### Abstract

We discuss the calculation of quantum-mechanical amplitudes for reactive scattering based on the Fock scheme for coupling arrangement channels and expansion of the coupled amplitude densities in terms of square-integrable (ℒ^{2}) basis functions. First, we provide a derivation of the coupled equations for the amplitude densities from the Fock-scheme integrodifferential equations for wavefunction components. Then we discuss the solution of these equations by ℒ^{2} techniques. The methods are applied to calculate the thresholds and tunnelling probabilities for the reactions O + H_{2}(υ = 0, 1) → OH + H and H + OH(υ = 0, 1) → O + H_{2}, where υ denotes the vibrational quantum number. The results, which represent accurate quantal dynamics for a given potential-energy surface, are used to test the predictions of variational transition-state theory for threshold energies and the least-action semiclassical method for tunnelling probabilities.

Original language | English (US) |
---|---|

Pages (from-to) | 371-385 |

Number of pages | 15 |

Journal | Faraday Discussions of the Chemical Society |

Volume | 84 |

DOIs | |

State | Published - 1987 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Faraday Discussions of the Chemical Society*,

*84*, 371-385. https://doi.org/10.1039/DC9878400371

**ℒ2 Calculations of accurate quantal-dynamical reactive scattering transition probabilities and their use to test semiclassical applications.** / Zhang, John; Zhang, Yici; Kouri, Donald J.; Garrett, Bruce C.; Haug, Kenneth; Schwenke, David W.; Truhlar, Donald G.

Research output: Contribution to journal › Article

*Faraday Discussions of the Chemical Society*, vol. 84, pp. 371-385. https://doi.org/10.1039/DC9878400371

}

TY - JOUR

T1 - ℒ2 Calculations of accurate quantal-dynamical reactive scattering transition probabilities and their use to test semiclassical applications

AU - Zhang, John

AU - Zhang, Yici

AU - Kouri, Donald J.

AU - Garrett, Bruce C.

AU - Haug, Kenneth

AU - Schwenke, David W.

AU - Truhlar, Donald G.

PY - 1987

Y1 - 1987

N2 - We discuss the calculation of quantum-mechanical amplitudes for reactive scattering based on the Fock scheme for coupling arrangement channels and expansion of the coupled amplitude densities in terms of square-integrable (ℒ2) basis functions. First, we provide a derivation of the coupled equations for the amplitude densities from the Fock-scheme integrodifferential equations for wavefunction components. Then we discuss the solution of these equations by ℒ2 techniques. The methods are applied to calculate the thresholds and tunnelling probabilities for the reactions O + H2(υ = 0, 1) → OH + H and H + OH(υ = 0, 1) → O + H2, where υ denotes the vibrational quantum number. The results, which represent accurate quantal dynamics for a given potential-energy surface, are used to test the predictions of variational transition-state theory for threshold energies and the least-action semiclassical method for tunnelling probabilities.

AB - We discuss the calculation of quantum-mechanical amplitudes for reactive scattering based on the Fock scheme for coupling arrangement channels and expansion of the coupled amplitude densities in terms of square-integrable (ℒ2) basis functions. First, we provide a derivation of the coupled equations for the amplitude densities from the Fock-scheme integrodifferential equations for wavefunction components. Then we discuss the solution of these equations by ℒ2 techniques. The methods are applied to calculate the thresholds and tunnelling probabilities for the reactions O + H2(υ = 0, 1) → OH + H and H + OH(υ = 0, 1) → O + H2, where υ denotes the vibrational quantum number. The results, which represent accurate quantal dynamics for a given potential-energy surface, are used to test the predictions of variational transition-state theory for threshold energies and the least-action semiclassical method for tunnelling probabilities.

UR - http://www.scopus.com/inward/record.url?scp=0042301140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042301140&partnerID=8YFLogxK

U2 - 10.1039/DC9878400371

DO - 10.1039/DC9878400371

M3 - Article

VL - 84

SP - 371

EP - 385

JO - Faraday Discussions

JF - Faraday Discussions

SN - 1359-6640

ER -