State-selection by an Unconventional Mechanism in Dissociative Double Ionization of Sulphur Dioxide

Using multi-electron-ion coincidence measurements combined with high level calculations, we show that double ionization of SO 2 at 40.81 eV can be state selective. It leads to high energy products, in good yield, via a newly identified mechanim, which is likely to apply widely to multiple ionization by almost all impact processes. both and at point-like overall extract complete mass single and double ionization This is done coincident a (relatively in the one case, coincident detection of an electron pair within the right energy range in As references - single and double ionization mass spectra of SO 2 photoionized at 40.8 eV are shown in the SI. These spectra confirm that the most abundant products at this energy are O + +SO + and that SO 2+ is the only doubly-charged ion formed.

since the charge separation channel (A + +B + ) is located in energy well below the charge retaining channels (AB 2+ or A+B 2+ ). 1,2 Upon fragmentation, such dications are expected to produce the low energy fragments (A + +B + ) predominantly. All fragmentations tend to produce the lowest energy accessible products, but recent experimental and theoretical studies have shown that state-to-state fragmentations of small neutral molecules may lead to unexpected results. For instance, in VUV photodissociation of CO2 there is no formation of ground state CO+O species. Instead the O photoproduct is formed in the 1 D or the 1 S excited states, 3 whose dipole forbidden emissions are prominent features in the visible spectra of terrestrial atmospheres. 4 Similarly, the VUV photodissociation of N2 by ns or fs lasers leads to at least one excited atomic nitrogen instead of two 4 S ground state nitrogen atoms. 5,6 Very recently, Zhou et al. showed that the UV photolysis of H2S produces excited S( 1 D) atoms (+SH) instead of ground state S( 3 P). 7 Fragmentation of even quite large singly charged molecular ions can also be state-selective rather than statistical, of which a classical example is the dissociation of C2F6 + . 8 These state specific processes are important to planetary atmospheres, plasmas and photochemistry at the fs and shorter time scales. By contrast, no such unexpected behavior has been reported hitherto for molecular dications.
As prototypes of bond-breaking process in molecular dications, the SO2 2+ spectra and dissociations induced by photoionization or electron impact have been studied for many years accompanied by molecular structure calculations at different levels of theory. These works are reviewed in Ref. 9 , which presents a resolved spectrum of the doubly-charged ions as obtained by the TOF-PEPECO method, and interpreted using high-level molecular structure theory. Also, double ionization of the SO2 molecule has continued to attract attention, 10,11 partly because of the great importance of the molecule in atmospheric and astrophysical contexts. 12,13 Indeed, SO2 is common in volcanic and biological emissions on Earth 14,15 and it is a crucial chemical compound in sulphur physical chemistry in Earth, 13 Venus, 16 Io 17,18 and exoplanet terrestrial atmospheres, where its photochemistry leads to the formation of sulphuric acid or sulphuric acid aerosols with well-known deleterious effects such as acid rains. 19 From existing studies, we know that double ionization of SO2 at energies below the triple ionization limit leads to dissociation in four principal ways: (1) SO2 2+  O + + SO + or (2)  A vital characteristic of this technique is that both ions and electrons from ionization at a pointlike source are collected and detected with high overall efficiency, being uniquely capable to extract complete mass spectra from single and double ionization separately. This is done by requiring the coincident detection of a single photoelectron of appropriate (relatively high) energy in the one case, and coincident detection of an electron pair within the right energy range in the other. As references -single and double ionization mass spectra of SO2 photoionized at 40.8 eV are shown in the SI. These spectra confirm that the most abundant products at this energy are O + +SO + and that SO 2+ is the only doubly-charged ion formed.  Table S1 and quoted for C2v symmetry. Fig. 1 shows the spectra of fragment ion pairs compared to a more highly resolved double ionization spectrum acquired earlier. 22 The bands in this spectrum due to the direct population of SO2 2+ states located in the Franck-Condon (FC) zone accessed from SO2(X 1 A1) have been identified in previous work, 9 (Table S3). This channel is populated with substantial quantum yield (about 1/3 of the O + +SO + yield) at all energies above threshold, and specifically by decay from a state or states between 37 and 38 eV, seen as a broad peak in the resolved spectrum and apparently correlated with the population of the 3 1 A1 (4 1 A′ in Cs) state. Contributions of the triplet states lying in the same energy range cannot be ruled out, in particular the {1 3 A1, 2 3 B1, 2 3 B2} set of states. Of the channels not shown in Fig. 1, the one leading to the three-body products O + +S + +O (cf. Fig. S2), sets in weakly at ~ 37 eV (thermodynamic threshold at 35.1 eV) and shows no distinctive features. These products are formed by sequential decay of primary SO + , as reflected in Newton diagrams. Its onset energy agrees with the limit for ground-state products plus the observed total kinetic energy release (KER). Channel (3) will be discussed in a separate paper.
Insights into the fragmentation mechanisms can be obtained from the kinetic energies released in the fragmentations. The KER magnitudes can be extracted from TOF peak widths and shapes, and for the charge-separating channels this has been done several times before with generally concordant results, but without initial state selection. The most detailed measurements made possible by use of a position-sensitive ion detector, gave the full KER distributions for 40.8 eV photoionization. Although we can accurately select ranges of ionization energy (IE), the present experimental data are not ideally suited to the extraction of KERs. Nevertheless, we can determine the mean KEs released from dications formed in limited ionization energy ranges. To use the available statistics efficiently we have extracted mass spectra from 1 eV wide IE ranges which correspond quite well to the main features in Fig. 1.
Results are given in Table S4.
For the charge separation reaction forming O + +SO + we find that the mean KER varies slightly, between 4.5±0.2 to 4.8±0.2 eV (cf . Table S4) over the range of ionization energies (IEs) from 34 to 40 eV. For this two-body dissociation the distributions are quite narrow (FWHM ca. 2 eV) and centered at about 5 eV. When the kinetic energy release is added to the thermodynamic threshold energy, the result (29.6+4.5 eV=34.1 eV) agrees with the observed onset energy. This proves that the products are formed in their ground states as SO + (X 2 )+O + ( 4 Su), at least at threshold.
For the reaction(s) producing SO 2+ the KER is much smaller and produces roughly triangular peak shapes. In the 34-40 eV range, this two-body channel SO 2+ +O shows two distinct energy distributions: (i) a close to zero KER (0.0-0.2 eV) for 35<IE<37eV range and ~0.5 eV for 37<EI<40 eV (cf. Table S4). These KERs are derived from the peak widths (FWHM) by first subtracting the thermal width assuming that it and the release width add quadratically. There is a clear increase in energy release as the IE increases, but as the absolute magnitudes are uncertain, we give no error limits. It is apparent from Fig. 1 that production of the SO 2+ ion starts at the estimated thermodynamic limit for its formation, 35.3 eV. The estimate depends on a theoretical value for the double ionization energy of SO, 23 but this is sufficiently accurate to confirm that ground-state products, SO 2+ (X 1 Σ + )+O( 3 P) must be formed at threshold. The rise in KER as a function of IE seems continuous, with no special excursion at the energy of the state(s) near 37.5 eV, which decay specifically to these products.
To investigate the fragmentation dynamics of the SO2 2+ ions more deeply we have performed ab initio computations on the potential energy surfaces (PESs) of the singlet and triplet mainly two-hole (2h) electronic states located in the whole 33-40 eV range above SO2(X 1 A1). These computations are done at the CASSCF/MRCI/aug-cc-pV(Q+d)Z level for a wide range of nuclear configurations (cf. Figs. S3-S6), which show a high density of states, consistent with the expected number (20 to 30) of 2h orbital combinations. Also, we anticipate the existence of a larger number of three-hole-one particle (3h-1p) states accessible in the same regions. Such a high density of electronic states normally implies multiple mutual interactions by vibronic and spin-orbit interactions. In the main dissociation channel, for example, no singlet states correlate to the lowest asymptote, SO + (X 2 )+O + ( 4 Su), so intersystem crossings (from singlets) and internal conversions (from higher triplets) are needed to populate the lowest triplet that leads to these products (Fig. 2). The formation of the other products, in particular SO 2+ +O, apparently from specific states is intriguing since the surfaces leading to these products are embedded in a dense manifold of surfaces, mostly leading to the lowest dissociation channel (cf. O + ( 4 S)+SO + (X 2 Π) via the following mechanism (Fig. 2): (i) Internal conversions within the singlets manifold of states populating the lowest 1 A′ state.
(ii) Spin-orbit conversion from this 1 A′ to the lowest 3 A″ potential. This triplet can be also reached via internal conversion within the triplets. For the SO 2+ +O channel, we refer to Fig. 2, which presents the minimal energy paths (MEPs) of the 1 A′, 1 A″, 3 A′ and 3 A″ PESs along the SO distance, and to the KERs listed in Table S4. For IE< 37 eV, computations suggest the production of these fragments occurs on the 1 A′ and/or the 1 A″ MEPs. For 1 A′, we find a Morse-like potential that leads to a plateau at intermediate bond extension (ca. 4 Bohr) very close in energy to the SO 2+ (X 1 + )+O( 3 Pg) asymptote. We also found a 1 A″ potential with a small potential barrier (of 0.04 eV) before a level at almost exactly the same energy. We suggest that production of ground-state SO 2+ may occur by intersystem crossing from these surfaces to one of the triplet surfaces correlated to SO 2+ (X 1 + )+O( 3 Pg), which are expected to be relatively flat at these distance in the presence of charge-induced dipole attraction and the absence of Coulomb repulsion. At such distances other competitive curve crossings, which could lead to eventual SO + +O + production are less frequent (cf. Figs. S3-S6). With this interpretation, the computed KERs and the measured ones are the same within the error bars. But in the FC region the MEPs concerned are iso-energetic with high vibronic levels of SO2 2+ (X 1 g + /X 1 A1) and levels of the vibrationally resolved 1 1 A2 state in regions where there are multiple curve crossings. There is also a weak peak at 35.7 eV on the SO 2+ yield curve in Fig. 1 which suggests that some vertically accessed levels of the resolved 1 1 A2 state at 35.3 eV, decay into this channel rather than to the lowest energy products. It follows that to support the proposed mechanisms, we still need an explanation of how the long O-SO bond extension required can be reached in significant yield, without undergoing prior conversion to lower energy states.
For production of SO 2+ in the range of IE above 37 eV, we measure a KER of ~0.5 eV. This value is sufficiently different from the previous case to suggest that a different potential surface is involved. Fig. 2 shows that the formation of this product coincides with the occurrence of the SO 2+ (X 1 + )+O( 1 Dg) asymptote where there is no difficulty over the spin.
Computations indicate that the SO2 2+ (4 1 A′/3 1 A1) state which leads directly to these products can be populated by direct ionization in the FC zone. Fig. 2 shows that the SO2 2+ (4 1 A′/3 1 A1) surface exhibits a potential barrier toward dissociation of ~0.4 eV, which is in good agreement with the measured KER at these IEs (cf . Table S4). Again, for this route to be followed in the high observed yield after direct vertical double ionization in the FC zone, the expected competitive internal conversions would need to be somehow turned-off to allow the necessary bond extension. Because this seems both ad hoc and inherently unlikely, we looked for another explanation.
The clue to an alternative mechanism is given by Because the present technique is the only existing means of acquiring such detailed information on dicationic decays, there are only six other molecules whose fragmentation after double ionization can be compared with that of SO2. In BrCN 2+ , ICN 2+ 27 and CF3I 2+ 28 decays no state-specific behavior can be seen. The N2O 2+ ion decays radiatively from specific states, but it shows no other state-specific decay behavior. The CS2 2+ ion both emits fluorescence from two specific excited states and also decays to C + +S2 + from states in a limited energy range, 29 and is the closest to SO2 2+ in respect of this behavior. The electron-electron coincidence map for CS2 at 40.81 eV shows evidence of autoionization 29 akin to that in SO2, further confirming the validity of the proposed mechanism.
We have here identified a new non-conventional mechanism involved in the unimolecular decomposition of doubly charged molecular dications which accounts for the observation of energy-disfavored dissociation channels with substantial quantum yield in the decay of doubly ionized SO2. The mechanism almost certainly operates more widely. In the case of SO2, we have identified particular electronic states as probable surfaces upon which the dissociations to high energy products occur. The mechanism is one of indirect ionization, akin to the usual Auger effect, providing a non-vertical overall pathway to double ionization of molecules, outside the FC zone. In many cases the outcome will be indistinguishable from vertical double ionization in the Franck-Condon region, but in some cases it can permit energetically disfavored pathways to be followed to a much greater extent than would be expected on the basis of free internal energy flow.

Experimental Method
Multi-electron multi-ion coincidence experiments were done at 304 Å (40.8 eV), well above the estimated adiabatic single-photon double ionization onset 33.5 eV. 30 The TOF-PEPEPIPICO apparatus which has been described before 27

Theoretical Methods
All the ab-initio electronic calculations with different levels of theory were performed using the MOLPRO program suite. 31 In the present study, we mapped the SO2 2+ six lowest A′ and six lowest A′′ three-dimensional potential energy surfaces (PESs) of singlet and triplet spin multiplicities along the SO distance and the in-plane angle, =OSO varying from 40° to 180°. The other SO distance is kept fixed at 2.7 Bohr i.e. its value in SO2(X 1 A1) at equilibrium.
The PESs have been generated using the Complete Active Space Self Consistent Field (CASSCF) 32,33 approach followed by the internally contracted multi reference configuration interaction method (MRCI) 34 uncontracted configurations for the singlet electronic states. For the triplet electronic states, we considered more than 26 x 10 8 uncontracted configurations. For these calculations, the aug-cc-pV(Q+d)Z and the aug-cc-pVQZ basis sets of Dunning and co-workers were used to describe the S and O atom receptively. 37,38,39 In fact, adding the tight-d functions to describe the sulfurs improve the accuracy of the results as shown in different works. 40,41,42 Furthermore, to investigate the spin-obit coupling at the crossings between some electronic SO2 2+ states, the spin orbit integrals where computed using the CASSCF wave functions and the uncontracted spd cc-pVTZ basis set. We used the Breit-Pauli spin-orbit Hamiltonian as implemented in MOLPRO. Indeed, the spin-orbit integrals were evaluated, in Cartesian coordinates, over the CASSCF wavefunctions, where the effective Breit-Pauli SO operator, HSO, as implemented in MOLPRO was used. 43 To evaluate the energies of the dissociation limits of SO2 2+ forming the [SO+ O] 2+ , the partially spin restricted coupled cluster method including perturbative treatment of triple excitation (RCCSD(T)) 44,45,46 was used. For the RCCSD(T) computations we used the aug-cc-pV(5+d)Z basis set for sulfur and the aug-cc-pV5Z for oxygen.

Data availability
The experimental and theoretical datasets generated during and/or analysed during the current study are available from the corresponding authors on reasonable request.