### Abstract

Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state-to-state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one-dimensional test problem (the Eckart barrier).

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

Pages (from-to) | 4889-4898 |

Number of pages | 10 |

Journal | The Journal of Chemical Physics |

Volume | 79 |

Issue number | 10 |

State | Published - 1983 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*79*(10), 4889-4898.

**Quantum mechanical rate constants for bimolecular reactions.** / Miller, William H.; Schwartz, Steven D; Tromp, John W.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 79, no. 10, pp. 4889-4898.

}

TY - JOUR

T1 - Quantum mechanical rate constants for bimolecular reactions

AU - Miller, William H.

AU - Schwartz, Steven D

AU - Tromp, John W.

PY - 1983

Y1 - 1983

N2 - Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state-to-state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one-dimensional test problem (the Eckart barrier).

AB - Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state-to-state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one-dimensional test problem (the Eckart barrier).

UR - http://www.scopus.com/inward/record.url?scp=0343791207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0343791207&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0343791207

VL - 79

SP - 4889

EP - 4898

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 10

ER -