Reactivity of the O +2 .(H 2 O) n and NO + .(H 2 O) n Cluster Ions in the D-region of the Ionosphere

The protonated water clusters present in the D-region of the ionosphere have been postulated to be formed from cluster ions such as O +2 .(H 2 O) n and NO + .(H 2 O) n , although the detailed mechanism of the underlying reactions is not understood. Second order Møller-Plesset perturbation theory based Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations of the reactions of the O +2 .(H 2 O) n and NO + .(H 2 O) n cluster ions to form protonated water clusters reveal diﬀerent mechanisms for the O +2 and NO + based ions. AIMD simulations of O +2 .(H 2 O) n =2 − 5 with initial velocities of the atoms sampled from the Maxwell-Boltzmann distribution at 220 K show that following charge transfer, a reaction to form a protonated water cluster and OH occurs rapidly where the neutral O 2 molecule is just a spectator. In contrast, the reaction of NO + .(H 2 O) n =4 , 5 has been hypothesised to involve an intracluster reaction, but no reaction is observed in AIMD simulations using thermal initial velocities. However, it is shown that reactions to form protonated water clusters do occur in simulations when a water molecule collides with a NO + .(H 2 O) 4 cluster.

though the detailed mechanism of the underlying reactions is not understood. Second

Introduction
The Earth's ionosphere is a region of the upper atmosphere that contains many ions, and is often considered to comprise several regions/layers. The most complicated chemistry occurs in the D-region, which lies from about 50 km to 90 km in altitude and is notable for the existence of cluster ions and its rich ion chemistry. 1 The composition of the D-layer has important consequences for the attenuation of radio signals. Neutral species can be readily ionised by solar radiation and the major positive ions ions in the atmosphere are predicted to be NO + , O + 2 and N + 2 in order of decreasing abundance in line with their ionization energies. 2 Once these ions have been formed they can be involved in complicated reactions, and characterizing the mechanisms of these reactions is important for our understanding of the chemical composition of the ionosphere. The nature of these reactions can be studied with quantum chemical calculations. However, some caution is required when applying quantum chemical methods to study these reactions since the ionic species involved can lead to unusual bonding, such as three-electron two-centre bonds, 3 and weak interactions that can be a challenge for methods such as density functional theory (DFT) to model accurately. [4][5][6] Measurements have shown O + 2 and NO + to have a high abundance in the upper E-and F-layers of the ionosphere. 7 However, at lower levels in the D-layer protonated water clusters are the major positively charged ions. 8-10 X + .(H 2 O) n clusters can be formed in a step-wise solvation process, and the resulting clusters can then undergo intracluster reactions to form protonated water clusters where in reaction (2) where O + 4 is produced from a 3-body reaction involving O + 2 and O 2 . Good et al. 12 proposed the following reaction mechanism for the formation of protonated water clusters under ionospheric conditions The formation of protonated water clusters from O + 2 was also studied using ion-drift mass spectrometry. 14  One key feature of the reaction involving NO + is the formation of nitrous acid. Experimental work based upon infrared spectroscopy has shown that the formation of HONO is dependent on the size and structure of the water cluster, in particular HONO formation occurs when n=4 and becomes dominant at n=5 (reaction (2)). 28 Temperature can also play a role since at increased temperatures higher energy isomers become more populated. 29 However, more recent work simulated the reactivity of the n=5 clusters using AIMD simulations with MP2 and found the clusters did not react to form HONO. 6 In the present paper the reaction of O + 2 and NO + ions with water are studied with AIMD simulations based upon second order Møller-Plesset perturbation theory, and it is shown that there are significant differences between the reactivity of the two ions.

Computational Details
The lowest energy structures of O + 2 .(H 2 O) n=1−5 were calculated using a hierarchical procedure where a lower level of theory is used to search the conformational space and identify low energy isomers that are then re-optimized at a higher level of theory. This approach has been used successfully in the study of related systems. [4][5][6]34,35 In this work the conformational search is performed using unrestricted HF with the 6-31+G* basis set with a random search approach. In this approach after an initial geometry optimization the oxygen and water molecules are subjected to 20 random moves that include translations and rotations and the resulting structure is re-optimized. The structural moves are subject to the constraints that the molecules are kept separated by a least 0.2 bohr at the point of closest contact and the molecules are kept within a box of length 10 bohr. This procedure was repeated 100 times to give a total of 101 (including the initial) structures. The structural searches were performed for both doublet and quartet spin states. The distinct low energy structures were then reoptimized at the unrestricted MP2/6-311++G** level and harmonic frequencies computed.
The computed harmonic frequencies were scaled by 0.95 and in the simulated spectra the  The computed IR spectra for the lowest energy structures are shown in Figure 3.
An example AIMD simulation for n=5 cluster is included in the SI with the initial and final structures for n=2-5 simulations illustrated in Figure 4. All of the simulations start with a structure where O 2 is bound to a cluster of water molecules. The calculations show that for these structures the positive charge is localized on a water molecule. This is consistent with the highest occupied molecular orbital for the neutral clusters corresponding to a lone pair on a water molecule. With the positive charge on a water molecule, as the simulation progresses with thermal initial velocities there is a rearrangement of the water molecules to form H 3 O + and OH, and during this process the O 2 molecule is largely just a spectator.
For all of the simulations the formation of OH occurs on a fast timescale and within the simulation length of 4.84 ps. We note that for analogous simulations for the n=1 cluster no reactions to form OH occur. For clusters with n ≥2 the process of charge transfer to the solvent followed by formation of H 3 O + and OH has been suggested in previous work. 18 However, in the experiments this reaction channel was smaller than the reaction channel where OH is not formed.