The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics: Applications to collisional energy transfer

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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 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.

Original languageEnglish
Pages (from-to)5220-5225
Number of pages6
JournalJournal of Chemical Physics
Volume66
Issue number11
Publication statusPublished - 1977

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molecular collisions
Energy transfer
energy transfer
Rigid rotors
Scattering
rigid rotors
expansion
inelastic collisions
Opacity
opacity
scattering
impulses
projection
moments
collisions
cross sections
approximation
energy

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics: Applications to collisional energy transfer",
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 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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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

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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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