Multi-State Electronic Quenching: Non-Adiabatic Pathways in NO 2+ + O2 X 3g- Scattering

The quenching of NO A 2 Σ + with O 2 as a collisional partner is important for combustion and atmospheric processes. There is still a lack of theoretical understanding of this event, especially concerning the nature of the different quenching pathways. In this work we provide potential energy surfaces (PESs) of 20 electronic states of this system. We computed the spin-doublet and spin-quartet PESs using SA-CASSCF and XMS-CASPT2. We ﬁnd two potential quenching pathways. The ﬁrst one ( Q 1 ) is a 2-step orientation-speciﬁc process. The system ﬁrst undergoes an electron transfer (NO + X 1 Σ + + O − 2 X 2 Π g ) at short distances, before crossing to lower neutral states, such as NO X 2 Π + O 2 a 1 ∆ g , O 2 b 1 Σ + g , O 2 X 3 Σ − g or even 2 O( 3 P). The second quenching pathway ( Q 2 ) is less orientation-dependent, and should be sudden without requiring the proximity conditioning Q 1 . The Q 2 cross-section will be enhanced with increasing initial vibrational level in both O 2 and NO. It is responsible for the production of NO X 2 Π with higher O 2 excited states, such as O 2 c 1 Σ − u , A (cid:48) 3 ∆ u , or A 3 Σ + u . Overall, this work provides a ﬁrst detailed theoretical investigation of the quenching of NO A 2 Σ + by O 2 X 3 Σ − g , as well as introducing a weighting scheme generally applicable to multireference, open-shell bimolecular systems. The effect of the spin-multiplicity on the different quenching pathways is also discussed.

The quenching of NO A 2 Σ + with O 2 as a collisional partner is important for combustion and atmospheric processes. There is still a lack of theoretical understanding of this event, especially concerning the nature of the different quenching pathways. In this work we provide potential energy surfaces (PESs) of 20 electronic states of this system. We computed the spin-doublet and spin-quartet PESs using SA-CASSCF and XMS-CASPT2. We find two potential quenching pathways. The first one (Q 1 ) is a 2-step orientation-specific process. The system first undergoes an electron transfer (NO + X 1 Σ + + O − 2 X 2 Π g ) at short distances, before crossing to lower neutral states, such as NO X 2 Π + O 2 a 1 ∆ g , O 2 b 1 Σ + g , O 2 X 3 Σ − g or even 2 O( 3 P). The second quenching pathway (Q 2 ) is less orientation-dependent, and should be sudden without requiring the proximity conditioning Q 1 . The Q 2 cross-section will be enhanced with increasing initial vibrational level in both O 2 and NO. It is responsible for the production of NO X 2 Π with higher O 2 excited states, such as O 2 c 1 Σ − u , A 3 ∆ u , or A 3 Σ + u . Overall, this work provides a first detailed theoretical investigation of the quenching of NO A 2 Σ + by O 2 X 3 Σ − g , as well as introducing a weighting scheme generally applicable to multireference, open-shell bimolecular systems. The effect of the spin-multiplicity on the different quenching pathways is also discussed.

I. INTRODUCTION
The nitric oxide radical has an important role in combustion 1 and atmospheric processes 2,3 . As such researchers have grown increasingly interested in studying this radical species. They have utilised Laser Induced Fluorescence (LIF) to measure its atmospheric concentration, probing the γ band transition NO X 2 Π ←− NO A 2 Σ + . However, these fluorescence measurements are impeded by a lack of radiative efficiency, which is due to quenching of NO A 2 Σ + by different collisional partners 4 . To address this problem NO A 2 Σ + quenching has been studied experimentally and computationally [5][6][7][8][9][10][11][12][13] with various quenchers, such as with NO X 2 Π , N 2 , O 2 , CO, CO 2 and H 2 O. Nevertheless, there is still a lack of theoretical work to explain the fate of NO A 2 Σ + electronic energy during NO A 2 Σ + + O 2 X 3 Σ − g quenching, which is of major interest since O 2 is the second most abundant species in the atmosphere. From previous experiments, several quenching mechanisms are already hypothesized. Early work by Asscher and Haas 14 found the quenching efficiency of NO A 2 Σ + to increase with the electron affinity of the quencher. Accordingly, they suggested that electron transfer can play an important role in the quenching process. This has been supported by the proposition of a harpoon mechanism by Paul et al. 15 , in agreement with their following results 16 for NO A 2 Σ + quenching at high temperatures. Such a mechanism is characterized by a two-step process, with the ionic state NO + X 1 Σ + + O − 2 X 2 Π g as a quenching intermediate. Later, Nee et al. 17 also concluded that a charge transfer (CT) mechanism was responsible of the quenching of NO A 2 Σ + by O 2 . Then, Settersten et al. 5 observed a product distribution proportional to the Franck-Condon overlap between NO A 2 Σ + and NO + X 1 Σ + . As a consequence, they also concluded that a harpoon mechanism was likely, but they also discussed the possibility of the formation of a collision complex. Indeed, on the other hand, a negative temperature dependence of the quenching cross-section was observed by Settersten et al. 6 , who proposed a well-depth of -41 cm −1 for the collision complex. This prediction was supported by Sánchez-González et al. 7 who predicted a comparable welldepth of -39 cm −1 for the collision complex. More recently, Few et al. 8 used Fourier Transformed IR spectroscopy to measure the vibrational population of NO X 2 Π and NO 2 quenching products. They found the non-reactive quenching of NO A 2 Σ + to be consistent with two quenching channels, either producing high or low vibrational levels in NO X 2 Π , being consistent with a long lived collision complex or a harpoon mechanism respectively. From all these experimental results, both quenching channels should be accessible at low energy collisions. It is very likely that their respective access should both be (essentially) barrierless. They also provided evidence to suggest the existence of different reactive quenching channels, producing NO 2 + O( 3 P) and supposedly NO X 2 Π + 2O( 3 P). Finally, Blackshaw et al. 9 recently supported the existence of a NO 3 collision complex due to long range attractive forces using velocity map imaging, and stressed on the importance of a conical intersection leading to NO X 2 Π (A ) population. They also found that O 2 c 1 Σ − u could be formed in its vibrational ground-state, which agrees with Few et al. 8 . The existence of a potential well on the NO A 2 Σ + + O 2 X 3 Σ − g PES due to long-range attractive forces has also been supported by our own recent theoretical work 18 .
To properly model such processes, it is important to investigate the shape of different regions on the PESs. First of all, the topology of the van der Waals (vdW) region on the excited state (NO A 2 Σ + + O 2 X 3 Σ − g ) potential energy surface (PES) help in understanding which orientations are preferred during 1.125Figure 1 Definition of Jacobi coordinates used for the NO + O 2 system the approach in a low-energy collision. Then, the short-range region of the initial excited-state describes which orientation will lead to the quenching event. Finally, the passage through a conical intersection will induce geometrical relaxations depending on the gradients and associated non-adiabatic couplings. The PESs involved in these quenching pathways define which products are accessible. Following our previous work 18 on the first step of this process, e.g. understanding the shape of the excited vdW PES of NO A 2 Σ + + O 2 X 3 Σ − g , we now focuses on the next step: identifying potential quenching pathways and their associated products. To do this, we explored 20 spin-doublet (D) and 9 spin-quartet (Q) PESs at the SA-CASSCF level of theory. Differing spin-states are possible as O 2 X 3 Σ − g has two unpaired electrons and NO A 2 Σ + has one, NO A 2 Σ + + O 2 X 3 Σ − g can therefore have a total spin of both a quartet and doublet. Additionally, we computed XMS-CASPT2 scans in the doublet manifold to describe important dynamic correlation effects on the accessibility and relaxation of the quenching event.

II. COMPUTATIONAL DETAILS
We performed our calculations using the MOLPRO 2021.3 ab initio quantum chemistry package 19,20 , unless specified otherwise. The energy convergence threshold was 1×10 −8 Hartree. In this paper, we use Jacobi 21 coordinates as shown in Fig.1.

A. Active-space and excited states
The PESs were computed at the CASSCF level 22,23 . This is because it can accurately model non-adiabatic effects, as well as multi-configurational character. This active space is composed of NO and O 2 2σ * ,3σ , π x , π y , π * x , π * y orbitals, as well as NO 4σ orbital, resulting in a CAS (19,13). A schematic representation of this active space at asymptotic inter-molecular separation is given in Figure 2.
To compute the PESs in different orientations, we used 1.125Figure 2 Qualitative energetic ordering of NO and O 2 active orbitals used in CASSCF (19,13) at asymptotic separation, with NO A 2 Σ + + O 2 X 3 Σ − g main configuration occupancy.
the C 1 point group, unless specified otherwise. As a consequence, many excited states had to be included in the CASSCF calculation for two reasons. Firstly, O 2 a 1 ∆ g and b 1 Σ + g states are lower in energy than NO A 2 Σ + state. In a vertical excitation framework at experimental bond-length for the states of interest, it means that NO X 2 Π degeneracy will couple with O 2 X, a and b states, leading to 8 doublet and 2 quartet surfaces lower in energy than NO A 2 Σ + + O 2 X 3 Σ − g . The state ordering in the asymptotic region (R = 15 Å) with fixed bond-length is presented in table I. Since Few et al. 8 suggested that O 2 c 1 Σ − u could be a potential quenching product, the active-space/number of state combination was set for spin-doublet states first. Accordingly, the minimum number of spin-doublet states required is 9. However, the NO A 2 Σ + + O 2 X 3 Σ − g state was challenging to converge due to the Rydberg nature of NO A 2 Σ + . The excited electron in NO A 2 Σ + populates the 4σ orbital which is mostly composed of diffuse s functions. Amongst the first 9 states, the NO A 2 Σ + + O 2 X 3 Σ − g is the only state with population in this orbital. The associated low state-averaged density leads to instability in the active-space, replacing the NO 4σ orbital by O 2 3σ * orbital, which persisted even when changing the weighting of the 9 th state. It was not possible to include simultaneously the NO 4σ and O 2 3σ * orbitals. Adding one extra virtual orbital led to the rotation of the NO 3σ * orbital into the active space, while adding two extra virtuals led to higher NO Rydberg orbitals. Similarly, including O 2 3σ * also led to instabilities in the active space, with unwanted rotations. To solve this problem we computed more excited states until the NO 4σ orbital was included in the active space. This technique works because to minimize the state average energy, it is better to include the NO 4σ orbital in the active space and have co-excited-states (excited NO and O 2 ) than highly energetic excited states of O 2 . Including the first 20 doublet states stabilised the active space as required. These excited-states are listed in table I. Additionally, because the system can exist both in the spin-doublet or spin-quartet framework, we computed two set of surfaces. However, all doublet states don't have a quartet counterpart, as those need to be composed of 2 NO states together with 3 O 2 states only, i.e., no 1 O 2 states coupled to 2 NO can give an overall quartet. As a result, a first set of surfaces (doublet and quartet) was computed at the SA(29)-CASSCF (19,13). Those surfaces will be referred to as SA-CASSCF surfaces. The second set of surfaces included spin-doublet states only, including a specific state weighting leading to SW(20)-CASSCF (19,13) calculations. These will be referred to as SW-CASSCF surfaces, and are discussed below. The experimental excitation energy of NO A 2 Σ + (5.45 eV 24 ) compares well with the calculated adiabatic value of 5.44 eV) (energy difference difference including zero-point corrections) for the super molecule at 50 Å with SW-CASSCF optimized bond-lengths. Asymptotic adiabatic excited energies for the O 2 a 1 ∆ g and O 2 b 1 Σ + g states (1.08 eV and 1.76 eV respectively) also compare well with experiment (0.98 eV and 1.64 eV respectively 24 ). We note that good agreement with experimental asymptotic energies can also be obtained from single molecule XMS-CASPT2 calculations for these states (1.139 eV and 1.845 eV respectively). Direct experimental comparison of adiabatic excitations for all states is problematic because of issues with stability of the active space for all states in the asymptotic region. We note however excellent agreement between CASPT2 and CCSD(T) state energies in intermediate regions, where applicable, and that CCSD(T) asymptotic excitation energies are in also good agreement with experiment 18 .

B. State-weighting
In a single-molecule system like NO, one would generally set-up the first 3 electronic states (2 NO X 2 Π micro-states, and NO A 2 Σ + state) to have a weight of 1 3 , arising from stateaveraging. However, a state-averaged CASSCF calculation of a bi-molecular system can introduce bias. Among the 20 bi-molecular doublet PESs we computed, the nitric oxide molecule is in its ground state in 16 surfaces, while NO A 2 Σ + is only present in 4. Accordingly, optimizing the orbitals in a state-average fashion would introduce a bias toward bi-molecular states including NO X 2 Π . To compensate for that, each bi-molecular state should be weighted so that the total weight of each single-molecule micro-state is equal within one molecule. The ideal weighting to provide a balanced description of each micro-state is given in table S2. Yet, it was not possible to use this ideal weighting for the SW-CASSCF surfaces, as it leads to root-flipping issues. Root-flipping arises when two states with different weighting are close in energy, and exchange their order, as well as their weight during an optimization step. As a solution, an identical weight was given to the upper states (9 th state and above), as described in table S2. In that way, the orbital optimization is less biased in the SW-CASSCF surfaces than in the SA-CASSCF surfaces, and the weights don't change the state ordering. Initial surfaces were computed with fixed experimental bond-length for the states of interest, i.e. 1.0634 Å for NO A 2 Σ + and 1.2075 Å for O 2 X 3 Σ − g 24 . Fixing the bondlengths as such describes the potential felt by NO A 2 Σ + and O 2 X 3 Σ − g in the Fourier transform infrared spectroscopy (FTIR) experiment of Few et al. 8 . For NO, it is a reasonable approach for two reasons. Firstly, they populated the lowest vibrational states of NO A 2 Σ + . Secondly, the potential well of NO A 2 Σ + is more narrow than an usual valence state because of its Rydberg character. Concerning O 2 , we also explore the PESs across O 2 bond-length in section III B. With the bond-length fixed, the system has 4 other internal coordinates to vary: the 3 angles Θ NO , Θ O 2 , Φ (the dihedral angle) and the inter-molecular distance R. To visualize the orientations to sample, we used the angle space shown in fig. 3. The inter-molecular distance R was one of the two dimensions of all our 2D scans shown below. It is essential to break NO diatomic symmetry to allow quenching from NO A 2 Σ + to NO X 2 Π . The second dimension was an angle with the other 2 fixed. We scanned through different unique geometries presented in fig. 3, namely linear (L), T-shape (T), hammer (H), parallel (P), cross (C), linear-O (LO) (with the oxygen of NO pointing towards O 2 ), and T-shape-O (TO) (with the oxygen of NO pointing towards O 2 ). Three scans were obtained by varying Θ NO from L to LO and from T to TO with Φ fixed at either 0 • (passing through P) or 90 • (passing through C). Four additional scans were obtained by changing Θ O 2 from L to T, H to P, H to C, and LO to TO. Another scan was performed while changing the dihedral angle, from P to C. All those scans were computed with both SW-CASSCF and SA-CASSCF. Lastly, another scan was computed along the dihedral angle with SW-CASSCF in a specific orientation, with Θ NO = 45 • and Θ O 2 = 90 • . The data for all 2D surfaces are available in ESI.
We used the t-aug-cc-pVTZ basis set for both O 2 and NO as diffuse functions are necessary to represent both the 4σ orbital of NO 18 , and possible ionic configurations with O 2 − and NO + . These calculations were obtained using the C 1 symmetry point group to keep our results comparable across all orientations.

D. XMS-CASPT2 scans
To explore the effect of dynamic correlation on the shape for the PESs, we performed multiple scans at the XMS-CASPT2 level in planar orientations 28,29 . These scans were performed using the internally contracted form of multi-reference Rayleigh-Schrödinger perturbation theory (RS2C) routine 28-30 of Molpro 2022.2. The CASSCF wavefunction of the previous 20 states was computed within the C s point group, resulting in 10 A and 10 A states. The state weighting described above (section II B) was used for fig. 5, but not for section III B due to CASSCF root-flipping issues at short distances. A smaller active space (11,9) and basis set (t-aug-cc-pVDZ) were used due to the computational cost of the following XMS-CASPT2 calculation. This smaller active space only contains the π and π * orbitals, together with NO 4σ orbital. We used an IPEA (Ionisation Potential Electron Affinity) level shift of 0.25 to compensate for CASPT2 systematic error in excitation energies and avoid intruder states 31 . Only the 10 A states were computed at the XMS-CASPT2 level as this is the symmetry of NO A 2 Σ + + O 2 X 3 Σ − g state in a planar geometry.

E. Non-adiabatic couplings
The non-adiabatic coupling matrix elements (NACME) χ iα of atom i on the axis α (α ∈ [x, y, z]) were computed analytically between NO A 2 Σ + + O 2 X 3 Σ − g and NO X 2 Π + O 2 c 1 Σ − u (A ) within the C s point group in planar geometries.
The scans were performed with the SW-CASSCF/t-aug-cc-pVTZ basis set as described in section II D. We used fixed bond-length (1.0634 Å) for NO and O 2 (1.24 Å). Then, the full length of the non-adiabatic coupling vector (NACV) ε was computed as follows: The full length of the non-adiabatic coupling vector is useful to understand non-radiative transition probabilities from one state to another. Indeed, this probability depends both on the energy difference between the 2 states, as well as the magnitude of their coupling. While the PESs in this work describe the former, the length of the NACV gives the latter.

III. RESULTS AND DISCUSSION
In this section, we first compare the doublet and quartet states across different orientations. We then investigate further the doublet PESs and identify a first quenching pathway Q 1 involving ionic configurations and discuss its accessibility. The associated geometrical relaxations are discussed, together with the possible quenching product. We also propose an alternative quenching channel Q 2 that doesn't involve ionic configurations and evaluate the NAC for a potential product.
A. Exploring the PESs across the angular space A total of 29 states, among which 20 doublets and 9 quartets, were plotted in 2 sets of 2D surfaces across the intermolecular distance R, and different set of angles with fixed bond-length as described in section II. The data points for all surfaces can be found in ESI material. Here we first discuss the SA-CASSCF surfaces, comparing the differences between the spin-quartet states and their spin-doublet counterpart. Furthermore, we describe the shape of the spin-doublet SW-CASSCF surfaces. We identify short-range geometries that present low-energy access to potential quenching pathways, and explain why those geometries provide such access by analysing the wave-function(s).

Comparison between doublet and quartet states
Firstly, the SA-CASSCF surfaces show that quartet states are degenerate with their spin-doublet counter-part in the asymptotic region. This is to be expected as the states are computed from the same orbital basis. However, this degeneracy is lifted in the short range region. This is due to spin-paired configurations stabilizing the spin-doublet states only. The c i coefficient of those spin-paired configurations increases as R decreases. Secondly, a common feature between all doublet and quartet surfaces, and across all orientations, is the repulsive wall at short distances, although, the shape and position along R is different. 1.125Figure 4 Doublet states obtained from SW-CASSCF/t-aug-cc-pVTZ calculation in the scan going from geometry T to TO.
The left plot (a) consist of a cut through the surfaces to observe the location of the entry to the quenching channel, and the right plot (b) corresponds to a zoom on the cut in polar coordinates. In polar coordinates, x=R×cos(Θ NO ), and y=R×sin(Θ NO ). The data point indicated corresponds to the maximum energy barrier discussed in III A 3. From bottom to top, the surfaces asymptotically correspond to NO X Thirdly, we observe a potential well on the 9 th adiabatic doublet PES (Figure 4). It is centered at Θ O 2 = 90 • , Θ NO = 45 • , Φ = 0 • and R = 2.5 Å which does not exist on the quartet surfaces. In this region, the main difference between the doublet and quartet state wave-functions is the increasing mixing of the charge-transfer configuration O − 2 X 2 Π g + NO + X 1 Σ + in the description of different adiabatic states with decreasing R. The ion-pair character could be identified both because of the increasing C i coefficient of the associated configurations, and because of large increase in the dipole moment of the state. Our results show that such configurations have an important role in the quenching process as proposed by earlier experimental studies 5-7,15-17 . Yet, rather than a harpoon mechanism (direct crossing with a ionic surface), the smooth transition from neutral to ionic resembles a diffuse avoided crossing region. This long-range mixing is potentially due to the diffuseness of the electronic density of both NO A 2 Σ + and O − 2 X 2 Π g . Since the quartet surfaces don't show any potential quenching pathways accessible with low collision energy within these coordinates, we now focus our efforts on the dou-blet surfaces.

Weight-adapted doublet surfaces
To accurately describe the different quenching pathways, we calculated another set of surfaces only including spindoublet states. For a better optimization of the orbitals, the bi-molecular states were weighted to avoid introducing a bias in excitation energies, as explained in section II B. As a consequence, the NO A 2 Σ + state is largely stabilized, lowering the energies of NO A 2 Σ + + O 2 X 3 Σ − g , O 2 a 1 ∆ g and O 2 b 1 Σ + g by almost 0.3 eV compared to the SA-CASSCF surfaces. Up to this point, only one 2D scan shows features that could lead to NO A 2 Σ + quenching with low translational energy. It goes from the T-shaped geometry with the nitrogen of NO pointing toward the center of O 2 , to the TO geometry, where the oxygen of NO points towards O 2 . The surfaces of this scan are presented in fig. 4a. The PES asymptotically corresponding to NO A 2 Σ + + O 2 X 3 Σ − g shows 3 important features with decreasing inter-molecular distance, in orientations centered around Θ NO = 45 • . Firstly, as R decreases, the wave-function of this state is increasingly described by the A configuration of the O − 2 X 2 Π g + NO + X 1 Σ + ionic state. Then, at short distances, approximately 2.6 Å, there is a conical intersection between the 9 th and 10 th adiabatic states. At this distance, they correspond to a crossing between the A and A states of O − 2 X 2 Π g + NO + X 1 Σ + . They do not couple in the plane, but the coupling is turned on by the dihedral angle, as it breaks the planar C s point group. The irreducible representations of NO A 2 Σ + + O 2 X 3 Σ − g and NO + X 1 Σ + + O − 2 X 2 Π g depending on the dihedral angle are given in table S3. Finally, both O − 2 X 2 Π g + NO + X 1 Σ + micro-states have a potential well at even shorter distances before hitting the repulsive wall.
3. Accessibility of Q 1 : CASSCF vs. CASPT2 In fig. 4a, the 9 th adiabatic surface (green, asymptotically NO A 2 Σ + + O 2 X 3 Σ − g ) shows a small potential energy barrier of approximately 1160 cm −1 , centered around 2.9 Å. Such a barrier could prevent access to the aforementioned potential well in a cold molecular beam experiment. However, as discussed below, we believe this potential energy barrier to be a computational artefact due to a lack of dynamical electronic correlation. Indeed, ion-pair states are more sensitive dynamical correlation than neutral states. This is the origin of the higher CASSCF barrier which is reduced at the CASPT2 level. Thus, we computed XMS-CASPT2 scans (see section II D) in the relevant orientation (Θ NO = 45 • , Θ O 2 = 90 • , Φ= 0 • ) to demonstrate the effect of increasing the amount of dynamical electronic correlation. Results in fig. 5 show two main differences compared to the CASSCF scan. Firstly, a long-range attractive potential is present in the CASPT2 scan. This has previously been noted when comparing CASPT2 to the accurate CCSD(T) in the VdW region. 18 . In addition, the potential energy barrier diminishes to approximately 20 cm −1 . Additionally, relaxing the NO bond-length along the approach does not decrease the barrier. This can be seen in Fig. S3 where we performed an XMS-CASPT2 scan with differing NO bond-lengths. This scan shows that the lowest energy barrier is obtained for the long-range optimized bond-length. This is to be expected as NO A 2 Σ + and NO + X 1 Σ + have very similar optimized bond-lengths (table  S4). To summarise, these results indicate that lower translational energies will lead to an increased number of collisions thanks to the long-range attractive forces. Additionally, some specific orientations can lead to an a priori, small or barrierless quenching pathway. 4. The role of orbital mixing in Q 1 quenching Before exploring further the details of the relaxation pathway we attempt to explain why the mixing between 1.125Figure 5 XMS-CASPT2/t-aug-cc-pVDZ scans of The 0 energy was set as the energy at 50 Å. the neutral and ionic configurations is orientation specific.
Indeed, an electron-transfer from NO A 2 Σ + to O 2 X 3 Σ − g should only depend on NO A 2 Σ + ionisation potential (IP) (5.4906±0.0004eV 10 ), O 2 X 3 Σ − g electron affinity (EA) (0.448±0.0060eV 32 ), and the inter-molecular distance that defines the coulomb attraction (CA) between the resulting ions. An electron transfer should occur when IP-CA≥EA, regardless of the orientation. Hence, we investigated which orbital mixing could explain this dependence. With Θ NO = 45 • , Θ O 2 = 90 • and Φ= 0 • , the O 2 in-plane π ( Figure S1) orbital has a strong mixing with NO in-plane π * orbital ( fig. 6). A lobe of the NO in-plane π * orbital points directly to the middle of the O 2 in-plane π orbital. An interpretation of this mixing is that in the NO A 2 Σ + + O 2 X 3 Σ − g state, where NO π * orbitals are empty, O 2 can relax some of its electronic density into NO π * , both increasing O 2 EA and decreasing NO IP to ultimately facilitate the electron transfer. According to this hypothesis, ionic configurations should be stabilised by this orbital overlap. To verify this, we scanned the PESs along the dihedral angle, rotating NO out of the plane, as this rotation should keep the former orbital mixing similar. The resulting surfaces are presented in fig. 6. This deformation breaks the in-plane C s symmetry to produce orientations belonging to the C 1 point group, until it reaches Φ= 90 • , which correspond to another C s geometry. The resulting PESs clearly display the same potential well along the dihedral rotation, which looks like a sink in polar coordinates. Hence, we consider this orbital overlap key to enter this quenching channel. With Φ= 90 • , both microstates of NO + X 1 Σ + + O − 2 X 2 Π g belong to the A irreducible representation, while NO A 2 Σ + + O 2 X 3 Σ − g is an A state (see table S3). Hence the coupling between NO A 2 Σ + + O 2 X 3 Σ − g and NO + X 1 Σ + + O − 2 X 2 Π g is turned off by turning on the dihedral angle. In planar geometries, the charge 1.125Figure 6 Adiabatic surfaces in polar coordinates computed at the SW-CASSCF/t-aug-cc-pVTZ level of theory across the dihedral rotation. In polar coordinates, x=R×cos(Φ), and y=R×sin(Φ). The front slice corresponds to Φ= 0 • . The associated orbital picture asymptotically corresponds to NO π * orbital, and was plotted with a 0.003 iso-density at R= 2.7 Å and Φ= 0 • . From bottom to top, the surfaces asymptotically correspond to NO transfer can occur if there is an overlap between NO 4σ orbital and O 2 in-plane π * orbital. The NO 4σ orbital is a diffuse stype Rydberg orbital, and so this overlap is non-zero at longrange in most of the angle space. The mixing between these two orbitals is anti-bonding. The associated rise in energy during the approach also facilitates the electron transfer. Then, because of associated changes in the wave-function (neutral to ionic) at short inter-molecular distances, further geometrical relaxation may occur along the different bond-lengths.

B. 2D PESs along O 2 bond-length
The experimental bond-length of each electronic states discussed in this paper are presented in table S4. From there, one can see that NO A 2 Σ + and NO + X 1 Σ + have similar optimized bond-length. This is not surprising since NO A 2 Σ + state can be seen as NO + with a surrounding diffuse Rydberg electron. However, O − 2 X 2 Π g has a much larger optimized bond-length than O 2 X 3 Σ − g . This is because of the extra electron that populates one of the two π * orbitals, weakening the bond. Hence, we explored this relaxation pathway. We calculated the PESs at the XMS-CASPT2 level across the stretching of O 2 with Θ NO = 45 • , Θ O 2 = 90 • , and Φ = 0 • . To discriminate between the states that couple together at a planar geometry, this scan was computed within the C s point group. Since NO A 2 Σ + belongs to the A irreducible representation, only A states are plotted in section III B. On fig. 7a, one can see the evolution of the gradient along O 2 bond-length for asymptotic NO A 2 Σ + + O 2 X 3 Σ − g state. When R > 3.5 Å, as the main configuration for O 2 corresponds to O 2 X 3 Σ − g , the computed optimized bond-length is approximately 1.2 Å. However, at short distances, the gradient of the PES evolves and drives the system towards longer O 2 bond-length. At the XMS-CASPT2 level, the short-range potential well described in fig. 7a is more pronounced than at the SW-CASSCF level (Fig. S2). Such shape of the PES has the effect of locking the two molecules in a temporary NO 3 complex while it relaxes through O 2 stretch.
As O 2 X, a and b states have similar optimized bond-length (table S4), extending O 2 bond-length destabilises those states, and stabilises O − 2 X 2 Π g as well as O 2 c 1 Σ − u excited states. This deformation closes the energetic gap between NO A 2 Σ + + O 2 X 3 Σ − g and NO X 2 Π + O 2 X, a and b states (8 micro-states). All of those 8 micro-states are purely repulsive between the two molecules, which can lead to the dissociation of the complex. Alternatively, the dissociation limit of O 2 into two O 3 P is energetically accessible as well, given the initial potential energy of NO A 2 Σ + + O 2 X 3 Σ − g . Finally, the surfaces also seems to show that NO 2 could be formed by an insertion of the nitrogen in the middle of the O 2 bond, eventually going through the D 3 h geometry. Although, such process would require a relaxation of NO bond-length, Θ NO , as well as O 2 stretch, which would be better described by dynamic calculations. A qualitative graphical description of this quenching pathway, denoted as Q 1 , is available in fig. 7a.
These results let us propose that Q 1 can then be described as follows: Regarding the vibrational distribution in the products, it is very likely that O 2 will be highly vibrationally excited. Concerning NO, the Franck-Condon (FC) overlap NO A 2 Σ + (ν = 0) to NO X 2 Π (ν = 0) is known to be large 5 . Since NO A 2 Σ + and NO + X 1 Σ + have similar optimized bondlength, it is very likely that NO + X 1 Σ + displays similar FC overlap, which would result in low vibrational level in quenched NO X 2 Π . However, due to the proximity between . The arrows correspond to the presumed pathway the system would undergo while being quenched through Q1. (b): 10 A states across stretching of O 2 bond-length in planar geometry at R = 15 Å. Computed with XMS-CASPT2/t-aug-cc-pVDZ. From bottom to top, at O 2 bond = 1.2 Å, the surfaces asymptotically correspond to NO , NO X 2 Π + O 2 A 3 ∆ u (dark green) and NO X 2 Π + O 2 A 3 Σ + u (magenta). The dotted lines correspond to the presumed pathway the system would undergo while being quenched through Q2.
NO and O 2 required by this quenching channel, it is very likely that there is some vibrational energy transfer from O 2 to NO. This would fit the experimental results concerning the first quenching channel described by Few et al. 8 .
Alternatively, fig. 7b shows a cut of the A PESs at the XMS-CASPT2 level along O 2 stretch. At the top, the cyan state (NO A 2 Σ + + O 2 a 1 ∆ g ) rise in energy with the stretch until it crosses with NO X 2 Π + O 2 c 1 Σ − u , A 3 ∆ u , and A 3 Σ + u states. Those three states go down in energy with the stretch because their O 2 optimised bond-length is longer than the other electronic states of O 2 (X 2 Π, a 1 ∆ g or b 1 Σ + g ). The same crossing is observed just below with the green surface (NO A 2 Σ + + O 2 X 3 Σ − g ) when O 2 bond-length is greater than 1.32 Å. This is the second quenching channel, Q 2 , proposed in this paper. The crossing between these PESs is not orientation specific, and doesn't depend on R. It only depends on the bond-length of the two molecules. This quenching can also happen on the quartet surfaces as long as the O 2 final electronic state is a spin-triplet state (A 3 ∆ u or A 3 Σ + u ). However, population transfer between different electronic states does not only depend on their energy difference, but also on their non-adiabatic couplings (NACs). The 1.125Figure 8 Length of the non-adiabatic coupling vector between NO A 2 Σ + + O 2 X 3 Σ − g and NO X 2 Π + O 2 c 1 Σ − u in planar geometries, at an inter-molecular distance of 5 Å.
Computed with SW-CASSCF/t-aug-cc-pVTZ. NACME between NO A 2 Σ + + O 2 X 3 Σ − g and NO X 2 Π + O 2 c 1 Σ − u were computed in planar orientations, as described in section II E. Figure S3 shows that the coupling exponentially increase with decreasing inter-molecular distance in different geometries. Also, the length of the non-adiabatic vector was computed in different orientations, at a fixed inter-molecular distance of 5 Å. Different maxima are found across the planar orientation, as shown in fig. 8, meaning that the quenching could happen in different orientations. The maximum in fig. 8 correspond to an orientation of Θ NO = 60 • with Θ O 2 = 130 • . The associated NAC vector are plotted in Figure S4, together with the gradient difference vector in Figure S5. Both correspond to a synchronised stretching of NO and O 2 , but are not perfectly parallel. They thus form a linearly independent basis for the branching space; the most physical representation being the separate stretching modes on each collision partner. Overall, Q 2 could lead to the following products:

IV. CONCLUSIONS
Overall, we computed several sets of spin-doublet and spinquartet PESs at the CASSCF and XMS-CASPT2 level. From our results, we propose two potential quenching pathways, Q 1 and Q 2 , that can lead to NO A 2 Σ + quenching when colliding with O 2 X 3 Σ − g . While Q 1 is limited to the spin-doublet framework, Q 2 can occur between both spin-doublet and spinquartet states. The ionic quenching pathway (Q 1 ) has an orientation-specific energetic access, but it shouldn't have an energy barrier. The gradient on the PES should lead to it because of long-range attractive forces. Q 2 should be favored by concerted vibrations of the two diatomic molecules, and high initial vibrational level of O 2 and NO. The cross-section of these quenching pathways will largely depends on the distribution of the collision energy, and should be estimated quantitatively only through dynamic calculations. Q 1 could lead to NO X 2 Π with either O 2 X 3 Σ − g , O 2 a 1 ∆ g , O 2 b 1 Σ + g , or even 2 O( 3 P), with high vibrational levels in O 2 due to the neutral -anion -neutral transition. Some of O 2 vibrational energy could be transferred to NO due to the proximity between the two molecules required by this quenching process. Q 2 should create mainly NO X 2 Π with high excited states in O 2 , like c 1 Σ − u , A 3 ∆ u , and A 3 Σ + u with probably lower vibrational level in NO, as this pathway does not require as much proximity as Q 1 . These two quenching channels are consistent with earlier experimental results 8 .

SUPPLEMENTARY INFORMATION
Potential energy surface data points are available as attached files in the Electronic Supplementary Information. These are in the folder surface which contains a sub-folder for each surface. Each sub-folder contains 2D arrays of energies labeled as Xi_surface.out, where X can be D or Q for spin-doublet and spin-quartet respectively, and i corresponds to the number of the state. Those sub-folders also contain the list of inter-molecular distances (R_list.out), the list of angles (param.out), and pictures of the corresponding surface.

CONFLICTS OF INTEREST
There are no conflicts to declare.