^{1,a)}, Frank Otto

^{1,b)}, Fabien Gatti

^{2,c)}and Hans-Dieter Meyer

^{3,d)}

### Abstract

We present the results of a full-dimensional quantum mechanical study of the rovibrational energy transfer in the collision between *ortho*- and *para*- in the energy range of . The multiconfiguration time-dependent Hartree algorithm has been used to propagate the wave packets on the global potential energy surface by Boothroyd *et al.* [J. Chem. Phys.116, 666 (2002)] and on a modification of this surface where the short range anisotropy is reduced. State-to-state attributes such as probabilities or integral cross sections are obtained using the formalism of Tannor and Weeks [J. Chem. Phys.98, 3884 (1993)] by Fourier transforming the correlation functions. The effect of initial rotation of the diatoms on the inelastic and de-excitation processes is investigated.

One of the authors (ANP) gratefully acknowledges a scholarship from the Alexander-von-Humboldt Foundation. Financial support by the Deutsche Forschungsgemeinschaft is also gratefully acknowledged.

I. INTRODUCTION

II. THEORY

A. The multiconfiguration time-dependent Hartree method

B. Coordinates and Hamiltonian

1. Kinetic energy operator

2. Potential energy operator

C. Initial wave packet

D. Final state analysis

1. Probabilities

2. Cross sections

III. RESULTS AND DISCUSSION

A. Numerical details

B. Probabilities and cross sections

IV. CONCLUSIONS

### Key Topics

- Potential energy surfaces
- 11.0
- Energy transfer
- 9.0
- Wave functions
- 8.0
- Elasticity
- 6.0
- Anisotropy
- 5.0

## Figures

Contributions from different partial waves for the transition for I1 at different collision energies.

Contributions from different partial waves for the transition for I1 at different collision energies.

Comparisons of state-to-state integral cross sections for collisions (process I1), on BMKP (-) and BMKPE (--) PESs. The numbers in the upper left corners denote the rotational transitions . The cross sections for the transition are multiplied by a factor of 8.

Comparisons of state-to-state integral cross sections for collisions (process I1), on BMKP (-) and BMKPE (--) PESs. The numbers in the upper left corners denote the rotational transitions . The cross sections for the transition are multiplied by a factor of 8.

Comparison of cross sections (summed over all final ) for the transition for the vibrational inelastic process I1 for different initial combinations as indicated in the figure.

Comparison of cross sections (summed over all final ) for the transition for the vibrational inelastic process I1 for different initial combinations as indicated in the figure.

Comparisons of the cross sections for different rotational transitions as indicated in each of the figures for the processes I1 (solid lines) and I2 (dashed lines). The cross sections for are multiplied by a factor of 10.

Comparisons of the cross sections for different rotational transitions as indicated in each of the figures for the processes I1 (solid lines) and I2 (dashed lines). The cross sections for are multiplied by a factor of 10.

Same as in Fig. 4 but for . The cross sections for are multiplied by a factor of 20.

Same as in Fig. 4 but for . The cross sections for are multiplied by a factor of 20.

Same as in Fig. 4 but for . The cross sections for are multiplied by a factor of 4.

Same as in Fig. 4 but for . The cross sections for are multiplied by a factor of 4.

Cross sections for (process I3). (a) , (b) , (c) . Different lines refer to different final states as indicated. The order of the cross sections at reads 21, 03, 23, 41, and 43 for (a); 23, 01, 21, 43, and 41 for (b); and 23, 41, 01, 43, and 03 for (c).

Cross sections for (process I3). (a) , (b) , (c) . Different lines refer to different final states as indicated. The order of the cross sections at reads 21, 03, 23, 41, and 43 for (a); 23, 01, 21, 43, and 41 for (b); and 23, 41, 01, 43, and 03 for (c).

Vibrational de-excitation cross sections for . (a) , (b) , (c) . Different lines refer to different final rotational states . The order of the cross sections at reads 23, 01, 43, 21, 41, and 03 for (a); 25, 03, 45, 23, 43, 01, 21, and 41 for (b); and 43, 21, 41, 23, 03, and 01 for (c).

Vibrational de-excitation cross sections for . (a) , (b) , (c) . Different lines refer to different final rotational states . The order of the cross sections at reads 23, 01, 43, 21, 41, and 03 for (a); 25, 03, 45, 23, 43, 01, 21, and 41 for (b); and 43, 21, 41, 23, 03, and 01 for (c).

## Tables

Parameters for the primitive basis sets employed for each degree of freedom. The brackets indicate the mode combinations, and the last column gives the number of single-particle functions used for the modes. FFT is a fast Fourier transform; HO is a harmonic oscillator (Hermite) DVR; and KLeg is a two-dimensional extended Legendre DVR (Ref. 50) similar to the one of Refs. 51 and 52.

Parameters for the primitive basis sets employed for each degree of freedom. The brackets indicate the mode combinations, and the last column gives the number of single-particle functions used for the modes. FFT is a fast Fourier transform; HO is a harmonic oscillator (Hermite) DVR; and KLeg is a two-dimensional extended Legendre DVR (Ref. 50) similar to the one of Refs. 51 and 52.

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