 − (H 2 O) n or OH − (H 2 O) n is therefore also conceivable. In fact, all three potential product species, NO 3 − (H 2 O) n , NO 2 − (H 2 O) n , and OH − (H 2 O) n , have been observed in our recent study, 14 where low-energy free electrons were brought to interact with neutral mixed nitric acid-water clusters (HNO 3 ) m (H 2 O) n , m ≈ 1-6, n ≈ 1-15.
The mechanism of the gas phase reaction between free electrons and HNO 3 was studied in detail using flowing afterglow techniques. Dissociative electron attachment to HNO 3 yields primarily NO 2 − in a very efficient exothermic process with an energy release of around 13 kJ mol -1 . [11][12][13][14] Shuman et al. 13 observed the formation of OH − as a minor channel, which is 30 kJ mol -1 endothermic. The formation of NO 3 − in the gas phase is even more endothermic with 43 kJ mol -1 and has recently been observed using a crossed-beam experiment. 14 However, electron driven processes often dramatically change upon solvation. [15][16][17][18] Hydration affects the electronic structure of transient negative ions and enhances or suppresses reaction channels. Furthermore, HNO 3 has a strong affinity to ice, 19 where it rapidly dissociates. [20][21][22] To experimentally resolve these issues, we studied the reaction of HNO 3 with (H 2 O) n − (n = 35-65) by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. The measurements are complemented with ab initio molecular dynamics simulations. ions. Analogous cluster ions were found as final products in gas-phase ion-molecule reactions 11,[24][25][26] and electrospray ionization of aqueous HNO 3 solution. 27 Our kinetic analysis assuming pseudo-first order kinetics, Fig. 2 clusters are formed as a secondary product, reaction (2). The perfect pseudo-first order behavior also indicates that the reaction rate is independent of the cluster size. Obviously, charge transfer to HNO 3 followed by dissociation is faster than the acidic dissociation of HNO 3 , which would lead to hydrogen formation analogous to the HCl reaction. Since a mixture of HNO 3 and H 2 O vapor is present in the ICR cell, we cannot derive a reliable pressure-independent rate constant. Using the total measured pressure as the partial pressure of HNO 3 , we obtain lower limits for the rate constants k(1) ≥ (2.8 ± 1.1) × 10 −10 cm 3 s −1 and k(2) ≥ (2.4 ± 0.9) × 10 −10 cm 3 s -1 , while the upper limits are given by the collision rates, Reaction (2) is the well-known acid-base reaction. 26,28 The NO 3 − anion is often seen as a terminal product in many ion-molecule reactions involving HNO 3 11,26,29 and also occurs naturally in the troposphere. 30  The minor product series NO 2 − (H 2 O) n may be formed via reaction (3) in competition with reaction (1). However, the presence of traces of HONO as a decomposition product of HNO 3 on the apparatus walls has to be taken into account, which would afford reactions (4) and (5). Unfortunately, the kinetic fits are ambiguous, due to the low intensity of this product. However, the overall shape of the kinetics curve over all six different experiments is most consistent with NO 2 − (H 2 O) n formation in the second reaction step, i.e., reaction (5), The plot of average cluster sizes as a function of time, Fig. 2(b), shows that the OH − (H 2 O) m ion distribution is significantly shifted to smaller cluster sizes relative to that of the hydrated electrons (H 2 O) n − . The loss of water molecules indicates an exothermic reaction. We therefore applied the nanocalorimetry approach, in which the exothermicity of the reaction is determined via the average number of evaporated water molecules. [7][8][9] The mean cluster sizes for reactants and products as well as their difference are plotted as a function of time, Figs. 2(b) and 2(c), and fitted with a set of differential equations that account for the water loss due to reaction as well as BIRD. 23 Note that the time dependence of the difference in Fig. 2(c) is due to a complex interplay of BIRD, reaction kinetics and the 2 s long fill cycle of the cell. Since the product ions present at 0 s arise from ions residing for longer times in the cell, they are smaller than expected, and the difference seems artificially large. As shown before, the differential equations used for the fit describe these effects faithfully. 8  kJ mol -1 for reaction (1) and -94 ± 11 kJ mol -1 for reaction (2).  (3), is only slightly less exothermic than for reaction (1), which would be consistent with its occurrence as a minor primary reaction pathway, as well as with the average cluster size of NO 2 − (H 2 O) m [ Fig. 2(b)]. However, since we know from other experiments 14,29 that traces of HONO are inevitably present in the reactant gas, formation of NO 2 − (H 2 O) m is most likely due to collisions with HONO.
To get a mechanistic understanding of the primary reaction, we performed ab initio molecular dynamics simulations on small model systems. We started the simulations with equilibrated hydrated electrons with 15 water molecules, where the vertical detachment energy (VDE) is above 1 eV. 38 The calculated values are slightly larger than the measured data for somewhat larger finite size clusters (see the supplementary material for details). 39 Then we let react a neutral HNO 3 molecule placed randomly at a distance of 7.5 Å from the center of mass of the water cluster. Figure 3 shows the evolution of quantities characterizing structures and charge distribution along two selected MD trajectories. Panel A displays a trajectory in which the CT takes place and the non-planar radical anion of nitric acid is formed. The vertical ionization energy of the isolated anionic water oscillates above 1 eV while the (adiabatic) electron affinity for HNO 3 was measured to be 0.6 eV. 40,41 The charge transfer reaction is facilitated by solvation of the nitric acid molecule. Indeed, the CT is exothermic for larger clusters (see the supplementary material), yet an energy barrier is expected for this process. In our simulations, the CT reaction was typically observed in tens of picoseconds after the HNO 3 molecule and the anionic cluster get in contact.
The trajectory presented in Fig. 1(b) displays a proton transfer taking place in 1.5 ps. The proton then hops several times before the H 3 O + accepts the electron and forms free neutral hydrogen at about 8 ps. In this particular case, the hydrogen atom remains trapped in the cluster for another 2.5 ps before it leaves.
Altogether, we have performed 25 simulations lasting up to 25 ps [the simulations were stopped once either the reaction (1) or (6) took place]. Within that time, we have seen 16 times charge transfer (in 10 cases, the reaction was followed by the subsequent decomposition reaction within the 25 ps time window) and 6 times the proton transfer reaction. No reactive event occurred within the first 25 ps in the three remaining trajectories. We thus observe that both the CT and PT processes are very fast; the fast PT is consistent with previous studies on HNO 3 dissociation. 42 We can safely conclude that both the CT and PT channels are ultrafast processes, i.e., the reaction rate is controlled by the collision rate between the nitric acid and anionic cluster. The exact branching ratio is however beyond the scope of the ab initio dynamics based on DFT methods. In fact, we know that the vertical detachment energies of the hydrated electron are overestimated in our MD simulations based on the BLYP functional (see the benchmark calculations in the supplementary material). The higher VDEs in a Marcus theory picture result in a higher activation barrier for the CT process. The calculated yield for the CT process thus represents a lower bound estimate. The reactivity of the hydrated electron depends also on its binding energy, which changes with the cluster size. The cluster sizes used in the experiment are greater than in the simulation to avoid competing electron detachment activated by black-body radiation which occurs in (H 2 O) n − , n < 30. 43,44 Therefore, the experiments were performed with a cluster size distribution that started only above this threshold, however, not tractable for ab initio simulations.
Our calculations show that the reaction enthalpy gradually decreases with increasing cluster size (n ≤ 15; see the supplementary material, Table S3) and, for reaction (1), it slowly reaches the experimental value. An extrapolation of the total energies to the bulk (Table I) by embedding a small anion water cluster in a dielectric continuum 45 results in a good agreement with literature thermochemical data from bulk aqueous solution for reactions (1) and (2); see the supplementary material. Note that reaction (2) is much less exothermic and this exothermicity decreases with increasing number of solvating water molecules.
In summary, we have demonstrated that the charge transfer reaction between hydrated electron and HNO 3 is an ultrafast process taking place on the picosecond time scale in finitesize water particles. The transient negative ion HNO 3 − is formed faster than the ionic dissociation of the acid molecule in the water cluster can occur. The excess electron

Supplementary Material
Refer to Web version on PubMed Central for supplementary material.