Theoretical Study of the Photochemical Mechanisms of the Electronic Quenching of NO(A2Σ+) with CH4, CH3OH, and CO2

The electronic quenching of NO(A2Σ+) with molecular partners occurs through complex non-adiabatic dynamics that occurs on multiple coupled potential energy surfaces. Moreover, the propensity for NO(A2Σ+) electronic quenching depends heavily on the strength and nature of the intermolecular interactions between NO(A2Σ+) and the molecular partner. In this paper, we explore the electronic quenching mechanisms of three systems: NO(A2Σ+) + CH4, NO(A2Σ+) + CH3OH, and NO(A2Σ+) + CO2. Using EOM-EA-CCSD calculations, we rationalize the very low electronic quenching cross-section of NO(A2Σ+) + CH4 as well as the outcomes observed in previous NO + CH4 photodissociation studies. Our analysis of NO(A2Σ+) + CH3OH suggests that it will undergo facile electronic quenching mediated by reducing the intermolecular distance and significantly stretching the O–H bond of CH3OH. For NO(A2Σ+) + CO2, intermolecular attractions lead to a series of low-energy ON–OCO conformations in which the CO2 is significantly bent. For both the NO(A2Σ+) + CH3OH and NO(A2Σ+) + CO2 systems, we see evidence of the harpoon mechanism and low-energy conical intersections between NO(A2Σ+) + M and NO(X2Π) + M. Overall, this work provides the first detailed theoretical study on the NO(A2Σ+) + M potential energy surface of each of these systems and will inform future velocity map imaging experiments.


■ INTRODUCTION
Nitric oxide (NO) is an atmospherically important free radical generated in the combustion of fossil fuels and biomass.−4 However, electronic quenching can interfere with the ability of LIF to provide an accurate quantification of NO.Electronic quenching occurs when a collision between NO(A 2 Σ + ) and an atomic or molecular partner causes nonradiative relaxation back to the electronic ground state, NO(X 2 Π).−7 Electronic quenching pathways can be separated into two general classes: reactive and nonreactive.In nonreactive electronic quenching, which is illustrated in eq 1, a collision between NO(A 2 Σ + ) and a molecular partner induces nonradiative relaxation down to NO(X 2 Π).The energy released by this nonradiative NO(A 2 Σ + ) → NO(X 2 Π) electronic transition is divided between the translational, rotational, and vibrational degrees of freedom of the two molecules.As a result, electronic quenching can cause a change in the vibrational and rotational states of both molecules.Equations 2a−2c illustrate different possible reactive electronic quenching pathways for NO(A 2 Σ + ) and CO 2 proposed in the literature. 8,9In all these, the collision between NO(A 2 Σ + ) and CO 2 causes a chemical reaction.−11 Table 1 summarizes the electronic quenching cross-section of NO(A 2 Σ + ) with four representative molecular partners.As seen in the table, H 2 O has the largest electronic quenching cross section, indicating that it is the most effective of these molecules at quenching NO(A 2 Σ + ).The electronic quenching cross section for NO(A 2 Σ + ) + CO 2 is also quite large at 68.3 Å 2 at 294 K.In contrast, NO(A 2 Σ + ) + CO has an electronic quenching cross section around 5% that of NO(A 2 Σ + ) + H 2 O while NO(A 2 Σ + ) + CH 4 does not undergo appreciable electronic quenching at 296 K.At lower temperatures, NO(A 2 Σ + ) + H 2 O, NO(A 2 Σ + ) + CO 2 , and NO(A 2 Σ + ) + CO have larger electronic quenching cross sections, consistent with collision complexes playing a role in facilitating the quenching.Though these experimental electronic quenching cross sections are helpful for correcting LIF measurements, they do not reveal the photochemical pathways responsible for electronic quenching.
−20 In the first of these, Few and co-workers used time-resolved Fourier-transform infrared emission spectroscopy to probe the pathways for nonreactive electronic quenching. 18Their analysis revealed a bimodal distribution of NO(X 2 Π, ν NO ′ = 2−22) products, suggesting the presence of two nonreactive electronic quenching channels.They attributed the formation of NO(X 2 Π) with high vibrational excitation to a channel with an O 2 (X 3 Σ g − ) or O 2 (a 1 Δ g ) coproduct.Few and co-workers speculated that the low ν NO ′ NO(X 2 Π) were generated in a second nonreactive electronic quenching channel which involves either the formation of O 2 (c 1 Σ u − ) via a harpoon mechanism or the generation of O 2 (X 3 Σ g − ) through an inefficient process.Recent work by Blackshaw and co-workers used velocity map imaging (VMI) to probe, with quantum state resolution, the formation of NO(X 2 Π, ν NO ′ = 0) through NO(A 2 Σ + ) + O 2 electronic quenching. 19By analyzing the total kinetic energy release (TKER), they concluded that O 2 receives a significant fraction of the available energy.Phase space theory simulations of the TKER distributions strongly suggested that the co-product of the nonreactive electronic quenching is O 2 (c 1 Σ u − ), consistent with most of the available energy inducing electronic excitation of the O 2 .Recent theoretical work by Souliéand Paterson, performed using the multireference methods SA-CASSCF and XMS-CASSCF, developed cuts of the NO + O 2 potential energy surfaces (PESs) to rationalize the experimental observations on this system. 20,21They argued that their PESs are consistent with two nonradiative relaxation channels for NO(A 2 Σ + ) + O 2 .The first proceeds through a transient ionpair generated by electron transfer from NO(A 2 Σ + ) to O 2 .This pathway exhibited a strong dependence on the intermolecular orientation and likely results in significant vibrational excitation in the products due to the large molecular geometry changes caused by the transient electron transfer.The second channel proceeds via conical intersections accessed when the O 2 bond length becomes significantly elongated.Collectively, the previous studies on NO(A 2 Σ + ) + O 2 illustrate the complex chemical physics that can be associated with NO(A 2 Σ + ) electronic quenching.
As summarized in Figure 1, our two recent computational studies provide insights into NO(A 2 Σ + ) + H 2 O and NO(A 2 Σ + ) + CO electronic quenching mechanisms. 22,23Here, we introduce the notation D 2 to represent the NO(A 2 Σ + ) + M electronic state, while D 0 and D 1 are associated with NO(X 2 Π) + M. Note that NO(X 2 Π) + M is doubly-degenerate at very large intermolecular distances but splits into two low-lying electronic states due to intermolecular interactions with the molecular partner.Figure 1a shows that the NO + H 2 O and NO + CO intermolecular interactions are attractive for the D 2

The Journal of Physical Chemistry A
state and strongly repulsive for D 1 .In our previous work, we demonstrated that the attractive intermolecular interactions on D 2 can be rationalized using the harpoon mechanism.Specifically, electron density shifts from the NO(A 2 Σ + ) 3sσ Rydberg orbital to the intermolecular partner's lowest unoccupied molecular orbital.This creates a transient ionpair that experiences attractive Coulombic intermolecular interactions.Figure 1 further shows that both NO + H 2 O and NO + CO possess D 1 −D 2 conical intersections that are energetically downhill in energy from the asymptotic limit.These D 2 −D 1 conical intersections facilitate the NO(A 2 Σ + ) + H 2 O and NO(A 2 Σ + ) + CO electronic quenching.Figure 1 also highlights significant differences between NO + H 2 O and NO + CO, which allow for a mechanistic rationalization of the large difference between the electronic quenching cross-sections of NO(A 2 Σ + ) + H 2 O and NO(A 2 Σ + ) + CO.NO + H 2 O has significantly stronger attractive intermolecular interactions on D 2 than NO + CO.Moreover, the D 2 PES of NO + H 2 O funnels a wide variety of initial intermolecular orientations to the same low-energy conformation shown in the inset of Figure 1a.In contrast, the NO + CO D 2 PES is much more anisotropic, with only a narrow range of initial intermolecular orientations producing attractive intermolecular interactions that lead to a D 2 −D 1 conical intersection.Figure 1b shows that the pathway to the D 2 −D 1 conical intersection for NO + H 2 O involves the significant stretching of one of the O−H bonds of H 2 O. Nonreactive electronic quenching will produce H 2 O with substantial vibrational excitation in an O−H local mode.Alternatively, a reactive electronic quenching channel is available, which will produce HONO and a H-atom, consistent with previous experimental observations made by Umemoto and co-workers. 24Only nonreactive electronic quenching is observed at low collision energies for NO(A 2 Σ + ) + CO.
In this computational study, three different systems are considered: NO(A 2 Σ + ) + CH 4 , NO(A 2 Σ + )+CH 3 OH, and NO(A 2 Σ + )+CO 2 .In choosing these systems, we sought to explore how the electronic structure of the molecular partner affects the photochemistry of NO(A 2 Σ + ).CH 4 is a larger polyatomic molecule than H 2 O with no low-lying π molecular orbitals (MOs).CO 2 represents a polyatomic extension of our previously studied CO, with multiple heavy atoms and frontier MOs with π-symmetry.CH 3 OH represents a hybrid between methane, which has a very small electronic quenching cross section, and H 2 O, which has a very large electronic quenching cross section.Before outlining the goals of our work, we summarize previous experimental and theoretical work on the NO + CH 4 and NO + CO 2 systems; to the best of our knowledge, the NO + CH 3 OH system has not been previously studied.
−28 Crespo-Otero et al. characterized the NO(X 2 Π) + CH 4 PESs at the RCCSD(T)/aug-cc-pVTZ level of theory. 25This study identified multiple complexes stabilized by intermolecular interactions between NO and a C−H bond or NO and a CH 3 face.The NO(X 2 Π) + CH 4 complexes were found to be significantly impacted by the Jahn−Teller effect, with the interaction potential driving geometric distortions away from more symmetric structures.As such, C s geometries were generally more stable than higher-symmetry C 3v geometries.The lowest-energy NO(X 2 Π) + CH 4 complex identified in this study has the NO interacting with a CH 3 face and oriented nearly perpendicular to the intermolecular bond.Experimentally, the earliest work used REMPI on the A ← X band to probe the structure of NO(X 2 Π) + CH 4 .Such spectra were interpreted by Musgrave et al. to reveal a vibrational progression in the NO bending mode that originally appeared to suggest effective C 3v structures for both NO(X 2 Π) + CH 4 and NO(A 2 Σ + ) + CH 4 . 26The direct observation of NO(X 2 Π) + CH 4 rovibrational transitions was accomplished by Wen and Meyer using near IR-REMPI double resonance spectroscopy. 27areful analysis of their spectra revealed that NO(X 2 Π) + CH 4 is best characterized as a Jahn−Teller distorted system with the NO preferentially oriented perpendicular to the intermolecular bond and undergoing large-amplitude vibrational motions.Recently, Kidwell and co-workers used VMI to probe the product state distributions associated with the infrared photodissociation of the NO(X 2 Π) + CH 4 complex. 28They rationalized the observed product state distributions through a careful analysis of symmetry-restrictions and a pair of Jahn− Teller NO(X 2 Π) + CH 4 PESs (D 0 and D 1 ).
The dissociation dynamics of the NO(A 2 Σ + ) + CH 4 complex have been experimentally interrogated in a series of studies by Lawrance and co-workers. 29,30These experiments begin by electronically exciting to above the dissociation threshold of NO(A 2 Σ + ) + CH 4 .The NO(A 2 Σ + ) generated by the fragmentation of the complex was then probed using REMPI.Changing the photon energy used in the REMPI scheme allows one to selectively analyze different ro-vibrational states of NO(A 2 Σ + ).Using VMI detection and energy conservation, Lawrance and co-workers obtained correlated product state distributions for the NO(A 2 Σ + ) and CH 4 products.The NO(A 2 Σ + ) is produced in a broad distribution of rotational states which span the entire energetically accessible range.In contrast, the dissociation of NO(A 2 Σ + ) + CH 4 strongly favors small changes to the rotational angular momentum of CH 4 , with the dominant product channels having ΔJ = 0 or ΔJ = 1 for CH 4 .Consistent with several previous studies, Lawrance and co-workers showed that NO + CH 4 is more strongly bound in the excited state than in the ground state.Specifically, the most recently measured NO(X 2 Π) + CH 4 and NO(A 2 Σ + ) + CH 4 binding energies are 108 ± 2 and 203 ± 2 cm −1 , respectively. 30Finally, note that while the NO(A 2 Σ + ) + CH 4 complex has been studied experimentally, it has not, to the best of our knowledge, been characterized computationally.
Turning to the NO(A 2 Σ + ) + CO 2 system, several experimental studies attempted to characterize the products of the reactive electronic quenching channel(s). 7,8,31,32Early work by Cohen and Heicklen used gas chromatography to identify CO as the major product of the reactive electronic quenching, which they attributed to eq 2b. 31 More recent work by Azcaŕate et al. utilized infrared spectroscopy to determine that 26% of NO(A 2 Σ + ) + CO 2 electronic quenching produces CO and NO 2 . 32Settersten and co-workers used LIF to monitor the kinetics associated with the regeneration of NO(X 2 Π, ν NO ′ = 0) through NO(A 2 Σ + ) + CO 2 electronic quenching. 7They found that approximately 60% of the electronic quenching results in the formation of NO(X 2 Π) in its vibrational ground state.Note that this population represents a portion of that following the nonreactive electronic quenching channel (eq 1) along with all the population following the reactive quenching channel given by eq 2a; the endothermicity of eq 2a ensures that NO(X 2 Π) will only be formed in its ground vibrational state.Interestingly, the The Journal of Physical Chemistry A formation of NO(X 2 Π, ν NO ′ = 0) accounts for only approximately 30% of the electronic quenching population for NO + CO, NO + O 2 , and NO + H 2 O. 7 The most complete experimental characterization of the NO(A 2 Σ + ) + CO 2 electronic quenching pathways was performed by Hancock and co-workers. 8Here, the reactive and nonreactive electronic quenching product distributions were measured using Fourier transform infrared emission spectroscopy.Focusing first on nonreactive electronic quenching, they found that CO 2 is produced in a wide range of vibrational states, with approximately 62% of the available energy ending up in the vibrational degrees of freedom of CO 2 .While NO(X 2 Π) is also observed in a broad distribution of vibrational states, approximately 80% of the electronic quenching results in the formation of NO(X 2 Π) with ν NO ′ = 0 or ν NO ′ = 1, with the major product being NO(X 2 Π) in its vibrational ground state.Hancock and co-workers attribute approximately 6% of this to nonreactive quenching (eq 1) based on an extrapolation of the distribution of NO(X 2 Π, ν NO ′ ≥ 2) population determined using infrared emission.The remaining 74% is ascribed to reactive quenching via eq 2a, along with additional nonreactive electronic quenching that exceeds that predicted by their extrapolation.
Hancock and co-workers further argue that the other reactive quenching pathways (eqs 2b and 2c) are inconsistent with the observed infrared emission spectra.Specifically, they rule out the second reactive electronic quenching pathway (eq 2b) due to the absence of vibrationally hot NO 2 and CO in the emission spectra.Because this reaction is highly exothermic, it should produce vibrationally excited NO 2 and CO.The formation of NO 2 observed in previous studies is instead ascribed to the reaction between O atoms generated via eq 2a and NO.Turning to eq 2c, the generated NCO is known to undergo reactions with NO.The infrared emission spectra associated with these reactions have previously been measured and are distinct from that measured by Hancock and coworkers.
In this study, we apply similar computational methodologies to those employed previously in the studies summarized in Figure 1.We identify the most important regions of the D 2 PES for NO + CH 4 , NO + CH 3 OH, and NO + CO 2 and develop a mechanistic analysis of the photochemical pathways responsible for electronic quenching in each of these systems.In doing so, we explore the viability of both nonreactive and reactive electronic quenching pathways.Throughout, we attempt to develop rationalizations for the experimentally known electronic quenching cross-sections and product state distributions.We additionally explore the extent to which the harpoon mechanism explains the long-range intermolecular attractive interactions in these systems.Finally, our work makes clear predictions about the NO(A 2 Σ + ) + M photochemistry of all three systems which will inform future experimental studies.

■ METHODS
As in our previous studies, we employ the equation-of-motion electron attachment coupled-cluster singles and doubles (EOM-EA-CCSD) methodology in this work. 22,23This allows us to use the closed-shell NO + + M reference to avoid the challenges associated with using an open-shell reference.EOM-EA-CCASD will accurately describe all target doublet states of NO + M whose dominant electron configurations can be generated by adding an electron to a virtual orbital of the NO + + M reference.−35 The EOM-EA-CCSD methodology provides dynamic electron correlation to the target states by incorporating electronic configurations that are doubly excited (and higher) from the NO + + M reference.EOM-EA-CCSD will have much lower accuracy for target states with significant double excitation character; such states would have dominant electronic configurations consistent with exciting an electron in the NO + + M reference and adding an electron to a virtual orbital. 33,34All states analyzed in this study were verified to consistently have dominant single excitation character; singly excited determinants accounted for over 93% of the D 0 , D 1 , and D 2 states for each geometry analyzed in this study.
Throughout this study, we employed a protocol designed to effectively balance accuracy and computational cost.The basis sets used for the geometry optimizations ranged from aug-cc-pVDZ to d-aug-cc-pVTZ and are clearly identified in the text.Larger basis sets were required for the geometry optimizations when the intermolecular interactions were especially weak and while mapping out pathways near D 2 −D 1 conical intersections.For NO−CO 2 , we performed the single-point calculations using the d-aug-cc-pVQZ basis set for the N and O atoms of NO and the aug-cc-pVQZ basis set for the C and O atoms of CO 2 ; we refer to this basis set below as AVQZ.Because NO(A 2 Σ + ) + M has significant Rydberg character, using a doubly augmented basis set is necessary to achieve accurate energetics.As described in the text, we did assess the impact of using the smaller d-aug-cc-pVTZ basis set for the single-point calculations and verified that doing so does not significantly affect the overall mechanistic picture; see Figures S24−S34 in the Supporting Information.Similar results were observed in our previous study of NO(A 2 Σ + ) + CO. 22 As a result, we used EOM-EA-CCSD/d-aug-cc-pVTZ to describe the energetics of NO(A 2 Σ + ) + CH 3 OH.Loẅdin spin densities and partial charges were investigated to determine the electronic properties of the D 2 and D 1 states.This analysis was performed at the EOM-EA-CCSD/aug-cc-pVTZ level of theory.All calculations were performed using Q-Chem 6.0 and analyzed using IQmol 3.0.1. 36For NO + CH 3 OH, we also analyzed natural transition orbitals using wxMacMolPlt. 37,38he weak intermolecular interactions associated with NO(A 2 Σ + ) + CH 4 necessitated a more careful treatment of basis set superposition and basis set incompleteness errors.As such, we performed a three-point extrapolation to the complete basis set (CBS) limit using the formula where E CBS is the extrapolated energy in the CBS limit and α is a fitting parameter. 39Our three-point extrapolations were based on N = 2, 3, and 4 with AVNZ taken to be d-aug-cc-pVNZ for the N and O atoms and aug-cc-pVNZ for C and H atoms. Figure S1 shows an example of our three-point extrapolation to the CBS limit.For all geometries analyzed, the R 2 of the linear regression was always greater than or equal to 0.999.

■ RESULTS AND DISCUSSION
NO + CH 4 .For the NO(A 2 Σ + ) + CH 4 system, we constructed a wide variety of initial intermolecular orientations and allowed each to optimize on D 2 using EOM-EA-CCSD/ aug-cc-pVTZ without any constraints.Each initial conforma- The Journal of Physical Chemistry A tion relaxed into one of four molecular geometries.Two of these, which are depicted in the inset of Figure 2, have the NO interacting with one of the CH 3 faces of CH 4 , while the other two have the NO interacting with a C−H bond.All four stationary points exhibited C 3v symmetry despite the geometry optimizations beginning from C 1 initial geometries.
In order to obtain accurate molecular geometries and interaction energies for the four stationary points, we reoptimized them using EOM-EA-CCSD with the d-aug-cc-pVTZ basis set for the N and O atoms and the aug-cc-pVTZ basis set for the C and H atoms. Harmonic vibrational frequency analysis demonstrated that the ON−H 3 CH and NO−H 3 CH complexes are true minima, while the ON−HCH 3 and NO−HCH 3 complexes are saddle points.For the saddle points, the vibrational modes with imaginary frequencies correspond to motions toward the ON−H 3 CH and NO− H 3 CH geometries.The minimum energy geometry of the ON−H 3 CH complex has an intermolecular distance of R NC = 3.17 Å and an electronic binding energy of 295.7 cm −1 in the CBS limit.This is in reasonable agreement with the NO(A 2 Σ + ) + CH 4 binding energy determined by recent velocity map imaging experiments, 203 ± 2 cm −1 . 30Better agreement with experiment would require the incorporation of anharmonic zero-point energy.Turning to the other minimum energy geometry, the NO−H 3 CH complex has an intermolecular distance of R OC = 3.25 Å and an electronic binding energy of 82.1 cm −1 .
Figure 2 shows the results of relaxed scans on D 2 for the ON−H 3 CH and NO−H 3 CH complexes along the intermolecular distance, R NC or R OC .We performed a three-point extrapolation to the CBS limit at every geometry in these scans and the energies are reported relative to the energy of the D 2 state when the molecules are 20 Å apart.The relative energies are negative for both potential energy curves at larger values of R, indicating attractive intermolecular interactions.Consistent with the analysis described above, Figure 2 shows that the ON−H 3 CH complex has a significantly deeper well than the NO−H 3 CH complex.Both potential energy curves become strongly repulsive at closer intermolecular distances.The molecular geometries remained in the C 3v point group throughout the attractive region of the PES and only dropped to lower symmetry in the repulsive region.
We now compare the D 2 PES with those of D 0 and D 1 .Previous computational work on NO(X 2 Π) + CH 4 revealed eight different local minima, encompassing ON−H 3 CH, NO− H 3 CH, ON−HCH 3 , and NO−HCH 3 complexes with both C 3v and C s symmetry. 25In contrast, NO(A 2 Σ + ) preferentially interacts with a CH 3 face of CH 4 ; we identified no minimumenergy geometries where NO(A 2 Σ + ) interacts with a C−H bond.Both theory and experiment agree that NO(X 2 Π) + CH 4 undergoes Jahn−Teller distortion away from C 3v structures, with the lowest energy conformations having C s symmetry with the NO oriented perpendicular to the intermolecular bond. 25,27In contrast, we find no evidence of Jahn−Teller distortions in the attractive region of the D 2 PES; all geometries in the attractive region of Figure 2 belonged to the C 3v point group.Repeating representative constrained geometry optimizations from molecular geometries distorted into the C 1 point group resulted in the same C 3v structures.Moreover, Figure S2 in the Supporting Information shows that the D 2 energy increases significantly as the O−N−C angle of ON−H 3 CH is decreased from 180°(C 3v ) to 90°(C s ). Figure S3 further shows the same behavior for the NO−H 3 CH complex.We posit that the preference for higher-symmetry structures on D 2 originates from the unpaired electron of NO residing in the more symmetric 3sσ MO instead of one of the 2pπ* MOs.
Our observation that the NO(A 2 Σ + ) + CH 4 PES supports only C 3v minimum energy structures is consistent with the recent experimental work reported by Lawrance and coworkers in which velocity map imaging was used to obtain correlated product state distributions for the photodissociation of NO(A 2 Σ + ) + CH 4 . 30Upon NO(X 2 Π) + CH 4 → NO(A 2 Σ + ) + CH 4 electronic excitation, the NO will re-orient itself from being perpendicular with the intermolecular bond (C s symmetry) to being oriented head-on with the CH 3 face (C 3v symmetry).As such, the vibrational relaxation on NO(A 2 Σ + ) + CH 4 will include hindered rotation of the NO resulting from a torque imposed on the NO by the D 2 PES.This supports the experimental observation that the photodissociation of NO(A 2 Σ + ) + CH 4 produces NO(A 2 Σ + ) in a broad range of final rotational states, including the highest rotational state that was energetically allowed under the experimental conditions.In contrast, the NO(A 2 Σ + ) + CH 4 photodissociation imparts little rotational energy to the CH 4 .
Figure 3 shows how the energies of the other electronic states vary with the intermolecular distance, R NC , for the ON− H 3 CH complex.The energy gap between the D 2 and D 1 states remain above 3.94 eV across all intermolecular distances despite the D 2 potential energy curve ranging from weakly attractive to strongly repulsive.As such, there is no pathway for electronic quenching at low-collision energies for NO(A 2 Σ + ) + CH 4 in the ON−H 3 CH conformation.Figure S4 in the Supporting Information shows that the same behavior is observed with the NO−H 3 CH conformation.This is consistent with the experimental observation that the electronic quenching cross section of NO(A 2 Σ + ) + CH 4 at T = 296 K is less than 0.001 Å 2 . 12O + CH 3 OH.We begin our analysis of this system by considering intermolecular orientations in which the NO-(A 2 Σ + ) is interacting with the CH 3 face of CH 3 OH.Figure 4a demonstrates that the D 2 PES supports weakly bound ON− H 3 COH and NO−H 3 COH complexes.For the ON−H 3 COH orientation, the strongest intermolecular attractions on D 2 occur at an intermolecular distance of 3.1 Å, where the energy The Journal of Physical Chemistry A is −0.018 eV relative to an optimized geometry with an intermolecular distance of 20 Å.The most stable NO− H 3 COH geometry occurs at a significantly larger intermolecular distance, 4.6 Å, but has a comparable energy, −0.017 eV.Both minimum-energy geometries exhibit nearly C 3v symmetry and have large D 2 −D 1 energy gaps of over 4.8 eV, suggesting that these pathways do not facilitate electronic quenching.Finally, as discussed in more detail in Figure S6 in the Supporting Information, the weak nature of these intermolecular attractions necessitated using a larger basis set for the geometry optimizations consisting of d-aug-cc-pVTZ for the C, N, and O atoms and aug-cc-pVDZ for the H atoms.
In order to ascertain the overall importance of the ON-H 3 COH complexes on the NO(A 2 Σ + ) + CH 3 OH photochemistry, we show in Figure 4b how the D 2 energy depends on the intermolecular N−C−O bond angle (θ NCO ) at fixed intermolecular distances, R NC , between the nitrogen atom of NO and the carbon atom of CH 3 OH.This varies the relative intermolecular orientation from the NO being head-on with the CH 3 face (θ NCO = 180°) to the NO approaching the methyl group from the side (θ NCO = 90°).At all four intermolecular distances considered in Figure 4b, the energy of the D 2 state is lower when the NO interacts with the methyl group from the side rather than head-on.Figure 4b shows that when R NC ≥ 3.6 Å, the D 2 potential supports a nearly barrierless transition from the local minimum at θ NCO = 180°t o the lower-energy conformations with θ NCO ≤ 90°.As R NC decreases, a barrier grows between the local minimum at θ NCO = 180°and the conformations with θ NCO ≤ 90°.Overall, the flatness of the D 2 potential at R NC ≥ 3.6 Å and θ NCO > 130°a nd the development of a barrier at smaller R NC suggest that collisions that begin with the NO approaching the methyl group can become trapped in the local minimum at θ NCO = 180°.For those collisions that reach conformations with θ ≤ 90°, unconstrained geometry optimizations on D 2 show that the system will ultimately reach conformations in which the nitrogen of NO is interacting with the oxygen of CH 3 OH.Finally, Figure S7 in the Supporting Information shows that NO−H 3 COH conformations with θ OCO = 180°are separated from lower-energy conformations with θ OCO = 90°by a very small barrier of 0.002−0.003eV.Unconstrained geometry optimizations from conformations with θ OCO = 90°lead to geometries in which the oxygen of NO is interacting with the oxygen of CH 3 OH.
Figure 5a shows how the electronic energies of the D 0 , D 1 , and D 2 states varies with the intermolecular distance, R NO , for conformations in which the nitrogen of NO interacts with the oxygen of CH 3 OH.At large intermolecular distances, R NO > 3.75 Å, the intermolecular interactions are very weakly attractive on D 2 .As the molecules move closer together, the strength of the intermolecular attractions increases significantly on D 2 , growing from E 0.09 eV when R NO = 1.78 Å.In contrast, the D 0 and D 1 states become strongly repulsive as the intermolecular distance is reduced, with E D 1 increasing by over 2.75 eV when R NO decreases from 3.95 to 1.78 Å. Figure S8 in the Supporting Information shows that the D 3 , D 4 , and D 5 states remain well separated from the D 2 throughout this range of intermolecular distances.Finally, note that the abrupt end to this figure reflects our difficulty obtaining converged optimized geometries at smaller intermolecular distances due to the presence

The Journal of Physical Chemistry A
of a D 2 −D 1 conical intersection; we will return to this point below.
In order to understand the physical origin of the intermolecular attractions on D 2 , we analyze in Figure S9 in the Supporting Information the total Loẅdin spin densities and partial charges on NO and CH 3 OH as a function of R NO .At large intermolecular distances, both molecules are neutral and the spin density is localized on the NO.As the molecules move closer together, the spin density begins to delocalize onto CH 3 OH, eventually becoming primarily localized onto CH 3 OH for R NO ≤ 2.55 Å.As this occurs, NO develops a partial positive charge and CH 3 OH a partial negative charge, consistent with intermolecular electron transfer.−43 In Figures S10−S12, we analyze the natural transition orbitals associated with the D 0 → D 1 and D 0 → D 2 transitions at representative intermolecular distances.Figure S10 shows that at large R NO , the D 1 and D 2 states exhibit clear 2pπ* and 3sσ electronic character, respectively.As the molecules move closer together, the singly occupied molecular orbital (SOMO) of the D 2 state becomes increasingly delocalized between the two molecules, with the region of space around the OH group of methanol especially gaining electron density.At R NO = 1.78 Å, the SOMO for D 2 has its greatest amplitude around the OH group of CH 3 OH; see Figure S12 in the Supporting Information.This further demonstrates that the D 0 → D 2 transition develops significant charge-transfer character as R NO is reduced, consistent with the harpoon mechanism.
Returning to Figure 5, panel (b) shows clear evidence for a D 2 −D 1 conical intersection at R NO = 1.78 Å and an extended O−H bond length of r OH ≈ 1.33 Å.On D 1 , stretching the O− H bond is associated with a significant increase in energy.In contrast, the D 2 potential is nearly flat along this coordinate, with the energy decreasing from −0.61 to −0.68 eV along the path shown in Figure 5b. Figure S13 in the Supporting Information shows a similar D 2 −D 1 conical intersection at an alternative conformation in which the NO lies above the methyl group of CH 3 OH and R NO = 1.78 Å. Figure S14 in the Supporting Information shows that at larger intermolecular distances, increasing r OH is not as energetically favorable on D 2 and does not as readily decrease E E D D is thermodynamically feasible.Specifically, the electronic ΔE = −52.8kcal/mol when both products are generated in their ground electronic states and CH 3 ONO is in its transconformation.
We additionally considered potential electronic quenching pathways associated with stretching the O−C bond of methanol, r OC .From a thermodynamic perspective, the reaction is feasible, with an electronic ΔE = −77.8kcal/mol when both products are generated in their ground electronic states and HONO is in its trans-conformation.In Figure S15 in the Supporting Information, we evaluate how the energies of the  The Journal of Physical Chemistry A intersection in Figure S15 along with the significant energetic cost of increasing r OC suggest that this pathway will not play an important role in NO(A 2 Σ + ) + CH 3 OH photochemistry.NO + CO 2 .We first considered the possibility that NO(A 2 Σ + ) favorably interacts with the carbon atom of CO 2 .We analyzed both ON−CO 2 and NO−CO 2 complexes and varied the intermolecular distance and the angle NO makes with the CO 2 (θ ONC for ON−CO 2 or θ NOC for NO−CO 2 ).Throughout these constrained geometry optimizations, the atom of NO interacting with CO 2 was constrained to be at a 90°angle from one of the C�O bonds.As shown in Figure S16 in the Supporting Information, the intermolecular interactions in these conformations become increasingly repulsive as the intermolecular distance is reduced from 4.0 to 3.0 Å.This is true for all intermolecular orientations that we considered.As a result, we did not further consider conformations in which the NO(A 2 Σ + ) directly interacts with the carbon atom of CO 2 .
We next considered pathways in which the nitrogen atom of NO interacts with one of the oxygen atoms of CO 2 .Figure 6 shows how the energy of the D 2 state varies with the intermolecular bond angle θ NOC for the larger intermolecular distances, R NO , of 3.5, 3.3, 3.1, and 2.9 Å.These data were obtained by performing constrained geometry optimizations on D 2 at fixed values of θ NOC and R NO using the EOM-EA-CCSD/AVQZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory; the AVQZ basis consists of d-aug-cc-pVQZ for the N and O atoms of NO and aug-cc-pVQZ for the C and O atoms of 2 .The analyzed in Figure 6 are all nearly planar; non-planar geometries were consistently found to be higher in energy.For each of the intermolecular distances, the energy increases as θ NOC decreases, suggesting an energetic preference for the nitrogen atom of NO and an oxygen atom of CO 2 to approach each other nearly head-on.Additionally, the intermolecular attractions between the two molecules increase as R NO decreases, causing the two molecules to move closer together.
In Figures S17−S19 in the Supporting Information, we compare the data summarized in Figure 6 to conformations in which the oxygen atom of NO is interacting with one of the oxygen atoms of CO 2 .The qualitative picture for these NO + OCO conformations is the same as that shown in Figure 6.However, the energies of the NO + OCO conformations are consistently less attractive than the corresponding ON + OCO conformations by as much as 0.023 eV.This indicates that while there are attractive intermolecular interactions for NO + OCO conformations, they are not as favorable as the orientations shown in Figure 6.
As shown in Figure 7, the cuts of the D 2 PES along θ NOC are dramatically different for intermolecular distances R ON ≤ 2.8 Å then what is seen in Figure 6.For R NO = 2.8 Å and R NO = 2.7 Å, there is a general increase in energy as θ NOC decreases until a barrier is reached around θ NOC = 97°and E 0.009 eV for R NO = 2.7 Å.At smaller θ NOC after the barrier, the energy sharply decreases as CO 2 adopts a bent conformation with a O−C−O bond angle of around 140°.In addition, the linear to bent isomerization of CO 2 is accompanied by an elongation of both C−O bond lengths, r OC , with the largest elongation occurring at the C−O bond that is interacting with the NO.For example, at R ON = 2.7 Å, the r OC are 1.167 and 1.172 Å when θ NOC = 180°and 1.218 and 1.258 Å when θ NOC = 80°.The barrier preceding the linear to bent isomerization of CO 2 further decreases at R NO = 2.6 Å and disappears for R NO ≤ 2.5 Å.As such, the D 2 PES drives ON−OCO into conformations in which the CO 2 is significantly bent.Finally, Figure 7 shows that the strength of the attractive intermolecular interactions between the two molecules increases as the molecules move closer together.For example, at R NO = 2.8 Å, the minimum energy is −0.12 eV, while at R NO = 2.4 Å, the minimum energy is −0.50 eV.At the minimum energy geometry with R NO = 2.4 Å, the O−C−O angle is 138.4°and the r OC are 1.210 and 1.268 Å.
Figure S20 shows the energies of the D 1 and D 2 states as a function of θ NOC for the representative intermolecular distances R NO = 2.8 Å, R NO = 2.6 Å, and R NO = 2.4 Å.The transition from linear to bent CO 2 , which causes a drop in the energy of the D 2 state, results in a significant increase in the energy of the D 1 state.As a result, this isomerization causes the two states to become significantly closer together in energy.

The Journal of Physical Chemistry
, is 4.80 eV when θ NOC = 180°and 2.68 eV when θ NOC = 160°, where CO 2 first isomerizes into a bent geometry.Collectively, our analysis suggests that decreasing R NO and the associated linear-to-bent isomerization of CO 2 play a significant role in pushing ON + CO 2 toward a D 2 −D 1 conical intersection that can facilitate electronic quenching.
Figure S21 in the Supporting Information extends the analysis shown in Figure 7 to NO + OCO conformations.Similar to the R NO = 2.8 Å and R NO = 2.7 Å data in Figure 7, the energy of D 2 initially increases as θ OOC decreases, reaching a barrier that precedes a drop in energy associated with CO 2 adopting a bent geometry.The energies in Figure S21 are significantly less negative than those shown in Figure 7, indicative of weaker intermolecular attractions in NO + OCO conformations than ON + OCO conformations.The intermolecular attractions in NO + OCO conformations become even weaker as the molecules move closer together.
Moreover, the barrier preceding the linear-to-bent isomerization of CO 2 in the NO + OCO conformations fall above the asymptotic limit.This is quite different from Figure 7, where the barrier to bent CO 2 for ON + OCO conformations consistently lies below the asymptotic limit and eventually disappears at closer intermolecular distances.Figure S21 therefore provides additional support for NO + OCO conformations being significantly less important for electronic quenching than ON−OCO conformations.
In order to better understand the origin of the attractive intermolecular interactions between NO(A 2 Σ ) and CO 2 shown in Figures 6 and 7, we analyze in Figures 8 and 9 the Loẅdin partial charges and spin densities for ON + OCO conformations at R ON = 2.9 and R ON = 2.5 Å.These figures additionally show the singly occupied molecule orbital (SOMO) of the D 2 state at representative θ NOC .The SOMOs shown in Figure 8 demonstrate that at R ON = 2.9 Å, an intermolecular distance where the linear-to-bent isomer-  Note that the electronic character of the SOMO changes from 3sσ on NO at θ NOC = 180°to 2pπ* on CO 2 for θ NOC < 140°.This, along with the increased charge and spin density on CO 2 for θ NOC < 140°, is consistent with electron transfer occurring between the two molecules, i.e., the harpoon mechanism.
The Journal of Physical Chemistry A ization of CO 2 does not occur, the electron in the 3sσ Rydberg orbital on NO becomes somewhat delocalized onto CO 2 as θ NOC is reduced.As a result, the Loẅdin analysis reveals evidence of charge-transfer, with CO 2 gaining a partial charge ranging from −0.19 to −0.37 and a spin density ranging from 0.20 to 0.38. Figure 9 shows that at R ON = 2.5, a distance where CO 2 does become bent for θ NOC < 140°, there is a dramatic change in the distribution of electron density in the complex.Specifically, CO 2 develops a partial charge of approximately −0.77 and nearly all of the spin density becomes localized on CO 2 , both of which clearly indicate electron transfer.At the same time, the SOMO changes from having 3sσ character on NO to 2pπ* character on the CO 2 .As such, the un-paired electron has transferred from a diffuse Rydberg orbital centered on NO to the LUMO of CO 2 .
Collectively, the analysis presented in Figure 9 allows us to rationalize several aspects of the D 2 PES shown in Figure 7. Specifically, the strong intermolecular attractions on the D 2 state of ON + OCO originate from the harpoon mechanism in which electron transfer from NO to CO 2 creates a transient ion-pair which coulombically attract one another.Moreover, the linear-to-bent isomerization of CO 2 reflects electron transfer from NO(A 2 Σ + ) to CO 2 as the CO 2 radical anion is experimentally known to exist in a significantly bent geometry with an O−C−O angle of approximately 127°± 8°. 44n overview of the photochemical pathway responsible for NO(A 2 Σ + ) + CO 2 electronic quenching is provided in Figure 10.Note that we employed the larger aug-cc-pVTZ basis set for these geometry optimizations to obtain an improved description of the region in the vicinity of the D 2 −D 1 conical intersection.Consistent with Figure 6, the two molecules initially approach each other head-on in a linear arrangement and experience relatively weak intermolecular attractions ranging from −0.03 to −0.11 eV as R NO is reduced.As in Figure 7, the sudden drop in E D 2 at R NO = 2.5 Å is associated with CO 2 adopting a bent conformation.As shown by the inset in Figure 10, the lowest energy complex at this intermolecular distance is non-planar.The D 2 potential becomes significantly more attractive after the linear-to-bent isomerization of the CO 2 .Figure 10  Figure S23 in the Supporting Information shows an alternative pathway to a D 2 −D 1 conical intersection for ON + OCO in which the O atom of NO remains oriented away from the C atom of CO 2 throughout.Beginning at R NO = 2.6 Å, the system adopts a planar conformation with a bent CO 2 .As in Figure 10, the linear-to-bent isomerization of CO 2 is associated with a significant increase in the attractive intermolecular interactions on D We now turn to the connection between our computational analysis of NO(A 2 Σ + ) + CO 2 photochemistry and existing experimental data.The large room temperature electronic quenching cross section of NO(A 2 Σ + ) + CO 2 reported in Table 1 is consistent with the presence of multiple pathways to D 2 −D 1 conical intersections that are downhill in energy from the asymptotic limit.Moreover, our analysis suggests that the D 2 PES can effectively funnel a wide range of initial intermolecular orientations to D 2 −D 1 conical intersections, particularly those in which the N atom of NO is oriented toward an O atom of CO 2 .The significant distortions to the geometry of CO 2 observed at our approximate D 2 −D 1 conical intersections are consistent with the experimental observation that NO(A 2 Σ + ) + CO 2 electronic quenching releases a large fraction of the available energy, approximately 62%, into the vibrational degrees of freedom of CO 2 . 8In particular, the pathways shown in Figures 10 and S23 are consistent with the formation of CO 2 with significant vibrational excitation in its bending and asymmetric stretching modes.Additionally, experiments show a clear preference for NO(X 2 Π) being produced with ν NO ′ = 0 or ν NO ′ = 1. 7This is consistent with the fact that the NO geometry is not nearly as distorted at the D 2 − D 1 conical intersection as CO 2 ; the N−O bond length is 1.09 Å at the D 2 −D 1 conical intersection and 1.16 Å at the equilibrium geometry of NO(X 2 Π).
Turning to reactive quenching, we do not believe that the pathways shown in Figures 10 and S23   The Journal of Physical Chemistry A significantly greater amount, 0.36−0.41Å.Second, because the most elongated O−C bond in Figures 10 and S23 contains the O atom that is interacting with the NO, these molecular geometries appear more consistent with the formation of NO 2 + CO via eq 2b than NO(X 2 Π) + CO + O( 3 P).This contrasts with the pathways shown in Figures 1 and 5 where the H atom of the stretched O−H bond is not directly interacting with the NO and hence can freely dissociate from the complex.Finally, the geometries of the D 2 −D 1 conical intersections shown in Figures 10 and S23 more closely resemble NO + CO 2 than the products of either eq 2a or 2b, consistent with nonreactive electronic quenching.Moreover, upon internal conversion from D 2 to D 1 , the D 1 PES will rapidly drive the NO(X 2 Π) and CO 2 molecules apart.
Based on our computational analysis and the existing experimental data, we hypothesize that the experimentally observed production of CO originates from the reaction between highly vibrationally excited CO 2 produced through eq 1 and NO(X 2 Π) Using standard thermodynamic values, eq 6 becomes exothermic if greater than 42.96% of the available energy from the NO(A 2 Σ + ) + CO 2 electronic quenching is partitioned into the vibrational degrees of freedom of the CO 2 .Hancock and co-workers experimentally demonstrated that NO(A 2 Σ + ) + CO 2 electronic quenching produces highly vibrationally excited CO 2 , with approximately 62% of the available energy partitioned into the vibrational degrees of freedom of CO 2 .As such, NO(A 2 Σ + ) + CO 2 electronic quenching readily produces CO 2 with enough internal energy to make eq 6 thermodynamically favorable.Note that eq 6 also accounts for the formation of NO 2 which has also been observed experimentally.

■ CONCLUSIONS
Our exploration of the electronic quenching of NO(A 2 Σ + ) with molecular partners provides new insights into the photochemistry of open-shell molecular systems.In the case of NO(A 2 Σ + ) + CH 4 , the only attractive complexes are of C 3v symmetry, which quickly become repulsive at smaller intermolecular distances.The absence of a low-energy D 2 − D 1 conical intersection is consistent with the near-zero electronic quenching cross sections of NO(A 2 Σ + ) + CH 4 observed experimentally.Our work supports the experimental observation that the photodissociation of NO(A 2 Σ + ) + CH 4 produces NO(A 2 Σ + ) in a broad range of final rotational states, while imparting little rotational energy to CH 4 .Specifically, upon NO(X 2 Π) + CH 4 →NO(A 2 Σ + ) + CH 4 electronic excitation, the NO re-orients itself from being perpendicular with the intermolecular bond (C s symmetry) to being oriented head-on with the CH 3 face (C 3v symmetry).As a result, vibrational relaxation on the D 2 PES away from the Franck− Condon region imposes a torque on the NO, consistent with NO(A 2 Σ + ) receiving much more rotational energy than CH 4 when the complex dissociates.NO(A 2 Σ + ) + CH 3 OH presents a very different story.Although there are weakly bound complexes where NO interacts with the CH 3 face, the strongest attractive intermolecular interactions occur in conformations where the N atom of NO interacts with the O atom of CH 3 OH.We attribute the strong attractive intermolecular interactions on D 2 to the harpoon mechanism, with transient electron transfer occurring from NO(A 2 Σ + ) to CH 3 OH.In addition, similar to NO(A 2 Σ + ) + H 2 O, our results suggest that NO(A 2 Σ + ) + CH 3 OH has the potential to undergo both reactive and nonreactive electronic quenching.This is because the downhill pathway to a D 2 −D 1 conical intersection involves both decreasing the intermolecular distance and significantly stretching the O−H bond of CH 3 OH.The reactive pathway will produce H and CH 3 ONO, while the nonreactive pathway will result in CH 3 OH being formed in a range of product states with a vibrational progression in the O−H stretch.Future experimental and ab initio dynamics studies on this system are warranted to test the mechanistic predictions made in this study as well as determine the relative branching between reactive and non-reactive electronic quenching.
Finally, we discuss the conclusions of our mechanistic study of the NO(A 2 Σ + ) + CO 2 system.We showed that the most energetically favorable conformations on the D 2 PES have the N atom of NO interacting with an O atom of CO 2 .The attractive intermolecular interactions increase as the molecules grow closer together and eventually drive the isomerization of CO 2 into a bent conformation.The linear-to-bent isomerization of CO 2 results in significantly increased intermolecular attractions and reflects the formation of a transient NO + + CO 2 − ion pair through the harpoon mechanism.We further showed that the D 2 PES provides multiple, energetically downhill pathways to D 2 −D 1 conical intersections which facilitate electronic quenching.These pathways induce significant geometric distortions to CO 2 , consistent with the experimental observation that NO(A 2 Σ + ) + CO 2 electronic quenching releases a large fraction of the available energy into the vibrational degrees of freedom of CO 2 .Finally, we hypothesize that the highly vibrationally excited CO 2 produced through NO(A 2 Σ + ) + CO 2 electronic quenching will subsequently react with ground-state NO to produce the experimentally observed CO and NO 2 .Future velocity map imaging experiments, in conjunction with ab initio dynamics simulations, on this system are needed to shed light on the electronic quenching pathways responsible for producing NO(X 2 Π, ν NO ′ ≤ 1) as well as test whether the CO and NO 2 products are produced directly (eqs 2a−2c) or through the subsequent reaction of vibrationally hot CO 2 (eq 6).
PESs of the NO + CH 4 system along with tabulated data to construct all PES plots; PESs of the NO + CH 3 OH system and tabulated data to construct all PES plots: Loẅdin spin and partial charge plots for NO + CH

Figure 1 .
Figure 1.Panel (a) shows the relative energies of the D 1 (dashed lines) and D 2 (solid lines) states of the NO + H 2 O (orange) and NO + CO (blue) systems as a function of the intermolecular distance.Panel (b) shows the relative energies of the D 1 and D 2 states of NO + H 2 O as a function of one of the OH bond lengths of water, r OHd A , at a fixed intermolecular distance of R ON = 1.787Å.All energies are reported relative to an optimized geometry on D 2 with an intermolecular distance of 10 Å. Adapted with permission from the American Chemical Society, ref 22, and the Royal Society of Chemistry, ref 23.

Figure 2 .
Figure 2. Energy of the D 2 state of the ON-H 3 CH (blue data) andNO-H 3 CH (red data) conformations plotted against the intermolecular distance of the two interacting atoms.The geometry optimizations were calculated using EOM-EA-CCSD/aug-cc-pVTZ and a three-point extrapolation to the CBS limit was performed for the electronic energies.All energies are reported relative to a D 2optimized geometry with an intermolecular distance of 20 Å.

Figure 3 .
Figure 3. Potential energy curves of the ON−H 3 CH complex showing how the relative energy depends on the intermolecular distance, R NC .The calculations were performed at the EOM-EA-CCSD/AVQZ//EOM-EA-CCSD/aug-cc-pVTZ level of theory, and all energies are reported relative to a D 2 -optimized geometry with an intermolecular distance of 20 Å.The AVQZ basis set uses d-aug-cc-pVQZ for the N and O atoms and aug-cc-pVQZ for the C and H atoms.

Figure 4 .
Figure 4. Panel (a) shows the energy of the D 2 state as a function of the intermolecular distance when the NO is interacting with the CH 3 group of CH 3 OH.The blue data are for ON−H 3 COH geometries, while the red data are for NO−H 3 COH geometries.Panel (b) shows the energy of the D 2 state as a function of the intermolecular N−C−O angle (θ NCO ) at fixed intermolecular distances R NC = 3.0 Å (red data), R NC = 3.2 Å (orange data), R NC = 3.4 Å (blue data), and R NC = 3.6 Å (purple data).The geometry optimizations were performed using EOM-EA-CCSD with a d-aug-cc-pVTZ basis set for the C, N, and O atoms and an aug-cc-pVDZ basis set for the H atoms.The singlepoint energies were evaluated at the EOM-EA-CCSD/d-aug-cc-pVTZ level of theory and all energies are reported relative to a D 2 -optimized geometry with an intermolecular distance of 20 Å.

2 1 . 2 1
For example, at R NO = 1.90 Å, E D 2 increases from −0.56 eV at r OH = 1.10 Å to −0.46 eV at r OH = 1.33 Å, while E E D D remains larger than 1.03 eV.As with NO(A 2 Σ + ) + H 2 O, we surmise that the pathways shown in Figure 5 support both nonreactive and reactive electronic quenching.Focusing first on nonreactive electronic quenching, Figure 5 shows an energetically downhill pathway toward a D 2 −D 1 conical intersection that will facilitate rapid internal conversion.Because reaching the D 2 −D 1 conical intersection requires the significant stretching of an O−H bond of CH 3 OH, we predict that nonreactive NO(A 2 Σ + ) + CH 3 OH electronic quenching will produce CH 3 OH in a range of product states with vibrational excitation in the O−H stretch.The similarities between Figures 1 and 5b suggest a competing reactive electronic quenching pathway with products H + CH 3 ONO.Our calculations show that the reaction

2 1 ranging from 1 .
D 2 and D 1 states change as r OC is increased at a fixed intermolecular distance of R NO = 1.78 Å.These potential energy curves differ markedly from those shown in Figure 5b.The energy of the D 2 state increases significantly as the O−C bond is stretched, ranging from −0.61 eV when r OC = 1.44 Å to −0.30 eV when r OC = 1.68 Å.At the same time, the D 2 and D 1 states remain energetically well separated, with E E D D 53 to 1.36 eV.The absence of a D 2 −D 1 conical

Figure 5 .
Figure 5. Panel (a) shows the energy of the D 0 (light orange), D 1 (orange), and D 2 (green) states as a function of the intermolecular distance, R NO , when the N of NO is interacting with O of CH 3 OH.The inset shows the optimized geometry with R NO = 1.78 Å. Panel (b) shows the energy of the D 1 and D 2 states as a function of the OHbond length (r OH ) at a fixed intermolecular distance of R NO = 1.78 Å.The geometry optimizations were performed using EOM-EA-CCSD with a d-aug-cc-pVTZ basis set for the C, N, and O atoms and an augcc-pVDZ basis set for the H atoms.The single-point energies were evaluated at the EOM-EA-CCSD/d-aug-cc-pVTZ level of theory and all energies are reported relative to a D 2 -optimized geometry with an intermolecular distance of 20 Å.

Figure 6 .
Figure 6.Energy of the D 2 state of ON + OCO as a function of the intermolecular angle θ NOC at the intermolecular distances R NO = 3.5 Å (blue), R NO = 3.3 Å (orange), R NO = 3.1 Å (green), and R NO = 2.9 Å (yellow).These data were calculated at the EOM-EA-CCSD/ AVQZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory.All energies are reported relative to a D 2 -optimized geometry with an intermolecular distance of 20 Å.

Figure 7 .
Figure 7. Energy of the D 2 state of ON + OCO as a function of the intermolecular angle θ NOC at the intermolecular distances R NO = 2.8 Å (blue), R NO = 2.7 Å (orange), R NO = 2.6 Å (green), R NO = 2.5 Å (yellow), and R NO = 2.4 Å (light blue).These data were calculated at the EOM-EA-CCSD/AVQZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory.All energies are reported relative to a D 2 -optimized geometry with an intermolecular distance of 20 Å.As indicated by the insets, the low-energy conformations at smaller θ NOC are associated with the linear-to-bent isomerization of CO 2 .

Figure 8 .
Figure 8. Panel (a) shows the Loẅdin population analysis of the total spin densities and partial charges of NO and CO 2 as a function of θ NOC at R NO = 2.9 Å.The total spin density of a molecule is obtained by summing together the spin densities of all atoms belonging to that molecule.The total partial charges are obtained analogously.Panel (b) shows the SOMOs for the D 2 state of ON + OCO at representative θ NOC and R NO = 2.9 Å.

Figure 9 .
Figure 9. Panel (a) shows the Loẅdin population analysis of the total spin densities and partial charges of NO and CO 2 as a function of θ NOC at R NO = 2.5 Å.The total spin density of a molecule is obtained by summing together the spin densities of all atoms belonging to that molecule.The total partial charges are obtained analogously.Panel (b) shows the SOMOs for the D 2 state of ON + OCO at representative θ NOC and R NO = 2.5 Å.Note that the electronic character of the SOMO changes from 3sσ on NO at θ NOC = 180°to 2pπ* on CO 2 for θ NOC < 140°.This, along with the increased charge and spin density on CO 2 for θ NOC < 140°, is consistent with electron transfer occurring between the two molecules, i.e., the harpoon mechanism.
further suggests that the D 2 PES is effective at funneling population to a D 2 −D 1 conical intersection which occurs at approximately R NO = 1.93 Å and E 1.08 D 2 = eV.At the approximate D 2 −D 1 conical intersection, the CO 2 molecule has an O−C−O bond angle of 133.1°andO−C bond lengths of 1.30 and 1.19 Å, while the N−O bond length of NO is 1.09 Å. Comparing this to the geometry at R NO = 20 Å, where the O−C−O bond angle is 180.0°, the O−C bond lengths are 1.16 Å, and the N−O bond length is 1.06 Å, we see that the pathway shown in Figure 10 causes a significant distortion to the geometry of CO 2 and a smaller change to the bond length NO.
2 .The D 2 potential funnels the two molecules closer together until a D 2 −D 1 conical intersection is reached.This D 2 −D 1 conical intersection occurs at a nonplanar geometry at approximately R NO = 1.925Å and E 1.14 D 2 = eV.At this approximate D 2 −D 1 conical intersection, the O−C−O bond angle is 134.3°, the O−C bond lengths are 1.30 and 1.18 Å, and the N−O bond length is 1.09 Å.
support the direct production of CO + O( 3 P) atoms via eq 2a for several reasons.First, these pathways only involve a modest increase in the O− C bond length of around 0.14 Å.In contrast, the pathways to a D 2 −D 1 conical intersection for NO + H 2 O and NO + CH 3 OH shown in Figures 1 and 5 require an O−H bond to stretch by a

Figure 10 .
Figure 10.Energy of the D 0 (light orange), D 1 (orange), and D 2 (green) states as a function of the intermolecular distance, R NO , when the N of NO is interacting with an O of CO 2 .The insets show representative molecular geometries along this pathway.These calculations were performed at the EOM-EA-CCSD/AVQZ//EOM-EA-CCSD/aug-cc-pVTZ level of theory and all energies are reported relative to a D 2 -optimized geometry with an intermolecular distance of 20 Å.
3 OH at various R NO ; SOMOs for NO + CH 3 OH over various intermolecular distances; comparison of O−H and O−C stretching pathways in the NO + CH 3 OH system with tabulated values; comparison of pathways for the NO + CO 2 system in which the C of CO 2 is interacting with the NO; comparison between the D 2 states of the NO + CO 2 system with either the O or N of NO approaching the O of CO 2 at various intermolecular distances; PESs of both long and short-range intermolecular distances based on the θ NOC or θ OOC of both NO + OCO and ON + OCO complexes along with tabulated data; PESs of conical intersection pathways for the NO + CO 2 system The Journal of Physical Chemistry A with the tabulated data; and results of assessing the basis set dependence for NO + CH 4 and NO + CO 2 (PDF) ■ AUTHOR INFORMATION Corresponding Author Andrew S. Petit − Department of Chemistry and Biochemistry, California State University�Fullerton, Fullerton, California 92834-6866, United States; orcid.org/0000-0002-9428-3499;Email: apetit@fullerton.edu