^{3}

*P*)+HF(

^{1}Σ

^{+}) reaction under hyperthermal conditions

^{1}, N. Bulut

^{2}, L. Bañares

^{3}and O. Roncero

^{4,a)}

### Abstract

We present wave packet calculations of total and state-to-state reaction probabilities and integral cross sections for the nonadiabaticdynamics of the O(^{3} *P*)+HF → F(^{2} *P*)+OH(^{2}Π) reaction at hyperthermal collision energies ranging from 1.2 to 2.4 eV. The validity of the centrifugal sudden approximation is discussed for the title reaction and a comprehensive investigation of the influence of nonadiabatic effects on the dynamics of this reactive system at high (hyperthermal) collision energies is presented. In general, nonadiabatic effects are negligible for averaged observables, such as total reaction probabilities and integral cross sections, but they are clearly observed in detailed observables such as rotationally state-resolved reaction probabilities. A critical discussion of nonadiabatic effects on the dynamics of the title reaction is carried out by comparing with the reverse reaction and the characteristics of the adiabatic and diabatic potential energy surfaces involved.

This work has been supported by the Spanish Ministerio de Ciencia e Innovación under Grant Nos. CSD2009-00038 (programa CONSOLIDER-INGENIO 2010 “Molecular Astrophysics: the Herschel and Alma era”), FIS2011-29596-C02, and CTQ2008-02578, and by Comunidad Autónoma de Madrid (CAM) under Grant No. S-0505/MAT/0303. We also acknowledge for a grant for computer time at CESGA computers. Partial financial support from the Scientific and Technological Research Council of TURKEY (TUBITAK) (Project No. TBAG-109T447) is gratefully acknowledged. Some computations have also been done on the High Performance and Grid Computing Center (TR-Grid) at ULAKBIM/TURKEY.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

A. Reaction probabilities

B. Cross sections

IV. CONCLUSIONS

### Key Topics

- Chemical reaction cross sections
- 44.0
- Collision induced chemical reactions
- 30.0
- Non adiabatic reactions
- 23.0
- Surface reactions
- 9.0
- Reaction mechanisms
- 8.0

## Figures

(Top) Minimum energy path for the O(^{3} *P*)+HF reaction (in eV) for the two first energy roots; (left) for the adiabatic 1^{3} *A* ^{″} and 2^{3} *A* ^{″} states, denoted *E* _{−} and *E* _{+}, respectively, resulting from the regularized diabatic states of Ref. 26; (right) for the diabatic ^{3}Σ^{−} and ^{3}Π states (denoted *E* _{0} and E_{1}) at a collinear geometry. (Bottom) Contour plots (in eV) of the two diabatic (left) ^{3}Σ^{−} and (right) ^{3}Π state at OHF collinear geometry, indicating with a line in black the conical intersection seams.

(Top) Minimum energy path for the O(^{3} *P*)+HF reaction (in eV) for the two first energy roots; (left) for the adiabatic 1^{3} *A* ^{″} and 2^{3} *A* ^{″} states, denoted *E* _{−} and *E* _{+}, respectively, resulting from the regularized diabatic states of Ref. 26; (right) for the diabatic ^{3}Σ^{−} and ^{3}Π states (denoted *E* _{0} and E_{1}) at a collinear geometry. (Bottom) Contour plots (in eV) of the two diabatic (left) ^{3}Σ^{−} and (right) ^{3}Π state at OHF collinear geometry, indicating with a line in black the conical intersection seams.

Total reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(*v* = 0, *j* = 0) reaction at total angular momentum *J* = 0. Top panel: sum over initial electronic states in the diabatic and adiabatic representations. Middle panel: comparison between the adiabatic 2^{3}A^{″} probability and that obtained in the 2×2 diabatic representation starting in the ^{3}Π state. Bottom panel: The same but for the ground adiabatic 1^{3}A^{″} state and for the initial diabatic ^{3}Σ state for each of the two diabatic electronic states (considering the 2×2 electronic diabatic Hamiltonian).

Total reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(*v* = 0, *j* = 0) reaction at total angular momentum *J* = 0. Top panel: sum over initial electronic states in the diabatic and adiabatic representations. Middle panel: comparison between the adiabatic 2^{3}A^{″} probability and that obtained in the 2×2 diabatic representation starting in the ^{3}Π state. Bottom panel: The same but for the ground adiabatic 1^{3}A^{″} state and for the initial diabatic ^{3}Σ state for each of the two diabatic electronic states (considering the 2×2 electronic diabatic Hamiltonian).

Total reaction probabilities as a function of the collision energy calculated for the O(^{3} *P*)+HF(*v* = 0, *j* = 0) reaction on the 1^{3} *A* ^{″} (left panels) and 2^{3} *A* ^{″} (right panels) initial adiabatic electronic states at several values of the total angular momentum *J* using the CS approximation in reactant (red) and product (black) Jacobi coordinates and the CC methodology (blue).

Total reaction probabilities as a function of the collision energy calculated for the O(^{3} *P*)+HF(*v* = 0, *j* = 0) reaction on the 1^{3} *A* ^{″} (left panels) and 2^{3} *A* ^{″} (right panels) initial adiabatic electronic states at several values of the total angular momentum *J* using the CS approximation in reactant (red) and product (black) Jacobi coordinates and the CC methodology (blue).

Electronically and vibrationally state-resolved reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(α,*v* = 0, *j* = 0)→OH(α^{′},*v*′ = 0–2)+F reaction at *J* = 0. Bottom panels: ending in the same diabatic electronic state of the initial wave packet (α = α^{′} = ^{3}Σ or ^{3}Π). Middle panels: with different initial and final electronic state (α ≠ α^{′}). Top panels: obtained in the adiabatic representation for the 1^{3} *A* ^{″} (left) and 2^{3} *A* ^{″} (right) states.

Electronically and vibrationally state-resolved reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(α,*v* = 0, *j* = 0)→OH(α^{′},*v*′ = 0–2)+F reaction at *J* = 0. Bottom panels: ending in the same diabatic electronic state of the initial wave packet (α = α^{′} = ^{3}Σ or ^{3}Π). Middle panels: with different initial and final electronic state (α ≠ α^{′}). Top panels: obtained in the adiabatic representation for the 1^{3} *A* ^{″} (left) and 2^{3} *A* ^{″} (right) states.

Electronically and rotationally state-resolved reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(α,*v* = 0, *j* = 0)→OH(α^{′},*v*′ = 0, *j* ^{′} = 0–3)+F reaction at *J* = 0. Bottom panels: ending in the same diabatic electronic state of the initial wave packet (α = α^{′} = ^{3}Σ or ^{3}Π). Middle panels: with different initial and final electronic state (α ≠ α^{′}). Top panels: obtained in the adiabatic representation for the 1^{3} *A* ^{″} (left) and 2^{3} *A* ^{″} (right) states.

Electronically and rotationally state-resolved reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(α,*v* = 0, *j* = 0)→OH(α^{′},*v*′ = 0, *j* ^{′} = 0–3)+F reaction at *J* = 0. Bottom panels: ending in the same diabatic electronic state of the initial wave packet (α = α^{′} = ^{3}Σ or ^{3}Π). Middle panels: with different initial and final electronic state (α ≠ α^{′}). Top panels: obtained in the adiabatic representation for the 1^{3} *A* ^{″} (left) and 2^{3} *A* ^{″} (right) states.

Rotationally state-resolved reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(*v* = 0, *j* = 0)→OH(*v*′ = 0, *j* ^{′} = 0–5)+F reaction at *J* = 0 calculated in the adiabatic (red) and diabatic (blue) representations.

Rotationally state-resolved reaction probabilities as a function of collision energy for the O(^{3} *P*)+HF(*v* = 0, *j* = 0)→OH(*v*′ = 0, *j* ^{′} = 0–5)+F reaction at *J* = 0 calculated in the adiabatic (red) and diabatic (blue) representations.

Total integral cross sections as a function of collision energy for the O(^{3} *P*) + HF(*v* = 0, *j* = 0)→OH+F reaction in the adiabatic and diabatic representations. Bottom panel: obtained for the adiabatic 1^{3} *A* ^{″} and 2^{3} *A* ^{″} and diabatic ^{3}Σ^{−} and ^{3}Π states. Middle panel: total diabatic versus total adiabatic. Top panel: diagonal and nondiagonal cross sections obtained in the diabatic representation for the two initial and final electronic states.

Total integral cross sections as a function of collision energy for the O(^{3} *P*) + HF(*v* = 0, *j* = 0)→OH+F reaction in the adiabatic and diabatic representations. Bottom panel: obtained for the adiabatic 1^{3} *A* ^{″} and 2^{3} *A* ^{″} and diabatic ^{3}Σ^{−} and ^{3}Π states. Middle panel: total diabatic versus total adiabatic. Top panel: diagonal and nondiagonal cross sections obtained in the diabatic representation for the two initial and final electronic states.

Vibrationally state-resolved integral cross section as a function of collision energy for the O(^{3} *P*)+HF(*v* = 0, *j* = 0)→OH(*v*′)+F reaction obtained for the 1^{3} *A* ^{″} and 2^{3} *A* ^{″} adiabatic states and for the ^{3}Σ^{−} and ^{3}Π coupled diabatic states as indicated. In the diabatic cases, the cross sections for the two possible final electronic states have been added.

Vibrationally state-resolved integral cross section as a function of collision energy for the O(^{3} *P*)+HF(*v* = 0, *j* = 0)→OH(*v*′)+F reaction obtained for the 1^{3} *A* ^{″} and 2^{3} *A* ^{″} adiabatic states and for the ^{3}Σ^{−} and ^{3}Π coupled diabatic states as indicated. In the diabatic cases, the cross sections for the two possible final electronic states have been added.

Product rotational distributions for the O(^{3} *P*)+HF(*v* = 0, *j* = 0)→OH(*v*′, *j* ^{′})+F reaction at selected collision energies: 1.8 eV (black squares), 2.0 eV (open circles), 2.2 eV (black circles), and 2.4 eV (open triangles), for the adiabatic 1^{3} *A* ^{″} and 2^{3} *A* ^{″} states and for the diabatic ^{3}Σ^{−} and ^{3}Π coupled states as indicated. In the diabatic states, the cross sections for the two possible final electronic states have been added.

Product rotational distributions for the O(^{3} *P*)+HF(*v* = 0, *j* = 0)→OH(*v*′, *j* ^{′})+F reaction at selected collision energies: 1.8 eV (black squares), 2.0 eV (open circles), 2.2 eV (black circles), and 2.4 eV (open triangles), for the adiabatic 1^{3} *A* ^{″} and 2^{3} *A* ^{″} states and for the diabatic ^{3}Σ^{−} and ^{3}Π coupled states as indicated. In the diabatic states, the cross sections for the two possible final electronic states have been added.

Total integral cross section as a function of the total energy for the O(^{3} *P*)+HF(*v* = 0,1,2, *j* = 0) reaction. Exact CC calculations for *v* = 0 (red). *J*-shifting calculations for *v* = 0 (blue), *v* = 1 (green), and *v* = 2 (grey). Notice the very good agreement between the exact CC and *J*-shifting calculations for *v* = 0.

Total integral cross section as a function of the total energy for the O(^{3} *P*)+HF(*v* = 0,1,2, *j* = 0) reaction. Exact CC calculations for *v* = 0 (red). *J*-shifting calculations for *v* = 0 (blue), *v* = 1 (green), and *v* = 2 (grey). Notice the very good agreement between the exact CC and *J*-shifting calculations for *v* = 0.

## Tables

Parameters used in the wave packet calculations in product Jacobi coordinates. Distances are in Å, and energies in eV.

Parameters used in the wave packet calculations in product Jacobi coordinates. Distances are in Å, and energies in eV.

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