The origin of enhanced \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{O}}}}}}}}}_{2}^{+}$$\end{document}O2+ production from photoionized CO2 clusters

CO2-rich planetary atmospheres are continuously exposed to ionising radiation driving major photochemical processes. In the Martian atmosphere, CO2 clusters are predicted to exist at high altitudes motivating a deeper understanding of their photochemistry. In this joint experimental-theoretical study, we investigate the photoreactions of CO2 clusters (≤2 nm) induced by soft X-ray ionisation. We observe dramatically enhanced production of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{O}}}}}}}}}_{2}^{+}$$\end{document}O2+ from photoionized CO2 clusters compared to the case of the isolated molecule and identify two relevant reactions. Using quantum chemistry calculations and multi-coincidence mass spectrometry, we pinpoint the origin of this enhancement: A size-dependent structural transition of the clusters from a covalently bonded arrangement to a weakly bonded polyhedral geometry that activates an exothermic reaction producing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{O}}}}}}}}}_{2}^{+}$$\end{document}O2+. Our results unambiguously demonstrate that the photochemistry of small clusters/particles will likely have a strong influence on the ion balance in atmospheres.

Supplementary Note 1 -Cluster production : Γ * formalism The CO 2 clusters were produced using a conical nozzle with opening angle of 20 • , nozzle diameter of 150 µm and nozzle temperature estimated to be −10 • C. The stagnation pressure of CO 2 gas behind the nozzle was varied from 0.2 to 0.82 bar. The size of the clusters in the beam after supersonic expansion into the vacuum chamber through the nozzle depends on the geometry and temperature of the nozzle, the properties of the molecule and the stagnation pressure of the gas. Hagena's condensation parameter Γ * is a dimensionless parameter 1 that is used to estimate the mean cluster size N mean at a given stagnation pressure. Supplementary   Fig. 1 shows the calculated N mean and Γ * values for our experimental conditions. Supplementary Figure 1: Mean cluster size N mean and condensation parameter Γ * at the different experimental stagnation pressures used in this data set. The error bars for the N mean values are calculated as described in Harnes et al. 2 In the cluster beam, most of the molecules do not condense and hence among the measured photo-dissociation fragments, most of the signal comes from this molecular background.
Quantitatively, we found that at N mean ∼ 20, only about 4% of the total double coincidence signal comes from the dissociation of cluster parent dications and the remaining 96% comes from free molecular dissociation. Therefore, when comparing dissociation channels originating from free molecules and clusters we must consider the difference in population of the free molecules and clusters in the beam. Supplementary Table 1 shows the change in the total molecular and cluster signals detected for increasing mean cluster size. For events with one ion (C1) and events with two ions (C2) most of the signal detected is attributed to dissociation of the molecular background. As the mean cluster size increases, the cluster signal increases but for very large clusters the signal is limited by the detection efficiency.
With an ideal spectrometer, the total cluster signal would increase as the mean cluster size and hence the population of clusters in the beam is increased.

Momentum imaging
A momentum-imaging spectrometer described in detail elsewhere 3,4 was used for experimental measurements. The ions were measured in the true coincidence regime with special care taken to have good alignment between the photon beam and the cluster beam. Additionally, to minimise false coincidences, we used low count rates with 50 µs acquisition time windows.
The acquisition of each event is triggered by an electron emitted from the cluster/molecule after photoionisation. We assumed that the probability of k molecules being ionised within the acquisition time window t is a Poisson distribution with shape parameter λ, λ is measured as the electron count rate and when λ ≤ 7kHz the probability of measuring a false coincidence is estimated to be less than 5%. The events discussed in this paper are double-coincidence events where two ions were recorded within the 50 µs acquisition time window. These ions were produced by multiply charged parents. Cluster fragments larger than (CO 2 ) + 10 were not observed in coincidence with other fragments, possibly due to the low detection efficiency of the heavy ions. We, therefore, acknowledge that the measurements have underestimated the yield of larger cluster fragments.
In general, if the probability of detecting an ion α + is P (α), then the probability of detecting n α + ions scales as P (α) n . For the O + 2 /(CO 2 ) + m channel, the probability of detecting these two ions within the acquisition time window is given as P (O + 2 ) * P ((CO 2 ) + m ). As the value of P ((CO 2 ) + m ) decreases for larger m, 5 our detection efficiency of the O + 2 /(CO 2 ) + m channel also decreases for larger m.

Dalitz plot : Visualising momentum correlation of ions
For the ions measured in this experiment, we calculate the lab-frame initial momentum vectors and deduce information about the kinetics of the dissociation. Dalitz plots were used to visualize the momentum correlation between the ions detected in coincidence, the guide to read it is shown in Supplementary Fig. 2. For the O + 2 /CO + 2 channel in the Dalitz plots, we identified two regions of interest (Regions A and B as indicated in Fig. 2 in main text). Momentum filtering of individual ions was used to isolate different events and each region was investigated independently in order to determine it's dependence on cluster size.
The cluster size dependence of data points lying outside of the filtered Region A and B is not discussed.
Supplementary Figure 2: Visual guide to interpret the Dalitz plot. The plot shows the momentum correlation between the particles a, b and the undetected particle with residual momentum. The sum of momentum vectors of three particles is assumed to be zero and the coordinates of each data point are given by i = | P i | 2 i | P i | 2 for each particle i. For selected point on the plot, a = 0.56, b = 0.2 and res = 0.28. The coordinates of all data points in the XY plane lie inside the purple circle due to conservation of momentum.
The Dalitz plot for the O + 2 /(CO 2 ) + 2 and O + 2 /(CO 2 ) + 3 channels are shown in Supplementary The total yield of O + 2 at different photon energies In the article, we discussed the photo-dissociation mechanisms of CO 2 clusters ionised using soft X-rays at 320 eV and explored the cluster size dependence of O + 2 production. Supplementary Fig. 4 shows the total yield of the all O + 2 events from the cluster normalised w.r.t the O + 2 /C + channel from the CO 2 molecule for two separate data sets. Note that the ratio changes dramatically as a function of photon energy because the O + 2 /C + channel is extremely sensitive to the photon energy. Also, the background signal of the CO 2 molecules decreases slightly as the condensation parameter is increased to produces larger clusters. The yield also depends on the alignment between the cluster and photon beam. Overall, we observe that the CO 2 clusters are about 50-100 times more efficient in producing O + 2 compared to the CO 2 molecule irrespective of photon energy. Supplementary

Supplementary Note 3 -'2Y structures'
Theoretical studies of the core-ionized CO 2 clusters were done for localised and delocalised Auger decay leading to different dicationic states as shown in Supplementary Fig. 5. When analyzing the stability of dicationic (CO 2 ) 2+ m clusters, we identified an interesting type of covalently bound structure for those clusters composed of less than m = 12 CO 2 molecules.
Supplementary Fig. 6 shows these structures for singlet and triplet electronic multiplicities, S = 1 and S = 3 respectively. All geometries were optimized with Density Functional Theory, using the M06-2X/6-31++G(d) level of theory. As can be seen in this figure, all clusters with size above m = 4 show the same core structure formed by 4 CO 2 molecules, resembling two opposing 'Y's. Hence the term 'double-Y structures' or '2Y structures'. For cluster sizes bigger than m = 12, we did not identify 2Y structures. We consider that this is due to the fact that the two positive charges are more easily redistributed along the cluster, therefore, resulting in a structure more closely resembling to the structure of the neutral cluster. are significantly different for each of the two suggested multiplicities. Notice how the second Vertical Ionization Potential (VIP2) for the CO 2 clusters in the triplet S=3 state is lower in energy than the corresponding VIP2 in the singlet state. However, the AIPs for the singlet 2Y structures lie lower in energy, therefore their formation is a thermodynamically favourable process. In contrast, the AIPs for the triplet 2Y structures lie above both vertical ionization potentials.
For both multiplicities, the smallest (CO 2 ) 2+ m clusters (m < 12) are observed to effectively redistribute the two extra charges without breaking (coulombic explosion) by creating covalently bonded 2Y structures. An atomic charge analysis for these structures has been analysed in the framework of the Mulliken population analysis. It is well known that the Mulliken results are very basis dependent and, therefore, inconsistencies may be obtained.
In order to avoid them, we have also studied the atomic charges by employing the NBO (Natural Bond Orbital) method. Supplementary Fig. 8  structure. From here the system can evolve in two ways, either by a homolytic or a heterolytic cleavage.
Supplementary Figure 9: Potential Energy Surface exploration for the evolution of the homolytic cleavage of (CO 2 ) 2+ 4 after the formation of a 2Y structure. Relative energies (in eV) are referred to the neutral cluster. Relative energies in black text were calculated at a DFT-M062X/6-31++G(d) level of theory and corrected with the zero-point energy (ZPE). Energies in red text in brackets were computed as single-point energy calculations at the DLPNO-CCSD(T)/def2-TZVP level of theory over the geometries calculated at DFT level. Supplementary Fig. 9 represents the homolytic cleavage of the (CO 2 ) 2+ 4 2Y structure.
In this mechanism an intermediate, CO 2 CO 2+ 3 , is formed with the release of neutral CO and CO 2 . This doubly-charged fragment can also evolve in two different ways, one pathway has a higher energy barrier leading to the direct formation of CO + 2 and the other is lower energy path leading to the formation of O + 2 . This reaction pathway was also calculated using a higher level of theory, DLPNO-CCSD(T)/def2-TZVP. The DFT results show a very good agreement with those computed using CCSD(T).Thus we can be confident on the DFT relative energies and using CCSD(T) is not required for the characterization of all the Potential Energy Surfaces.
Supplementary Figure 10: Potential Energy Surface exploration for the evolution of the heterolytic cleavage of (CO 2 ) 2+ 4 after the formation of a 2Y structure. Relative energies (in eV) are referred to the neutral cluster and corrected with the zero-point energy (ZPE).
On the other hand, Supplementary Fig. 10 shows the heterolytic cleavage of the (CO 2 ) 2+ 4 2Y structure. In this case two singly-charged molecules are produced; CO 2 CO + 3 and CO 2 CO + .
Further fragmentation of each charged fragment barely differs in energy barriers. The highest-energy transition state for each mechanism only differs by 0.02 eV (30.55 eV for CO 2 CO + and 30.57 for CO 2 CO + 3 ). Therefore, the production of CO + 2 and O + 2 via this mechanism can simultaneously occur from the fragmentation of CO 2 CO + and CO 2 CO + 3 respectively.
Supplementary Figure 11: Potential Energy Surface exploration for the evolution of the heterolytic and homolytic cleavage of (CO 2 ) 2+ 3 after the formation of a 'hook'-like structure. Relative energies (in eV) are referred to the neutral cluster and corrected with the zero-point energy (ZPE).
Other cluster sizes, such as (CO 2 ) 2+ 3 , have also been considered, in contemplation of the possibility of other covalent dicationic species. In Supplementary Fig. 11 the evolution of a so-called 'hook' dicationic structure can again lead to a heterolytic and homolytic cleavage.
The homolytic cleavage, is higher in energy and leads to the production of the desired CO + 2 /O + 2 exit channel, while the heterolytic mechanism leads to the production of another interesting exit channel, CO + /O + 2 , also observed in our experiments.

Localized Auger
A local Auger decay leads to the production of a doubly ionised single molecule, CO

Supplementary Note 5 -Dissociation energies (DE) and vertical ionization potentials (VIP)
As explained in the main article, the CO + 2 /O + 2 exit channel, while interesting, is not the most populated one in the experiments. The channel CO + 2 /CO + 2 is observed to be the most prevalent. The results of our theoretical calculations also indicate that the channel CO + 2 /CO + 2 is the most favourable after ionization. These observations are also supported by considering the difference between the dissociation energy and the first + second vertical ionization potential, of the desired exit channel as shown in schematic in Supplementary Fig.   13 (a). Supplementary Fig. 13 Table 2 shows the percentage of trajectories where a (CO 2 ) 2+ 5 cluster evolved toward channels CO + 2 /CO + 2 , CO + 2 /O + 2 and CO + 2 /O + , for three values of internal excitation energy E exc = 25, 40 and 50 eV, and assuming the cluster in a singlet and in a triplet spin multiplicity. Our calculations were restricted to ground electronic state with singlet or triplet multiplicity, and at very specific excitation energy values, nevertheless, the same tendencies and a qualitative agreement is obtained from the comparison of the yield's ratio of the three channels between theory and experiments. The closest agreement between the simulations and experiment corresponds to the triplet spin multiplicity with excitation energy of 50 eV. The Auger spectra of a single CO 2 molecule shows the lowest energy peak centred at ∼ 50 eV, 9,10 and we thus expect similar excitation energies for the clusters.