^{1}, N. Balakrishnan

^{1}and Brian K. Kendrick

^{2}

### Abstract

A quantum dynamics study of the O(^{1} *D*) + H_{2}(*v* = 0 − 2, *j* = 0) system has been carried out using the potential energy surfaces of Dobbyn and Knowles [Mol. Phys.91, 1107 (Year: 1997)10.1080/002689797170842]. A time-independent quantum mechanical method based on hyperspherical coordinates is adopted for the dynamics calculations. Energy dependent cross section, probability, and rate coefficients are computed for the elastic, inelastic, and reactive channels over collision energies ranging from the ultracold to thermal regimes and for total angular momentum quantum number *J* = 0. The effect of initial vibrational excitation of the H_{2} molecule on vibrational and rotational populations of the OH product is investigated as a function of the collision energy. Comparison of results for vibrational levels *v* = 0 − 2 of H_{2} demonstrates that the vibrational excitation of H_{2} and its non-reactive relaxation pathway play a minor role in the overall collisional outcome of O(^{1} *D*) and H_{2}. It is also found that while the state-resolved product vibrational distributions are sensitive to the initial collision energy and H_{2} vibrational level, the product rotational distribution depicts an inverted population that is largely insensitive to initial conditions. Rate coefficients evaluated using a *J*-shifting approximation show reasonable agreement with available theoretical and experimental results suggesting that the *J*-shifting approximation may be used to evaluate the rate coefficients for O(^{1} *D*) + H_{2} reaction.

This work was supported in part by NSF Grant Nos. PHY-1205838 (N.B.) and ATM-0635715 (N.B.), and ARO MURI Grant No. W911NF-12-1-0476. Computational support by National Supercomputing Center for Energy and the Environment at UNLV is gratefully acknowledged. B.K.K. acknowledges that part of this work was done under the auspices of the US Department of Energy at Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the National Security Administration of the US Department of Energy under Contract No. DE-AC52-06NA25396.

I. INTRODUCTION

II. METHODOLOGY AND COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

IV. SUMMARY AND CONCLUSIONS

### Key Topics

- Hydrogen reactions
- 34.0
- Ultracold collisions
- 13.0
- Collision induced chemical reactions
- 11.0
- Non adiabatic reactions
- 11.0
- Excited state reaction dynamics
- 10.0

## Figures

Total reaction probability for O(^{1} *D*) + H_{2}(*v* = 0 − 2, *j* = 0) collisions as functions of the collision energy for zero total angular momentum (*J* = 0).

Total reaction probability for O(^{1} *D*) + H_{2}(*v* = 0 − 2, *j* = 0) collisions as functions of the collision energy for zero total angular momentum (*J* = 0).

Cross sections for O(^{1} *D*) + H_{2}(*v*, *j* = 0) collisions as functions of the incident kinetic energy in K for zero total angular momentum (*J* = 0). Red curve (*v* = 0); blue curve (*v* = 1); black curve (*v* = 2). Elastic cross sections are labeled by dotted lines, inelastic cross sections are labeled by dashed lines, whereas reactive cross sections are labeled by solid lines.

Cross sections for O(^{1} *D*) + H_{2}(*v*, *j* = 0) collisions as functions of the incident kinetic energy in K for zero total angular momentum (*J* = 0). Red curve (*v* = 0); blue curve (*v* = 1); black curve (*v* = 2). Elastic cross sections are labeled by dotted lines, inelastic cross sections are labeled by dashed lines, whereas reactive cross sections are labeled by solid lines.

Rate coefficients for O(^{1} *D*) + H_{2} collisions as functions of the incident kinetic energy in K for zero total angular momentum (*J* = 0). Red curve (*v* = 0); blue curve (*v* = 1); black curve (*v* = 2). Elastic rate coefficients are labeled by dotted lines, inelastic rate coefficients are labeled by dashed lines, whereas reactive rate coefficients are labeled by solid lines.

Rate coefficients for O(^{1} *D*) + H_{2} collisions as functions of the incident kinetic energy in K for zero total angular momentum (*J* = 0). Red curve (*v* = 0); blue curve (*v* = 1); black curve (*v* = 2). Elastic rate coefficients are labeled by dotted lines, inelastic rate coefficients are labeled by dashed lines, whereas reactive rate coefficients are labeled by solid lines.

Vibrational distribution of the product OH molecule in O(^{1} *D*) + H_{2}(*v* = 0 − 2, *j* = 0) → OH(*v* _{ f }) + H reaction at four different collision energies for zero total angular momentum (*J* = 0). Left panel is for H_{2}(*v* = 0), middle panel is for H_{2}(*v* = 1), and right panel for H_{2}(*v* = 2).

Vibrational distribution of the product OH molecule in O(^{1} *D*) + H_{2}(*v* = 0 − 2, *j* = 0) → OH(*v* _{ f }) + H reaction at four different collision energies for zero total angular momentum (*J* = 0). Left panel is for H_{2}(*v* = 0), middle panel is for H_{2}(*v* = 1), and right panel for H_{2}(*v* = 2).

Rotational distribution of the product OH molecule in O(^{1} *D*) + H_{2}(*v* = 0, *j* = 0) → OH(*v* _{ f }, *j* _{ f }) + H reaction at two different collision energies for zero total angular momentum (*J* = 0). The Left panel corresponds to a collision energy of 10^{−10} eV and the right panel corresponds to a collision energy of 0.1 eV.

Rotational distribution of the product OH molecule in O(^{1} *D*) + H_{2}(*v* = 0, *j* = 0) → OH(*v* _{ f }, *j* _{ f }) + H reaction at two different collision energies for zero total angular momentum (*J* = 0). The Left panel corresponds to a collision energy of 10^{−10} eV and the right panel corresponds to a collision energy of 0.1 eV.

Same as Fig. 5 but for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) → OH(*v* _{ f }, *j* _{ f }) + H reaction.

Same as Fig. 5 but for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) → OH(*v* _{ f }, *j* _{ f }) + H reaction.

Same as Fig. 5 but for O(^{1} *D*) + H_{2}(*v* = 2, *j* = 0) → OH(*v* _{ f }, *j* _{ f }) + H reaction.

Same as Fig. 5 but for O(^{1} *D*) + H_{2}(*v* = 2, *j* = 0) → OH(*v* _{ f }, *j* _{ f }) + H reaction.

Upper panel: Comparison of O(^{1} *D*) + H_{2}(*v* = 0, *j* = 0) reactive rate coefficients from the present study (black solid lines) with the quantum wave packet calculations of Lin and Guo ^{ 37 } (black dashed lines), SQM (blue dots), and MPPST (green dashed lines) results of Rivero-Santamaría *et al.* ^{ 46 } Experimental results are from Talukdar *et al.*, ^{ 81 } Atkinson *et al.*, ^{ 82 } and Vranckx *et al.* ^{ 83 } Lower panel: Reactive rate coefficients for H_{2}(*v* = 0) (black solid lines), H_{2}(*v* = 1) (red dashed lines), and H_{2}(*v* = 2) (blue dots) as functions of the temperature.

Upper panel: Comparison of O(^{1} *D*) + H_{2}(*v* = 0, *j* = 0) reactive rate coefficients from the present study (black solid lines) with the quantum wave packet calculations of Lin and Guo ^{ 37 } (black dashed lines), SQM (blue dots), and MPPST (green dashed lines) results of Rivero-Santamaría *et al.* ^{ 46 } Experimental results are from Talukdar *et al.*, ^{ 81 } Atkinson *et al.*, ^{ 82 } and Vranckx *et al.* ^{ 83 } Lower panel: Reactive rate coefficients for H_{2}(*v* = 0) (black solid lines), H_{2}(*v* = 1) (red dashed lines), and H_{2}(*v* = 2) (blue dots) as functions of the temperature.

## Tables

Convergence of the elastic cross section in units of 10^{−13} cm^{2} molecule^{−1} with the matching distance ρ_{ m } for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) collisions.

Convergence of the elastic cross section in units of 10^{−13} cm^{2} molecule^{−1} with the matching distance ρ_{ m } for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) collisions.

Convergence of the nonthermal reactive rate coefficient in units of 10^{−10} cm^{3} molecule^{−1} s^{−1} with the matching distance ρ_{ m } for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) collisions. *v* _{ rel } is the relative velocity for the collision defined as , where *E* _{ kin } is the relative collision energy and μ is the reduced mass of the O + H_{2} system.

Convergence of the nonthermal reactive rate coefficient in units of 10^{−10} cm^{3} molecule^{−1} s^{−1} with the matching distance ρ_{ m } for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) collisions. *v* _{ rel } is the relative velocity for the collision defined as , where *E* _{ kin } is the relative collision energy and μ is the reduced mass of the O + H_{2} system.

Convergence of the nonthermal reactive rate coefficient in units of 10^{−10} cm^{3} molecule^{−1} s^{−1} with basis set size for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) reaction, at a matching distance ρ_{ m } = 19.61 *a* _{0}.

Convergence of the nonthermal reactive rate coefficient in units of 10^{−10} cm^{3} molecule^{−1} s^{−1} with basis set size for O(^{1} *D*) + H_{2}(*v* = 1, *j* = 0) reaction, at a matching distance ρ_{ m } = 19.61 *a* _{0}.

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