Although the Born-Oppenheimer (BO) approximation,1 which assumes separability of nuclear and electronic motion, is widely accepted for characterizing reactions in their ground electronic states, there is general agreement that reaction dynamics can be significantly impacted by excited electronic states near an electronic degeneracy, where the motion of the electrons is strongly coupled with that of the nuclei. While ultrafast nonadiabatic transitions near conical intersections (CIs) have been intensively studied in photochemistry,2–8 non-BO effects have seldom been investigated in detail for collisions and bimolecular reactions.9 Existing first-principles theory of nonadiabatic reaction dynamics have mostly dealt with open-shell atoms, focusing on geometric phase effects10–12 or spin-orbit excited electronic states.13–18 In the present work, we extend the detailed first-principles theory to the collision of electronically excited molecules, namely the hydroxyl radical in the OH(A2Σ+) state, by studying the following processes in full dimensionality:

OH(A2Σ+) + H2 → H + H2O (reactive quenching) (R1a)

→ OH(X2Π) + H2 (non-reactive quenching) (R1b)

→ OH(A2Σ+) + H2 (elastic and inelastic scattering) (R1c)

Here, both non-radiative quenching channels (R1a and R1b) necessarily require transitions from a higher to lower electronic state, due to nonadiabatic couplings near degeneracies such as conical intersections (CIs).19, 20 This system not only offers a prototype for understanding fundamental nonadiabatic dynamics in bimolecular collisions, but is also of great practical relevance to the laser-induced fluorescence (LIF) monitoring of the omnipresent OH radicals in atmospheric chemistry and in combustion.21, 22

Pioneering experiments by Lester and coworkers identified the reactive quenching channel (R1a)23 and measured the kinetic energy release of the hydrogen co-product.24–26 These kinetic energy distributions were found to be bimodal, suggesting complex dynamics with at least two reaction pathways. These intrabeam measurements were confirmed by a crossed molecular beam experiment by Ortiz-Suárez et al.27 Later experiments by the Lester group investigated the nonreactive quenching channel (R1b) with quantum state resolution.25, 28–30 The OH(X2Π) product was found to be vibrationally cold but rotationally hot. A propensity for the A′ component of the OH(X2Π) Λ-doublet was also observed. Furthermore, this group reported the branching ratio between the R1a and R1b channels, which favors the former.25 The existence of quantum state-resolved experimental data makes this system a fertile proving ground for theoretical understanding of nonadiabatic dynamics in bimolecular collisions.

Several electronic states are involved in the nonadiabatic quenching channels. In the entrance channel, the OH(A2Σ+) + H2 asymptote correlates adiabatically with the 32A state, while the doubly degenerate OH(X2Π) + H2 asymptote correlates with the 12A and 22A states. In the reactive quenching channel, the 12A state correlates adiabatically with the H2O + H asymptote. For Cs geometries, the 12A and 22A states carry irreducible representations (irreps) A′′ and A′, while the higher 32A state belongs to the A′ irrep. Early *ab initio* calculations identified a T-shaped (C2v) CI seam between the 32A(2A1) and 22A(2B2) states, with OH pointing its O-end to H2.31 It was hypothesized that this CI was responsible for efficient quenching of OH(A2Σ+), leading to both reactive and nonreactive quenching channels. Subsequent studies by Yarkony and coworkers revealed, however, that this CI seam actually spans the entire planar (Cs) geometry, extending from the C2v to C∞ v geometries,32, 33 where the irreps of the two states involved are A′/A′, B2/A1, and Π/Σ, respectively. In Fig. 1(a), this confluence of the CI seam is shown as a function of the H2-OH distance and the H2 rotational angle, with O always pointing to H2. This planar CI seam is responsible for nonadiabatic transitions involved in R1a and R1b, and represents the focal point of the current dynamics investigation. Further studies by Dillon and Yarkony explored the non-planar portion of the configuration space. They identified an additional CI seam between the 12A and 22A states, facilitating a non-planar insertion pathway of HO into H2,34, 35 leading to H and H2O. This CI seam facilitates the population of the A′ and A′′ Λ-doublet states of the OH(X2Π) product, and presumably also for the bimodality of the H kinetic energy distribution in the R1a channel.

Based on this electronic structure understanding, several multi-dimensional coupled potential energy surfaces (PESs) have been reported.29, 36–40 For nonadiabatic dynamics involving more than one electronic state, it is advantageous to express the Hamiltonian in a diabatic representation5, 41 to avoid singularities in the kinetic energy operator and cusps in the potential energy operator at the CI seams. While the resulting diabatic potential energy matrix (DPEM) is difficult to construct from adiabatic electronic structure calculations, once established, it greatly simplifies the dynamical calculations. To this end, reduced- and full-dimensional DPEMs considering two,29, 37 three,38, 39 and four40 electronic states have been reported. Based on a large number of multi-reference configuration interaction calculations, the latest global DPEM offers the highest fidelity in reproducing ab initio energies of the four lowest states and their couplings.40

These high-quality DPEMs have opened the door for dynamical studies.36–38, 42 While the dynamics can only be accurately characterized quantum mechanically, such calculations are challenging because of the large energy release (> 4 eV), a large accessible phase space, and the complex multi-state dynamics.9 Until now, quantum dynamics calculations have been restricted to planar geometries with two electronic states.37, 42 However, such a model is insufficient38 since it neglects the 22A state and important non-planar dynamics. On the other hand, full-dimensional trajectory surface hopping (TSH) studies have been employed to gain insights into the quenching events, but the results had no quantum state resolution. Interestingly, the TSH results favored the nonreactive quenching channel, in sharp contrast to the experiment.25 The R1a/R1b branching ratio is a fundamental quantity in this nonadiabatic process, the experimental/theoretical discrepancy is therefore of considerable importance. It could be due to the semi-classical treatment of the nonadiabatic dynamics and/or inaccuracies in the DPEM. This issue is thus only resolvable by a full-dimensional quantum dynamics study on a globally accurate DPEM.

In this work, we report the first full-dimensional investigation of the nonadiabatic collisional quenching of OH(A2Σ+) by H2 using a time-dependent quantum wave packet method on the recently developed DPEM.40 We aim to resolve the aforementioned experiment-theory discrepancy, to validate the DPEM by comparing quantum state resolved product distributions with experiment, and to gain insight into the (stereo)dynamics of this prototypical nonadiabatic process.