Abstract
Quantum scattering calculations of vibration-vibration (VV) and vibration-translation (VT) energy transfer for non-reactive H_{2}-H_{2} collisions on a full-dimensional potential energy surface are reported for energies ranging from the ultracold to the thermal regime. The efficiency of VV and VT transfer is known to strongly correlate with the energy gap between the initial and final states. In H_{2}(v = 1, j = 0) + H_{2}(v = 0, j = 1) collisions, the inelastic cross section at low energies is dominated by a VV process leading to H_{2}(v = 0, j = 0) + H_{2}(v = 1, j = 1) products. At energies above the opening of the v = 1, j = 2 rotational channel, pure rotational excitation of the para-H_{2} molecule leading to the formation of H_{2}(v = 1, j = 2) + H_{2}(v = 0, j = 1) dominates the inelastic cross section. For vibrationally excited H_{2} in the v = 2 vibrational level colliding with H_{2}(v = 0), the efficiency of both VV and VT process is examined. It is found that the VV process leading to the formation of 2H_{2}(v = 1) molecules dominates over the VT process leading to H_{2}(v = 1) + H_{2}(v = 0) products, consistent with available experimental data, but in contrast to earlier semiclassical results. Overall, VV processes are found to be more efficient than VT processes, for both distinguishable and indistinguishable H_{2}-H_{2} collisions confirming room temperature measurements for v = 1 and v = 2.
This work was supported by NSF grants PHY-1205838, (N.B.), ATM-0635715 (N.B.), PHY-1203228 (R.C.F.), and AST-0607733 (P.C.S.). This research was supported in part by NSF through XSEDE resources provided by the National Institute for Computational Sciences through Grant No. CHE100039 (N.B.).
I. INTRODUCTION
II. THEORY AND COMPUTATIONAL DETAILS
III. RESULTS
A. Cross sections
1. Rovibrational transitions from v = 1
2. Rovibrational transitions from v=2
B. Rate coefficients
IV. DISCUSSION
V. CONCLUSION
Key Topics
- Energy transfer
- 11.0
- Semiclassical theories
- 10.0
- Angular momentum
- 7.0
- Excitation energies
- 6.0
- Collision theories
- 5.0
Figures
Jacobi coordinates for the tetratomic system.
Jacobi coordinates for the tetratomic system.
Cross sections for the 1001 initial state as a function of the center-of-mass collision energy. The top curve denotes the elastic cross section and the thick dotted curve represents the total inelastic cross section. The main contribution to the inelastic process comes from the 0011 final state and, above 540 K, from the 1201 channel. Rotational transitions are more predominant than the VV transition at higher collision energies.
Cross sections for the 1001 initial state as a function of the center-of-mass collision energy. The top curve denotes the elastic cross section and the thick dotted curve represents the total inelastic cross section. The main contribution to the inelastic process comes from the 0011 final state and, above 540 K, from the 1201 channel. Rotational transitions are more predominant than the VV transition at higher collision energies.
Cross sections for the 1201 initial state as a function of the center-of-mass collision energy. As in Fig. 2 , the top curve denotes the elastic cross section while the thick dotted curve represents the total inelastic cross section. The latter is dominated by the 1201 → 1001 transition. At higher energies, additional transitions involving rotational changes in one or both molecules make significant contributions to the inelastic cross section.
Cross sections for the 1201 initial state as a function of the center-of-mass collision energy. As in Fig. 2 , the top curve denotes the elastic cross section while the thick dotted curve represents the total inelastic cross section. The latter is dominated by the 1201 → 1001 transition. At higher energies, additional transitions involving rotational changes in one or both molecules make significant contributions to the inelastic cross section.
Cross sections for the 2000 initial state as a function of the center-of-mass collision energy. The solid curve on the top represents the elastic cross section. The contribution to the total inelastic cross section (thick dotted curve) arises mainly from VT process (1000) at low energies and the VV process (1010) in the small window of 340-470 K. At higher energies, mainly rotational excitation contributes to the inelastic cross section.
Cross sections for the 2000 initial state as a function of the center-of-mass collision energy. The solid curve on the top represents the elastic cross section. The contribution to the total inelastic cross section (thick dotted curve) arises mainly from VT process (1000) at low energies and the VV process (1010) in the small window of 340-470 K. At higher energies, mainly rotational excitation contributes to the inelastic cross section.
Cross sections for the 2002 initial state as a function of the center-of-mass collision energy. The solid dark curve corresponds to the elastic cross section which dominates at energies above 3 × 10^{−4} K. The dominant inelastic channel is the quasi-resonant RR transition that leads to the 2200 final state. This process is equivalent to the QRRR transfer discussed in Ref. ^{ 55 } .
Cross sections for the 2002 initial state as a function of the center-of-mass collision energy. The solid dark curve corresponds to the elastic cross section which dominates at energies above 3 × 10^{−4} K. The dominant inelastic channel is the quasi-resonant RR transition that leads to the 2200 final state. This process is equivalent to the QRRR transfer discussed in Ref. ^{ 55 } .
Cross sections for the 2001 initial state as a function of the center-of-mass collision energy. As in Fig. 4 , the total inelastic cross section has three different regions in which a single process dominates the cross section. This is comprised of the resonant VV transition 2001 → 0021, followed by the non-resonant 2001 → 1011 VV transition, and finally, the rotational excitation channels.
Cross sections for the 2001 initial state as a function of the center-of-mass collision energy. As in Fig. 4 , the total inelastic cross section has three different regions in which a single process dominates the cross section. This is comprised of the resonant VV transition 2001 → 0021, followed by the non-resonant 2001 → 1011 VV transition, and finally, the rotational excitation channels.
Rate constants for different VV and VT transitions as functions of the temperature. The symbol “*” on the legend of the 0011 → 1001 and 1010 → 2000 indicates that the curves were obtained by detailed balance from the 1001 → 1100 and 2000 → 1010 transitions, respectively. The acronyms in parenthesis, VT and VV denote vibration-translation and vibration-vibration transitions, while Res VV denotes resonant VV transition.
Rate constants for different VV and VT transitions as functions of the temperature. The symbol “*” on the legend of the 0011 → 1001 and 1010 → 2000 indicates that the curves were obtained by detailed balance from the 1001 → 1100 and 2000 → 1010 transitions, respectively. The acronyms in parenthesis, VT and VV denote vibration-translation and vibration-vibration transitions, while Res VV denotes resonant VV transition.
Tables
The first and second columns show the choice of the basis set and the cut-off energies. In the first column o-H_{2} and p-H_{2} stands for ortho-H_{2} and para-H_{2}, respectively. The basis set is denoted by the maximum rotational quantum number j included in each relevant vibrational level v of the H_{2} molecule. For instance, for ortho-para H_{2} {0,9;1,7-0,10;1,6} means that for the ortho-H_{2} we have included rotational states up to j _{ v = 0} = 9 in the v = 0 vibrational level and j _{ v = 1} = 7 in v = 1. The third column shows the number of channels involved at each step of the calculations. Para-para and ortho-para H_{2} require calculations for each inversion symmetry (positive and negative), while for ortho-ortho H_{2} collisions, besides inversion, positive and negative exchange-permutation symmetries also need to be accounted for.
The first and second columns show the choice of the basis set and the cut-off energies. In the first column o-H_{2} and p-H_{2} stands for ortho-H_{2} and para-H_{2}, respectively. The basis set is denoted by the maximum rotational quantum number j included in each relevant vibrational level v of the H_{2} molecule. For instance, for ortho-para H_{2} {0,9;1,7-0,10;1,6} means that for the ortho-H_{2} we have included rotational states up to j _{ v = 0} = 9 in the v = 0 vibrational level and j _{ v = 1} = 7 in v = 1. The third column shows the number of channels involved at each step of the calculations. Para-para and ortho-para H_{2} require calculations for each inversion symmetry (positive and negative), while for ortho-ortho H_{2} collisions, besides inversion, positive and negative exchange-permutation symmetries also need to be accounted for.
Comparison of H_{2}-H_{2} rate coefficients for different transitions from the present study and available experimental and theoretical data.
Comparison of H_{2}-H_{2} rate coefficients for different transitions from the present study and available experimental and theoretical data.
Article metrics loading...
Full text loading...
Commenting has been disabled for this content