### Abstract

We present an approximate semiclassical method for determining state to state transition probabilities for reactions which proceed via tunneling which uses a trajectory integrated along purely real and purely imaginary time contours from reagents through the barrier to products. The real and imaginary time portions of the trajectory are connected by introducing separable approximations to the potential near certain translational turning points in the trajectory. For atom-diatom collinear reactions, the use of a vibrationally adiabatic approximation from these turning points to the asymptotic region leads to a very simple expression for the imaginary part of the action involving a nonseparable contribution from a purely real valued portion of the trajectory passing through the barrier along an imaginary time contour, and a separable contribution from a path which follows part of the locus of outer vibrational turning points. At very low translational energies E_{0}, we find that the nonseparable contribution dominates in determining the reaction probability, and there we find very good agreement with the analogous semiclassical complex trajectory (SCCT) results of George and Miller for collinear H+H_{2}. At higher E_{0}, just below the classical threshold for reaction, the separable contribution dominates, and our method reduces to one proposed by Marcus and Coltrin (MC), which also shows good agreement with the SCCT results. Comparison of our results with exact quantum (EQ) results on both the Porter-Karplus and Truhlar-Kuppermann potential surfaces indicates agreement to within better than a factor of 2.5 over a wide range of relative translational energies (0.040≤0.23 eV), with the accuracy generally comparable to that of the SCCT, MC, and periodic trajectory (PT) methods. This method is, however, much easier to apply than SCCT (only a real valued portion of a trajectory is used), is capable of determining state to state transition probabilities (in contrast to PT) and is a more dynamical (trajectory oriented) approach than MC. The computational effort associated with this approach is roughly comparable to that of the PT method, which makes it easier than SCCT but harder than MC to implement. Results are also presented for H+H_{2} using the very accurate Siegbahn-Liu-Truhlar-Horowitz potential, and we examine the influence of using harmonic vs Morse potentials to generate vibrationally adiabatic separable approximations.

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

Pages (from-to) | 3337-3347 |

Number of pages | 11 |

Journal | Journal of Chemical Physics |

Volume | 72 |

Issue number | 5 |

Publication status | Published - 1979 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*72*(5), 3337-3347.

**A new method for determining semiclassical tunneling probabilities in atom-diatom reactions.** / Altkorn, Robert I.; Schatz, George C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 72, no. 5, pp. 3337-3347.

}

TY - JOUR

T1 - A new method for determining semiclassical tunneling probabilities in atom-diatom reactions

AU - Altkorn, Robert I.

AU - Schatz, George C

PY - 1979

Y1 - 1979

N2 - We present an approximate semiclassical method for determining state to state transition probabilities for reactions which proceed via tunneling which uses a trajectory integrated along purely real and purely imaginary time contours from reagents through the barrier to products. The real and imaginary time portions of the trajectory are connected by introducing separable approximations to the potential near certain translational turning points in the trajectory. For atom-diatom collinear reactions, the use of a vibrationally adiabatic approximation from these turning points to the asymptotic region leads to a very simple expression for the imaginary part of the action involving a nonseparable contribution from a purely real valued portion of the trajectory passing through the barrier along an imaginary time contour, and a separable contribution from a path which follows part of the locus of outer vibrational turning points. At very low translational energies E0, we find that the nonseparable contribution dominates in determining the reaction probability, and there we find very good agreement with the analogous semiclassical complex trajectory (SCCT) results of George and Miller for collinear H+H2. At higher E0, just below the classical threshold for reaction, the separable contribution dominates, and our method reduces to one proposed by Marcus and Coltrin (MC), which also shows good agreement with the SCCT results. Comparison of our results with exact quantum (EQ) results on both the Porter-Karplus and Truhlar-Kuppermann potential surfaces indicates agreement to within better than a factor of 2.5 over a wide range of relative translational energies (0.040≤0.23 eV), with the accuracy generally comparable to that of the SCCT, MC, and periodic trajectory (PT) methods. This method is, however, much easier to apply than SCCT (only a real valued portion of a trajectory is used), is capable of determining state to state transition probabilities (in contrast to PT) and is a more dynamical (trajectory oriented) approach than MC. The computational effort associated with this approach is roughly comparable to that of the PT method, which makes it easier than SCCT but harder than MC to implement. Results are also presented for H+H2 using the very accurate Siegbahn-Liu-Truhlar-Horowitz potential, and we examine the influence of using harmonic vs Morse potentials to generate vibrationally adiabatic separable approximations.

AB - We present an approximate semiclassical method for determining state to state transition probabilities for reactions which proceed via tunneling which uses a trajectory integrated along purely real and purely imaginary time contours from reagents through the barrier to products. The real and imaginary time portions of the trajectory are connected by introducing separable approximations to the potential near certain translational turning points in the trajectory. For atom-diatom collinear reactions, the use of a vibrationally adiabatic approximation from these turning points to the asymptotic region leads to a very simple expression for the imaginary part of the action involving a nonseparable contribution from a purely real valued portion of the trajectory passing through the barrier along an imaginary time contour, and a separable contribution from a path which follows part of the locus of outer vibrational turning points. At very low translational energies E0, we find that the nonseparable contribution dominates in determining the reaction probability, and there we find very good agreement with the analogous semiclassical complex trajectory (SCCT) results of George and Miller for collinear H+H2. At higher E0, just below the classical threshold for reaction, the separable contribution dominates, and our method reduces to one proposed by Marcus and Coltrin (MC), which also shows good agreement with the SCCT results. Comparison of our results with exact quantum (EQ) results on both the Porter-Karplus and Truhlar-Kuppermann potential surfaces indicates agreement to within better than a factor of 2.5 over a wide range of relative translational energies (0.040≤0.23 eV), with the accuracy generally comparable to that of the SCCT, MC, and periodic trajectory (PT) methods. This method is, however, much easier to apply than SCCT (only a real valued portion of a trajectory is used), is capable of determining state to state transition probabilities (in contrast to PT) and is a more dynamical (trajectory oriented) approach than MC. The computational effort associated with this approach is roughly comparable to that of the PT method, which makes it easier than SCCT but harder than MC to implement. Results are also presented for H+H2 using the very accurate Siegbahn-Liu-Truhlar-Horowitz potential, and we examine the influence of using harmonic vs Morse potentials to generate vibrationally adiabatic separable approximations.

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M3 - Article

AN - SCOPUS:36749115684

VL - 72

SP - 3337

EP - 3347

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 5

ER -