### Abstract

A generalized cumulant expansion method is developed for applying stochastic reductions to molecular collision processes. We begin by introducing an approximate partitioning of a collision system into two subsystems S _{r} and S_{i} which are assumed to be weakly correlated. Cumulant expansion methods are then used to simultaneously perform a stochastic reduction over S_{i}, and a projection of the diagonal elements of the reduced density matrix for S_{r} thereby leading to a Pauli master equation describing S_{r}. We then apply this general equation using an impulse approximation partitioning to problems in inelastic V-T and R-T scattering. For He+ H_{2} vibrationally inelastic collisions, the stochastic theory predicts low order moments and some probabilities in very good agreement with exact quantum results. In applications to He+ H_{2} rigid rotor scattering, integral cross sections and opacity functions within 10%-30% of exact results are obtained at most energies.

Original language | English |
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Pages (from-to) | 5220-5225 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 66 |

Issue number | 11 |

Publication status | Published - 1977 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics : Applications to collisional energy transfer.** / Schatz, George C.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics

T2 - Applications to collisional energy transfer

AU - Schatz, George C

PY - 1977

Y1 - 1977

N2 - A generalized cumulant expansion method is developed for applying stochastic reductions to molecular collision processes. We begin by introducing an approximate partitioning of a collision system into two subsystems S r and Si which are assumed to be weakly correlated. Cumulant expansion methods are then used to simultaneously perform a stochastic reduction over Si, and a projection of the diagonal elements of the reduced density matrix for Sr thereby leading to a Pauli master equation describing Sr. We then apply this general equation using an impulse approximation partitioning to problems in inelastic V-T and R-T scattering. For He+ H2 vibrationally inelastic collisions, the stochastic theory predicts low order moments and some probabilities in very good agreement with exact quantum results. In applications to He+ H2 rigid rotor scattering, integral cross sections and opacity functions within 10%-30% of exact results are obtained at most energies.

AB - A generalized cumulant expansion method is developed for applying stochastic reductions to molecular collision processes. We begin by introducing an approximate partitioning of a collision system into two subsystems S r and Si which are assumed to be weakly correlated. Cumulant expansion methods are then used to simultaneously perform a stochastic reduction over Si, and a projection of the diagonal elements of the reduced density matrix for Sr thereby leading to a Pauli master equation describing Sr. We then apply this general equation using an impulse approximation partitioning to problems in inelastic V-T and R-T scattering. For He+ H2 vibrationally inelastic collisions, the stochastic theory predicts low order moments and some probabilities in very good agreement with exact quantum results. In applications to He+ H2 rigid rotor scattering, integral cross sections and opacity functions within 10%-30% of exact results are obtained at most energies.

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M3 - Article

VL - 66

SP - 5220

EP - 5225

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

ER -