^{1,2,a)}, Ke-Li Han

^{1,b)}, Marlies Hankel

^{3,c)}, Gabriel G. Balint-Kurti

^{4,d)}, Aron Kuppermann

^{5,e)}and Ravinder Abrol

^{5,f)}

### Abstract

Real wave packet propagations were carried out on both a single ground electronic state and two-coupled-electronic states of the title reaction to investigate the extent of nonadiabaticeffects on the distinguishable-atom reaction cross sections. The latest diabatic potential matrix of Abrol and Kuppermann [J. Chem. Phys.116, 1035 (2002)] was employed in the present nonadiabatic quantum state-to-state scattering calculations over a total energy range-from threshold (the zero point of the reagent ) to 3.0 eV. Based on the assumption that the hydrogen atoms are distinguishable in the collisions where the inelastic and elastic ones are excluded, no significant nonadiabaticeffects have been found in the calculations of the full state-to-state integral and differential cross sections up to a total energy of 3.0 eV for product vibrational levels . Our results therefore confirm the recent and the previous studies of the geometric phase effects in employing a different diabatic double many-body expansion potential matrix or a different BKMP2 potential energy surface.

This work was supported by the NSFC (Grant Nos. 2083308, 20633070, and 10874096) and QDUF (Grant No. 063-06300510). One of the authors (M.H.) would like to thank The University of Queensland, the Queensland Smart State Research Facilities Fund and Sun Microsystems for funding.

I. INTRODUCTION

II. APPROACH TO THE DYNAMICS

A. Initial wave packet construction

B. Real wave packet propagation on two-coupled diabatic potential energy surfaces

C. Derivation of the state-to-state dynamics quantities

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Non adiabatic reactions
- 33.0
- Quantum effects
- 15.0
- Chemical reaction cross sections
- 12.0
- Exchange reactions
- 12.0
- Hydrogen reactions
- 12.0

## Figures

The converged total reaction cross sections as a function of total energy over the range of threshold −3.0 eV for the hydrogen exchange reaction . The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed, dotted, and dashed-dotted lines are the results obtained on , on and the sum over and , respectively, calculated from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects. The atoms were assumed distinguishable in all the calculations presented in this paper.

The converged total reaction cross sections as a function of total energy over the range of threshold −3.0 eV for the hydrogen exchange reaction . The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed, dotted, and dashed-dotted lines are the results obtained on , on and the sum over and , respectively, calculated from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects. The atoms were assumed distinguishable in all the calculations presented in this paper.

(a) The state-to-state reaction probabilities as a function of total energy in the range of threshold −3.0 eV for the hydrogen exchange reaction with total angular momentum , 10, 20, 30, 40, and 50. (b) The corresponding total reaction probabilities as a function of total energy over the range of threshold –3.0 eV summed over all final product states. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed, dotted, and dashed-dotted lines are the results obtained on , on and the sum over and , respectively, calculated from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

(a) The state-to-state reaction probabilities as a function of total energy in the range of threshold −3.0 eV for the hydrogen exchange reaction with total angular momentum , 10, 20, 30, 40, and 50. (b) The corresponding total reaction probabilities as a function of total energy over the range of threshold –3.0 eV summed over all final product states. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed, dotted, and dashed-dotted lines are the results obtained on , on and the sum over and , respectively, calculated from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The converged state-to-state ICSs over the total energy range of threshold −3.0 eV. (a) For the product quantum states , , 2, 4, 6. (b) For the product quantum states , , 3, 5, 7. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed, dotted, and dashed-dotted lines are the results on , on and the sum over and , respectively, calculated from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The converged state-to-state ICSs over the total energy range of threshold −3.0 eV. (a) For the product quantum states , , 2, 4, 6. (b) For the product quantum states , , 3, 5, 7. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed, dotted, and dashed-dotted lines are the results on , on and the sum over and , respectively, calculated from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

Same as Fig. 3, but for product vibrational state .

Same as Fig. 3, but for product vibrational state .

Same as Fig. 3, but for product vibrational state .

Same as Fig. 3, but for product vibrational state .

Same as Fig. 3, but for product vibrational state .

Same as Fig. 3, but for product vibrational state .

Product rotational distributions for vibrational levels , 1, 2, and 3 at , 2.0, 2.3, 2.5, 2.8, and 3.0 eV. The solid line with open circles is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

Product rotational distributions for vibrational levels , 1, 2, and 3 at , 2.0, 2.3, 2.5, 2.8, and 3.0 eV. The solid line with open circles is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The converged state-to-state DCSs as a function of scattering angle at , 2.0, 2.5, and 3.0 eV for product states , (a) , 6 and (b) , 7. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The converged state-to-state DCSs as a function of scattering angle at , 2.0, 2.5, and 3.0 eV for product states , (a) , 6 and (b) , 7. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The full state-to-state DCSs as a function of scattering angle at , 2.0, 2.5, and 3.0 eV for product states , (a) , 4 and (b) , 5. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The full state-to-state DCSs as a function of scattering angle at , 2.0, 2.5, and 3.0 eV for product states , (a) , 4 and (b) , 5. The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The full state-to-state DCSs as a function of scattering angle at , 2.0, 2.5, and 3.0 eV for product states (a) , ; , and (b) , ; , . The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The full state-to-state DCSs as a function of scattering angle at , 2.0, 2.5, and 3.0 eV for product states (a) , ; , and (b) , ; , . The solid line is the result from the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The converged state-to-state DCSs as a function of total energy over the total energy range of threshold −3.0 eV at three scattering angles 0°, 90°, and 180° for eight product states (0,0), (1,0), (1,1), (2,0), and (2,6), (2,7), (3,4), (3,7). The solid line is the result of the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

The converged state-to-state DCSs as a function of total energy over the total energy range of threshold −3.0 eV at three scattering angles 0°, 90°, and 180° for eight product states (0,0), (1,0), (1,1), (2,0), and (2,6), (2,7), (3,4), (3,7). The solid line is the result of the one-adiabatic-electronic-state scattering calculation without nonadiabatic effects, the dashed line is the result summed over and from the two-coupled-diabatic-electronic-state scattering calculation with nonadiabatic effects.

## Tables

Numerical parameters used in the DIFFREALWAVE code for the reaction.

Numerical parameters used in the DIFFREALWAVE code for the reaction.

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