### Abstract

In this paper, cross sections and J = 0 reaction probabilities from the results of quasiclassical trajectory (QCT) and accurate quantum reactive scattering calculations are presented and compared for H + H_{2} (ν = 0) and H + H_{2} (ν = 1). For both ν = 0 and ν = 1, the energies associated with the effective thresholds for reaction in the quantum results are consistent with the adiabatic treatment of bending motions along the reaction coordinate. This is best illustrated by comparing the 3DJ = 0 reaction probabilities with those from analogous collinear calculations, and with collinear calculations in which the bending zero point energy is added in adiabatically at every point in collinear configuration space. The quasiclassical trajectory cross sections and probabilities, on the other hand, have thresholds which are well below the quantum thresholds, primarily because of reactive trajectories which have little or no energy in bending near the effective reaction bottleneck. This effect is especially important for H + H_{2} (ν = 1) and leads to QCT rate constants which are much higher than the quantum ones at 300 K. Classical methods designed to reduce this threshold error are studied, and the most successful of these is one in which the local bending zero point energy is added adiabatically in the full dimensional configuration space. The origin of the threshold error is examined, and it is found that the constraints associated with the uncertainty principle rather than with vibrational adiabaticity are the most important in determining the threshold behavior associated with bending. These constraints lead to the prediction that the vibrationally adiabatic (ground bending state) threshold is the correct one, which means that the quantum threshold appears to be governed by adiabatic theory even when motional time scales are such that the adiabatic approximation is invalid. The classical threshold, on the other hand, is close to the adiabatic threshold only when motional time scales are appropriate.

Original language | English |
---|---|

Pages (from-to) | 5386-5391 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 79 |

Issue number | 11 |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**The origin of cross section thresholds in H+H _{2} : Why quantum dynamics appears to be more vibrationally adiabatic than classical dynamics.** / Schatz, George C.

Research output: Contribution to journal › Article

_{2}: Why quantum dynamics appears to be more vibrationally adiabatic than classical dynamics',

*Journal of Chemical Physics*, vol. 79, no. 11, pp. 5386-5391.

}

TY - JOUR

T1 - The origin of cross section thresholds in H+H2

T2 - Why quantum dynamics appears to be more vibrationally adiabatic than classical dynamics

AU - Schatz, George C

PY - 1983

Y1 - 1983

N2 - In this paper, cross sections and J = 0 reaction probabilities from the results of quasiclassical trajectory (QCT) and accurate quantum reactive scattering calculations are presented and compared for H + H2 (ν = 0) and H + H2 (ν = 1). For both ν = 0 and ν = 1, the energies associated with the effective thresholds for reaction in the quantum results are consistent with the adiabatic treatment of bending motions along the reaction coordinate. This is best illustrated by comparing the 3DJ = 0 reaction probabilities with those from analogous collinear calculations, and with collinear calculations in which the bending zero point energy is added in adiabatically at every point in collinear configuration space. The quasiclassical trajectory cross sections and probabilities, on the other hand, have thresholds which are well below the quantum thresholds, primarily because of reactive trajectories which have little or no energy in bending near the effective reaction bottleneck. This effect is especially important for H + H2 (ν = 1) and leads to QCT rate constants which are much higher than the quantum ones at 300 K. Classical methods designed to reduce this threshold error are studied, and the most successful of these is one in which the local bending zero point energy is added adiabatically in the full dimensional configuration space. The origin of the threshold error is examined, and it is found that the constraints associated with the uncertainty principle rather than with vibrational adiabaticity are the most important in determining the threshold behavior associated with bending. These constraints lead to the prediction that the vibrationally adiabatic (ground bending state) threshold is the correct one, which means that the quantum threshold appears to be governed by adiabatic theory even when motional time scales are such that the adiabatic approximation is invalid. The classical threshold, on the other hand, is close to the adiabatic threshold only when motional time scales are appropriate.

AB - In this paper, cross sections and J = 0 reaction probabilities from the results of quasiclassical trajectory (QCT) and accurate quantum reactive scattering calculations are presented and compared for H + H2 (ν = 0) and H + H2 (ν = 1). For both ν = 0 and ν = 1, the energies associated with the effective thresholds for reaction in the quantum results are consistent with the adiabatic treatment of bending motions along the reaction coordinate. This is best illustrated by comparing the 3DJ = 0 reaction probabilities with those from analogous collinear calculations, and with collinear calculations in which the bending zero point energy is added in adiabatically at every point in collinear configuration space. The quasiclassical trajectory cross sections and probabilities, on the other hand, have thresholds which are well below the quantum thresholds, primarily because of reactive trajectories which have little or no energy in bending near the effective reaction bottleneck. This effect is especially important for H + H2 (ν = 1) and leads to QCT rate constants which are much higher than the quantum ones at 300 K. Classical methods designed to reduce this threshold error are studied, and the most successful of these is one in which the local bending zero point energy is added adiabatically in the full dimensional configuration space. The origin of the threshold error is examined, and it is found that the constraints associated with the uncertainty principle rather than with vibrational adiabaticity are the most important in determining the threshold behavior associated with bending. These constraints lead to the prediction that the vibrationally adiabatic (ground bending state) threshold is the correct one, which means that the quantum threshold appears to be governed by adiabatic theory even when motional time scales are such that the adiabatic approximation is invalid. The classical threshold, on the other hand, is close to the adiabatic threshold only when motional time scales are appropriate.

UR - http://www.scopus.com/inward/record.url?scp=0009060832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009060832&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0009060832

VL - 79

SP - 5386

EP - 5391

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

ER -